Daily Papers

Instruction-based language modeling has received significant attention in pretrained language models. However, the efficiency of instruction engineering remains low and hinders the development of instruction studies. Recent studies have focused on automating instruction generation, but they primarily aim to improve performance without considering other crucial objectives that impact instruction quality, such as instruction length and perplexity. Therefore, we propose a novel approach (i.e., InstOptima) that treats instruction generation as an evolutionary multi-objective optimization problem. In contrast to text edition-based methods, our approach utilizes a large language model (LLM) to simulate instruction operators, including mutation and crossover. Furthermore, we introduce an objective-guided mechanism for these operators, allowing the LLM to comprehend the objectives and enhance the quality of the generated instructions. Experimental results demonstrate improved fine-tuning performance and the generation of a diverse set of high-quality instructions.

The network pruning algorithm based on evolutionary multi-objective (EMO) can balance the pruning rate and performance of the network. However, its population-based nature often suffers from the complex pruning optimization space and the highly resource-consuming pruning structure verification process, which limits its application. To this end, this paper proposes an EMO joint pruning with multiple sub-networks (EMO-PMS) to reduce space complexity and resource consumption. First, a divide-and-conquer EMO network pruning framework is proposed, which decomposes the complex EMO pruning task on the whole network into easier sub-tasks on multiple sub-networks. On the one hand, this decomposition reduces the pruning optimization space and decreases the optimization difficulty; on the other hand, the smaller network structure converges faster, so the computational resource consumption of the proposed algorithm is lower. Secondly, a sub-network training method based on cross-network constraints is designed so that the sub-network can process the features generated by the previous one through feature constraints. This method allows sub-networks optimized independently to collaborate better and improves the overall performance of the pruned network. Finally, a multiple sub-networks joint pruning method based on EMO is proposed. For one thing, it can accurately measure the feature processing capability of the sub-networks with the pre-trained feature selector. For another, it can combine multi-objective pruning results on multiple sub-networks through global performance impairment ranking to design a joint pruning scheme. The proposed algorithm is validated on three datasets with different challenging. Compared with fifteen advanced pruning algorithms, the experiment results exhibit the effectiveness and efficiency of the proposed algorithm.

Reasoning models have demonstrated remarkable capabilities in solving complex problems by leveraging long chains of thought. However, this more deliberate reasoning comes with substantial computational overhead at inference time. The Long-to-Short (L2S) reasoning problem seeks to maintain high accuracy using fewer tokens, but current training-free model merging approaches rely on scalarized, fixed-hyperparameter arithmetic methods that are highly brittle and force suboptimal compromises. To address this gap, we introduce Evo-L2S, a novel framework that formulates L2S reasoning as a multi-objective optimization challenge. By leveraging evolutionary model merging, Evo-L2S explicitly optimizes the trade-off between accuracy and output length to produce a robust Pareto front of merged models. To make this search computationally tractable for large language models, we propose an entropy-based subset sampling technique that drastically reduces the overhead of fitness estimation. Comprehensive experiments across 1.5B, 7B, and 14B parameter scales on six mathematical reasoning benchmarks demonstrate that Evo-L2S can reduce the length of generated reasoning traces by over 50% while preserving, or even improving, the problem-solving accuracy of the original reasoning models.

Gradient-based preference optimization methods for large language model (LLM) alignment suffer from preference collapse, converging to narrow behavioral modes while neglecting preference diversity. We introduce EvoPref, a multi-objective evolutionary algorithm that maintains populations of Low-Rank Adaptation (LoRA) adapters optimized across helpfulness, harmlessness, and honesty objectives using Non-dominated Sorting Genetic Algorithm II (NSGA-II) selection with archive-based diversity preservation. Our primary contribution is demonstrating that population-based methods discover substantially more diverse alignments than gradient descent. On standard benchmarks, EvoPref improves preference coverage by 18% (median 82.5% vs. 70.0% for ORPO, p<0.001, Wilcoxon, n=30) and reduces collapse rates by 47% (11.0% vs. 20.6%, p<0.001), while achieving competitive alignment quality (median 75.5% RewardBench vs. 75.0% for ORPO, p<0.05). We provide theoretical motivation extending recent multi-objective evolutionary algorithm (MOEA) runtime analysis (Dang et al., 2025) suggesting why archive-based methods escape collapse more effectively than single-trajectory optimization. Comprehensive comparisons against MOEA/D, SMS-EMOA, CMA-ES, and gradient baselines (DPO, IPO, KTO, ORPO) with rigorous statistical testing (Friedman with Holm correction, Vargha-Delaney effect sizes, median with IQR) confirm that multi-objective selection with diversity preservation is essential. This work establishes evolutionary optimization as a principled paradigm for diverse LLM alignment.

In offline multi-objective optimization (MOO), we leverage an offline dataset of designs and their associated labels to simultaneously minimize multiple objectives. This setting more closely mirrors complex real-world problems compared to single-objective optimization. Recent works mainly employ evolutionary algorithms and Bayesian optimization, with limited attention given to the generative modeling capabilities inherent in such data. In this study, we explore generative modeling in offline MOO through flow matching, noted for its effectiveness and efficiency. We introduce ParetoFlow, specifically designed to guide flow sampling to approximate the Pareto front. Traditional predictor (classifier) guidance is inadequate for this purpose because it models only a single objective. In response, we propose a multi-objective predictor guidance module that assigns each sample a weight vector, representing a weighted distribution across multiple objective predictions. A local filtering scheme is introduced to address non-convex Pareto fronts. These weights uniformly cover the entire objective space, effectively directing sample generation towards the Pareto front. Since distributions with similar weights tend to generate similar samples, we introduce a neighboring evolution module to foster knowledge sharing among neighboring distributions. This module generates offspring from these distributions, and selects the most promising one for the next iteration. Our method achieves state-of-the-art performance across various tasks.

Dynamic multi-objective optimization requires continuous tracking of moving Pareto fronts. Existing methods struggle with irregular mutations and data sparsity, primarily facing three challenges: the non-linear coupling of dynamic modes, negative transfer from outdated historical data, and the cold-start problem during environmental switches. To address these issues, this paper proposes a decoupled basis-vector-driven generative framework (DB-GEN). First, to resolve non-linear coupling, the framework employs the discrete wavelet transform to separate evolutionary trajectories into low-frequency trends and high-frequency details. Second, to mitigate negative transfer, it learns transferable basis vectors via sparse dictionary learning rather than directly memorizing historical instances. Recomposing these bases under a topology-aware contrastive constraint constructs a structured latent manifold. Finally, to overcome the cold-start problem, a surrogate-assisted search paradigm samples initial populations from this manifold. Pre-trained on 120 million solutions, DB-GEN performs direct online inference without retraining or fine-tuning. This zero-shot generation process executes in milliseconds, requiring approximately 0.2 seconds per environmental change. Experimental results demonstrate that DB-GEN improves tracking accuracy across various dynamic benchmarks compared to existing algorithms.

Existing key-value (KV) cache compression methods typically rely on heuristics, such as uniform cache allocation across layers or static eviction policies, however, they ignore the critical interplays among layer-specific feature patterns and task performance, which can lead to degraded generalization. In this paper, we propose EvolKV, an adaptive framework for layer-wise, task-driven KV cache compression that jointly optimizes the memory efficiency and task performance. By reformulating cache allocation as a multi-objective optimization problem, EvolKV leverages evolutionary search to dynamically configure layer budgets while directly maximizing downstream performance. Extensive experiments on 11 tasks demonstrate that our approach outperforms all baseline methods across a wide range of KV cache budgets on long-context tasks and surpasses heuristic baselines by up to 7 percentage points on GSM8K. Notably, EvolKV achieves superior performance over the full KV cache setting on code completion while utilizing only 1.5% of the original budget, suggesting the untapped potential in learned compression strategies for KV cache budget allocation.

Large language models (LLMs) have revolutionized natural language processing by solving a wide range of tasks simply guided by a prompt. Yet their performance is highly sensitive to prompt formulation. While automatic prompt optimization addresses this challenge by finding optimal prompts, current methods require a substantial number of LLM calls and input tokens, making prompt optimization expensive. We introduce CAPO (Cost-Aware Prompt Optimization), an algorithm that enhances prompt optimization efficiency by integrating AutoML techniques. CAPO is an evolutionary approach with LLMs as operators, incorporating racing to save evaluations and multi-objective optimization to balance performance with prompt length. It jointly optimizes instructions and few-shot examples while leveraging task descriptions for improved robustness. Our extensive experiments across diverse datasets and LLMs demonstrate that CAPO outperforms state-of-the-art discrete prompt optimization methods in 11/15 cases with improvements up to 21%p in accuracy. Our algorithm achieves better performances already with smaller budgets, saves evaluations through racing, and decreases average prompt length via a length penalty, making it both cost-efficient and cost-aware. Even without few-shot examples, CAPO outperforms its competitors and generally remains robust to initial prompts. CAPO represents an important step toward making prompt optimization more powerful and accessible by improving cost-efficiency.

In statistical modelling the biggest threat is concept drift which makes the model gradually showing deteriorating performance over time. There are state of the art methodologies to detect the impact of concept drift, however general strategy considered to overcome the issue in performance is to rebuild or re-calibrate the model periodically as the variable patterns for the model changes significantly due to market change or consumer behavior change etc. Quantitative research is the most widely spread application of data science in Marketing or financial domain where applicability of state of the art reinforcement learning for auto-learning is less explored paradigm. Reinforcement learning is heavily dependent on having a simulated environment which is majorly available for gaming or online systems, to learn from the live feedback. However, there are some research happened on the area of online advertisement, pricing etc where due to the nature of the online learning environment scope of reinforcement learning is explored. Our proposed solution is a reinforcement learning based, true self-learning algorithm which can adapt to the data change or concept drift and auto learn and self-calibrate for the new patterns of the data solving the problem of concept drift. Keywords - Reinforcement learning, Genetic Algorithm, Q-learning, Classification modelling, CMA-ES, NES, Multi objective optimization, Concept drift, Population stability index, Incremental learning, F1-measure, Predictive Modelling, Self-learning, MCTS, AlphaGo, AlphaZero

Prompt injection attacks pose a significant challenge to the safe deployment of Large Language Models (LLMs) in real-world applications. While prompt-based detection offers a lightweight and interpretable defense strategy, its effectiveness has been hindered by the need for manual prompt engineering. To address this issue, we propose AEGIS , an Automated co-Evolutionary framework for Guarding prompt Injections Schema. Both attack and defense prompts are iteratively optimized against each other using a gradient-like natural language prompt optimization technique. This framework enables both attackers and defenders to autonomously evolve via a Textual Gradient Optimization (TGO) module, leveraging feedback from an LLM-guided evaluation loop. We evaluate our system on a real-world assignment grading dataset of prompt injection attacks and demonstrate that our method consistently outperforms existing baselines, achieving superior robustness in both attack success and detection. Specifically, the attack success rate (ASR) reaches 1.0, representing an improvement of 0.26 over the baseline. For detection, the true positive rate (TPR) improves by 0.23 compared to the previous best work, reaching 0.84, and the true negative rate (TNR) remains comparable at 0.89. Ablation studies confirm the importance of co-evolution, gradient buffering, and multi-objective optimization. We also confirm that this framework is effective in different LLMs. Our results highlight the promise of adversarial training as a scalable and effective approach for guarding prompt injections.

Modern computer vision requires balancing predictive accuracy with real-time efficiency, yet the high inference cost of large vision models (LVMs) limits deployment on resource-constrained edge devices. Although Evolutionary Neural Architecture Search (ENAS) is well suited for multi-objective optimization, its practical use is hindered by two issues: expensive candidate evaluation and ranking inconsistency among subnetworks. To address them, we propose EvoNAS, an efficient distributed framework for multi-objective evolutionary architecture search. We build a hybrid supernet that integrates Vision State Space and Vision Transformer (VSS-ViT) modules, and optimize it with a Cross-Architecture Dual-Domain Knowledge Distillation (CA-DDKD) strategy. By coupling the computational efficiency of VSS blocks with the semantic expressiveness of ViT modules, CA-DDKD improves the representational capacity of the shared supernet and enhances ranking consistency, enabling reliable fitness estimation during evolution without extra fine-tuning. To reduce the cost of large-scale validation, we further introduce a Distributed Multi-Model Parallel Evaluation (DMMPE) framework based on GPU resource pooling and asynchronous scheduling. Compared with conventional data-parallel evaluation, DMMPE improves efficiency by over 70% through concurrent multi-GPU, multi-model execution. Experiments on COCO, ADE20K, KITTI, and NYU-Depth v2 show that the searched architectures, termed EvoNets, consistently achieve Pareto-optimal trade-offs between accuracy and efficiency. Compared with representative CNN-, ViT-, and Mamba-based models, EvoNets deliver lower inference latency and higher throughput under strict computational budgets while maintaining strong generalization on downstream tasks such as novel view synthesis. Code is available at https://github.com/EMI-Group/evonas

Traditional approaches to portfolio optimization, often rooted in Modern Portfolio Theory and solved via quadratic programming or evolutionary algorithms, struggle with scalability or flexibility, especially in scenarios involving complex constraints, large datasets and/or multiple conflicting objectives. To address these challenges, we introduce a benchmark framework for multi-objective portfolio optimization (MPO) using gradient descent with automatic differentiation. Our method supports any optimization objective, such as minimizing risk measures (e.g., CVaR) or maximizing Sharpe ratio, along with realistic constraints, such as tracking error limits, UCITS regulations, or asset group restrictions. We have evaluated our framework across six experimental scenarios, from single-objective setups to complex multi-objective cases, and have compared its performance against standard solvers like CVXPY and SKFOLIO. Our results show that our method achieves competitive performance while offering enhanced flexibility for modeling multiple objectives and constraints. We aim to provide a practical and extensible tool for researchers and practitioners exploring advanced portfolio optimization problems in real-world conditions.

Multiobjective combinatorial optimization (MOCO) problems can be found in many real-world applications. However, exactly solving these problems would be very challenging, particularly when they are NP-hard. Many handcrafted heuristic methods have been proposed to tackle different MOCO problems over the past decades. In this work, we generalize the idea of neural combinatorial optimization, and develop a learning-based approach to approximate the whole Pareto set for a given MOCO problem without further search procedure. We propose a single preference-conditioned model to directly generate approximate Pareto solutions for any trade-off preference, and design an efficient multiobjective reinforcement learning algorithm to train this model. Our proposed method can be treated as a learning-based extension for the widely-used decomposition-based multiobjective evolutionary algorithm (MOEA/D). It uses a single model to accommodate all the possible preferences, whereas other methods use a finite number of solutions to approximate the Pareto set. Experimental results show that our proposed method significantly outperforms some other methods on the multiobjective traveling salesman problem, multiobjective vehicle routing problem, and multiobjective knapsack problem in terms of solution quality, speed, and model efficiency.

Neural architecture search (NAS) automates neural network design, improving efficiency over manual approaches. However, efficiently discovering high-performance neural network architectures that simultaneously optimize multiple objectives remains a significant challenge in NAS. Existing methods often suffer from limited population diversity and inadequate exploration of the search space, particularly in regions with extreme complexity values. To address these challenges, we propose MOEA-BUS, an innovative multi-objective evolutionary algorithm based on bi-population with uniform sampling for neural architecture search, aimed at simultaneously optimizing both accuracy and network complexity. In MOEA-BUS, a novel uniform sampling method is proposed to initialize the population, ensuring that architectures are distributed uniformly across the objective space. Furthermore, to enhance exploration, we deploy a bi-population framework where two populations evolve synergistically, facilitating comprehensive search space coverage. Experiments on CIFAR-10 and ImageNet demonstrate MOEA-BUS's superiority, achieving top-1 accuracies of 98.39% on CIFAR-10, and 80.03% on ImageNet. Notably, it achieves 78.28% accuracy on ImageNet with only 446M MAdds. Ablation studies confirm that both uniform sampling and bi-population mechanisms enhance population diversity and performance. Additionally, in terms of the Kendall's tau coefficient, the SVM achieves an improvement of at least 0.035 compared to the other three commonly used machine learning models, and uniform sampling provided an enhancement of approximately 0.07.

Designing sequences that satisfy multiple, often conflicting, objectives is a central challenge in therapeutic and biomolecular engineering. Existing generative frameworks largely operate in continuous spaces with single-objective guidance, while discrete approaches lack guarantees for multi-objective Pareto optimality. We introduce AReUReDi (Annealed Rectified Updates for Refining Discrete Flows), a discrete optimization algorithm with theoretical guarantees of convergence to the Pareto front. Building on Rectified Discrete Flows (ReDi), AReUReDi combines Tchebycheff scalarization, locally balanced proposals, and annealed Metropolis-Hastings updates to bias sampling toward Pareto-optimal states while preserving distributional invariance. Applied to peptide and SMILES sequence design, AReUReDi simultaneously optimizes up to five therapeutic properties (including affinity, solubility, hemolysis, half-life, and non-fouling) and outperforms both evolutionary and diffusion-based baselines. These results establish AReUReDi as a powerful, sequence-based framework for multi-property biomolecule generation.

Molecular discovery, when formulated as an optimization problem, presents significant computational challenges because optimization objectives can be non-differentiable. Evolutionary Algorithms (EAs), often used to optimize black-box objectives in molecular discovery, traverse chemical space by performing random mutations and crossovers, leading to a large number of expensive objective evaluations. In this work, we ameliorate this shortcoming by incorporating chemistry-aware Large Language Models (LLMs) into EAs. Namely, we redesign crossover and mutation operations in EAs using LLMs trained on large corpora of chemical information. We perform extensive empirical studies on both commercial and open-source models on multiple tasks involving property optimization, molecular rediscovery, and structure-based drug design, demonstrating that the joint usage of LLMs with EAs yields superior performance over all baseline models across single- and multi-objective settings. We demonstrate that our algorithm improves both the quality of the final solution and convergence speed, thereby reducing the number of required objective evaluations. Our code is available at http://github.com/zoom-wang112358/MOLLEO

Evolutionary multiobjective optimization (EMO) has made significant strides over the past two decades. However, as problem scales and complexities increase, traditional EMO algorithms face substantial performance limitations due to insufficient parallelism and scalability. While most work has focused on algorithm design to address these challenges, little attention has been given to hardware acceleration, thereby leaving a clear gap between EMO algorithms and advanced computing devices, such as GPUs. To bridge the gap, we propose to parallelize EMO algorithms on GPUs via the tensorization methodology. By employing tensorization, the data structures and operations of EMO algorithms are transformed into concise tensor representations, which seamlessly enables automatic utilization of GPU computing. We demonstrate the effectiveness of our approach by applying it to three representative EMO algorithms: NSGA-III, MOEA/D, and HypE. To comprehensively assess our methodology, we introduce a multiobjective robot control benchmark using a GPU-accelerated physics engine. Our experiments show that the tensorized EMO algorithms achieve speedups of up to 1113x compared to their CPU-based counterparts, while maintaining solution quality and effectively scaling population sizes to hundreds of thousands. Furthermore, the tensorized EMO algorithms efficiently tackle complex multiobjective robot control tasks, producing high-quality solutions with diverse behaviors. Source codes are available at https://github.com/EMI-Group/evomo.

Multi-objective evolutionary algorithms (MOEAs) are among the most widely and successfully applied optimizers for multi-objective problems. However, to store many optimal trade-offs (the Pareto optima) at once, MOEAs are typically run with a large, static population of solution candidates, which can slow down the algorithm. We propose the dynamic NSGA-II (dNSGA-II), which is based on the popular NSGA-II and features a non-static population size. The dNSGA-II starts with a small initial population size of four and doubles it after a user-specified number tau of function evaluations, up to a maximum size of mu. Via a mathematical runtime analysis, we prove that the dNSGA-II with parameters mu geq 4(n + 1) and tau geq 256{50} e n computes the full Pareto front of the OneMinMax benchmark of size n in O(log(mu) tau + mu log(n)) function evaluations, both in expectation and with high probability. For an optimal choice of mu and tau, the resulting O(n log(n)) runtime improves the optimal expected runtime of the classic NSGA-II by a factor of Theta(n). In addition, we show that the parameter tau can be removed when utilizing concurrent runs of the dNSGA-II. This approach leads to a mild slow-down by a factor of O(log(n)) compared to an optimal choice of tau for the dNSGA-II, which is still a speed-up of Theta(n / log(n)) over the classic NSGA-II.

Many modern deep learning applications require balancing multiple objectives that are often conflicting. Examples include multi-task learning, fairness-aware learning, and the alignment of Large Language Models (LLMs). This leads to multi-objective deep learning, which tries to find optimal trade-offs or Pareto-optimal solutions by adapting mathematical principles from the field of Multi-Objective Optimization (MOO). However, directly applying gradient-based MOO techniques to deep neural networks presents unique challenges, including high computational costs, optimization instability, and the difficulty of effectively incorporating user preferences. This paper provides a comprehensive survey of gradient-based techniques for multi-objective deep learning. We systematically categorize existing algorithms based on their outputs: (i) methods that find a single, well-balanced solution, (ii) methods that generate a finite set of diverse Pareto-optimal solutions, and (iii) methods that learn a continuous Pareto set of solutions. In addition to this taxonomy, the survey covers theoretical analyses, key applications, practical resources, and highlights open challenges and promising directions for future research. A comprehensive list of multi-objective deep learning algorithms is available at https://github.com/Baijiong-Lin/Awesome-Multi-Objective-Deep-Learning.

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control - potentially with non-smoothness both on the level of the objectives or in the system dynamics. This results in new challenges such as dealing with expensive models (e.g., governed by partial differential equations (PDEs)) and developing dedicated algorithms handling the non-smoothness. Since in contrast to single-objective optimization, the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in the field of multiobjective optimization of non-smooth PDE-constrained problems. In particular we report on the advances achieved within Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems - Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm 1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization".

In many applications of machine learning, like drug discovery and material design, the goal is to generate candidates that simultaneously maximize a set of objectives. As these objectives are often conflicting, there is no single candidate that simultaneously maximizes all objectives, but rather a set of Pareto-optimal candidates where one objective cannot be improved without worsening another. Moreover, in practice, these objectives are often under-specified, making the diversity of candidates a key consideration. The existing multi-objective optimization methods focus predominantly on covering the Pareto front, failing to capture diversity in the space of candidates. Motivated by the success of GFlowNets for generation of diverse candidates in a single objective setting, in this paper we consider Multi-Objective GFlowNets (MOGFNs). MOGFNs consist of a novel Conditional GFlowNet which models a family of single-objective sub-problems derived by decomposing the multi-objective optimization problem. Our work is the first to empirically demonstrate conditional GFlowNets. Through a series of experiments on synthetic and benchmark tasks, we empirically demonstrate that MOGFNs outperform existing methods in terms of Hypervolume, R2-distance and candidate diversity. We also demonstrate the effectiveness of MOGFNs over existing methods in active learning settings. Finally, we supplement our empirical results with a careful analysis of each component of MOGFNs.

Optimizing the performance of many objectives (instantiated by tasks or clients) jointly with a few Pareto stationary solutions (models) is critical in machine learning. However, previous multi-objective optimization methods often focus on a few number of objectives and cannot scale to many objectives that outnumber the solutions, leading to either subpar performance or ignored objectives. We introduce Many-objective multi-solution Transport (MosT), a framework that finds multiple diverse solutions in the Pareto front of many objectives. Our insight is to seek multiple solutions, each performing as a domain expert and focusing on a specific subset of objectives while collectively covering all of them. MosT formulates the problem as a bi-level optimization of weighted objectives for each solution, where the weights are defined by an optimal transport between the objectives and solutions. Our algorithm ensures convergence to Pareto stationary solutions for complementary subsets of objectives. On a range of applications in federated learning, multi-task learning, and mixture-of-prompt learning for LLMs, MosT distinctly outperforms strong baselines, delivering high-quality, diverse solutions that profile the entire Pareto frontier, thus ensuring balanced trade-offs across many objectives.

Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This article surveys algorithms designed for sequential decision-making problems with multiple objectives. Though there is a growing body of literature on this subject, little of it makes explicit under what circumstances special methods are needed to solve multi-objective problems. Therefore, we identify three distinct scenarios in which converting such a problem to a single-objective one is impossible, infeasible, or undesirable. Furthermore, we propose a taxonomy that classifies multi-objective methods according to the applicable scenario, the nature of the scalarization function (which projects multi-objective values to scalar ones), and the type of policies considered. We show how these factors determine the nature of an optimal solution, which can be a single policy, a convex hull, or a Pareto front. Using this taxonomy, we survey the literature on multi-objective methods for planning and learning. Finally, we discuss key applications of such methods and outline opportunities for future work.

Recent work such as AlphaEvolve has shown that combining LLM-driven optimization with evolutionary search can effectively improve programs, prompts, and algorithms across domains. In this paradigm, previously evaluated solutions are reused to guide the model toward new candidate solutions. Crucially, the effectiveness of this evolution process depends on the search strategy: how prior solutions are selected and varied to generate new candidates. However, most existing methods rely on fixed search strategies with predefined knobs (e.g., explore-exploit ratios) that remain static throughout execution. While effective in some settings, these approaches often fail to adapt across tasks, or even within the same task as the search space changes over time. We introduce EvoX, an adaptive evolution method that optimizes its own evolution process. EvoX jointly evolves candidate solutions and the search strategies used to generate them, continuously updating how prior solutions are selected and varied based on progress. This enables the system to dynamically shift between different search strategies during the optimization process. Across nearly 200 real-world optimization tasks, EvoX outperforms existing AI-driven evolutionary methods including AlphaEvolve, OpenEvolve, GEPA, and ShinkaEvolve on the majority of tasks.

Multi-objective optimization involving Quadratic Unconstrained Binary Optimization (QUBO) problems arises in various domains. A fundamental challenge in this context is the effective balancing of multiple objectives, each potentially operating on very different scales. This imbalance introduces complications such as the selection of appropriate weights when scalarizing multiple objectives into a single objective function. In this paper, we propose a novel technique for scaling QUBO objectives that uses an exact computation of the variance of each individual QUBO objective. By scaling each objective to have unit variance, we align all objectives onto a common scale, thereby allowing for more balanced solutions to be found when scalarizing the objectives with equal weights, as well as potentially assisting in the search or choice of weights during scalarization. Finally, we demonstrate its advantages through empirical evaluations on various multi-objective optimization problems. Our results are noteworthy since manually selecting scalarization weights is cumbersome, and reliable, efficient solutions are scarce.

The Unmanned Aerial Vehicle (UAV) path planning problem is a complex optimization problem in the field of robotics. In this paper, we investigate the possible utilization of this problem in benchmarking global optimization methods. We devise a problem instance generator and pick 56 representative instances, which we compare to established benchmarking suits through Exploratory Landscape Analysis to show their uniqueness. For the computational comparison, we select twelve well-performing global optimization techniques from both subfields of stochastic algorithms (evolutionary computation methods) and deterministic algorithms (Dividing RECTangles, or DIRECT-type methods). The experiments were conducted in settings with varying dimensionality and computational budgets. The results were analyzed through several criteria (number of best-found solutions, mean relative error, Friedman ranks) and utilized established statistical tests. The best-ranking methods for the UAV problems were almost universally the top-performing evolutionary techniques from recent competitions on numerical optimization at the Institute of Electrical and Electronics Engineers Congress on Evolutionary Computation. Lastly, we discussed the variable dimension characteristics of the studied UAV problems that remain still largely under-investigated.

Heuristic design with large language models (LLMs) has emerged as a promising approach for tackling combinatorial optimization problems (COPs). However, existing approaches often rely on manually predefined evolutionary computation (EC) optimizers and single-task training schemes, which may constrain the exploration of diverse heuristic algorithms and hinder the generalization of the resulting heuristics. To address these issues, we propose Meta-Optimization of Heuristics (MoH), a novel framework that operates at the optimizer level, discovering effective optimizers through the principle of meta-learning. Specifically, MoH leverages LLMs to iteratively refine a meta-optimizer that autonomously constructs diverse optimizers through (self-)invocation, thereby eliminating the reliance on a predefined EC optimizer. These constructed optimizers subsequently evolve heuristics for downstream tasks, enabling broader heuristic exploration. Moreover, MoH employs a multi-task training scheme to promote its generalization capability. Experiments on classic COPs demonstrate that MoH constructs an effective and interpretable meta-optimizer, achieving state-of-the-art performance across various downstream tasks, particularly in cross-size settings.

Developing efficient multi-objective optimization methods to compute the Pareto set of optimal compromises between conflicting objectives remains a key challenge, especially for large-scale and expensive problems. To bridge this gap, we introduce SPREAD, a generative framework based on Denoising Diffusion Probabilistic Models (DDPMs). SPREAD first learns a conditional diffusion process over points sampled from the decision space and then, at each reverse diffusion step, refines candidates via a sampling scheme that uses an adaptive multiple gradient descent-inspired update for fast convergence alongside a Gaussian RBF-based repulsion term for diversity. Empirical results on multi-objective optimization benchmarks, including offline and Bayesian surrogate-based settings, show that SPREAD matches or exceeds leading baselines in efficiency, scalability, and Pareto front coverage.

We present a genetic algorithm framework for automatically discovering deep learning optimization algorithms. Our approach encodes optimizers as genomes that specify combinations of primitive update terms (gradient, momentum, RMS normalization, Adam-style adaptive terms, and sign-based updates) along with hyperparameters and scheduling options. Through evolutionary search over 50 generations with a population of 50 individuals, evaluated across multiple vision tasks, we discover an evolved optimizer that outperforms Adam by 2.6% in aggregate fitness and achieves a 7.7% relative improvement on CIFAR-10. The evolved optimizer combines sign-based gradient terms with adaptive moment estimation, uses lower momentum coefficients than Adam (β_1=0.86, β_2=0.94), and notably disables bias correction while enabling learning rate warmup and cosine decay. Our results demonstrate that evolutionary search can discover competitive optimization algorithms and reveal design principles that differ from hand-crafted optimizers. Code is available at https://github.com/mmarfinetz/evo-optimizer.

Expensive multi-objective optimization problems (EMOPs) are common in real-world scenarios where evaluating objective functions is costly and involves extensive computations or physical experiments. Current Pareto set learning methods for such problems often rely on surrogate models like Gaussian processes to approximate the objective functions. These surrogate models can become fragmented, resulting in numerous small uncertain regions between explored solutions. When using acquisition functions such as the Lower Confidence Bound (LCB), these uncertain regions can turn into pseudo-local optima, complicating the search for globally optimal solutions. To address these challenges, we propose a novel approach called SVH-PSL, which integrates Stein Variational Gradient Descent (SVGD) with Hypernetworks for efficient Pareto set learning. Our method addresses the issues of fragmented surrogate models and pseudo-local optima by collectively moving particles in a manner that smooths out the solution space. The particles interact with each other through a kernel function, which helps maintain diversity and encourages the exploration of underexplored regions. This kernel-based interaction prevents particles from clustering around pseudo-local optima and promotes convergence towards globally optimal solutions. Our approach aims to establish robust relationships between trade-off reference vectors and their corresponding true Pareto solutions, overcoming the limitations of existing methods. Through extensive experiments across both synthetic and real-world MOO benchmarks, we demonstrate that SVH-PSL significantly improves the quality of the learned Pareto set, offering a promising solution for expensive multi-objective optimization problems.

Evolutionary multitasking (EMT) has emerged as a popular topic of evolutionary computation over the past decade. It aims to concurrently address multiple optimization tasks within limited computing resources, leveraging inter-task knowledge transfer techniques. Despite the abundance of multitask evolutionary algorithms (MTEAs) proposed for multitask optimization (MTO), there remains a need for a comprehensive software platform to help researchers evaluate MTEA performance on benchmark MTO problems as well as explore real-world applications. To bridge this gap, we introduce the first open-source benchmarking platform, named MToP, for EMT. MToP incorporates over 50 MTEAs, more than 200 MTO problem cases with real-world applications, and over 20 performance metrics. Based on these, we provide benchmarking recommendations tailored for different MTO scenarios. Moreover, to facilitate comparative analyses between MTEAs and traditional evolutionary algorithms, we adapted over 50 popular single-task evolutionary algorithms to address MTO problems. Notably, we release extensive pre-run experimental data on benchmark suites to enhance reproducibility and reduce computational overhead for researchers. MToP features a user-friendly graphical interface, facilitating results analysis, data export, and schematic visualization. More importantly, MToP is designed with extensibility in mind, allowing users to develop new algorithms and tackle emerging problem domains. The source code of MToP is available at: https://github.com/intLyc/MTO-Platform

Many optimization problems are inherently multi-objective. To address them, we formalize Jacobian descent (JD), a direct generalization of gradient descent for vector-valued functions. Each step of this algorithm relies on a Jacobian matrix consisting of one gradient per objective. The aggregator, responsible for reducing this matrix into an update vector, characterizes JD. While the multi-task learning literature already contains a variety of aggregators, they often lack some natural properties. In particular, the update should not conflict with any objective and should scale proportionally to the norm of each gradient. We propose a new aggregator specifically designed to satisfy this. Emphasizing conflict between objectives, we then highlight direct applications for our methods. Most notably, we introduce instance-wise risk minimization (IWRM), a learning paradigm in which the loss of each training example is considered a separate objective. On simple image classification tasks, IWRM exhibits promising results compared to the direct minimization of the average loss. The performance of our aggregator in those experiments also corroborates our theoretical findings. Lastly, as speed is the main limitation of JD, we provide a path towards a more efficient implementation.

Evolutionary Reinforcement Learning (ERL), which integrates Evolutionary Algorithms (EAs) and Reinforcement Learning (RL) for optimization, has demonstrated remarkable performance advancements. By fusing both approaches, ERL has emerged as a promising research direction. This survey offers a comprehensive overview of the diverse research branches in ERL. Specifically, we systematically summarize recent advancements in related algorithms and identify three primary research directions: EA-assisted Optimization of RL, RL-assisted Optimization of EA, and synergistic optimization of EA and RL. Following that, we conduct an in-depth analysis of each research direction, organizing multiple research branches. We elucidate the problems that each branch aims to tackle and how the integration of EAs and RL addresses these challenges. In conclusion, we discuss potential challenges and prospective future research directions across various research directions. To facilitate researchers in delving into ERL, we organize the algorithms and codes involved on https://github.com/yeshenpy/Awesome-Evolutionary-Reinforcement-Learning.

Multi-objective optimization problems are ubiquitous in robotics, e.g., the optimization of a robot manipulation task requires a joint consideration of grasp pose configurations, collisions and joint limits. While some demands can be easily hand-designed, e.g., the smoothness of a trajectory, several task-specific objectives need to be learned from data. This work introduces a method for learning data-driven SE(3) cost functions as diffusion models. Diffusion models can represent highly-expressive multimodal distributions and exhibit proper gradients over the entire space due to their score-matching training objective. Learning costs as diffusion models allows their seamless integration with other costs into a single differentiable objective function, enabling joint gradient-based motion optimization. In this work, we focus on learning SE(3) diffusion models for 6DoF grasping, giving rise to a novel framework for joint grasp and motion optimization without needing to decouple grasp selection from trajectory generation. We evaluate the representation power of our SE(3) diffusion models w.r.t. classical generative models, and we showcase the superior performance of our proposed optimization framework in a series of simulated and real-world robotic manipulation tasks against representative baselines.

In this paper, we introduce a novel approach for addressing the multi-objective optimization problem in large language model merging via black-box multi-objective optimization algorithms. The goal of model merging is to combine multiple models, each excelling in different tasks, into a single model that outperforms any of the individual source models. However, model merging faces two significant challenges: First, existing methods rely heavily on human knowledge or intuition. Second, it's difficult to obtain the great model merging configuration in limited evaluations. To address these challenges, we formalize model merging as a multi-objective optimization problem and propose an automated optimization approach named MM-MO. This method leverages multi-objective optimization algorithms to autonomously search for optimal merging configurations across various tasks, alleviating the need for human intervention. In MM-MO, a weak-to-strong method is employed to enhance the acquisition function, allowing previously evaluated superior configurations to guide the search for new ones. Meanwhile, Fisher information is applied to screen these configurations, increasing the possibility of identifying high-quality merging configuration. Additionally, we designed a sparsity metric as an additional optimization objective to enhance the model's generalization performance across different tasks. We conducted comprehensive experiments with other mainstream model merging methods, demonstrating that the proposed MM-MO algorithm is competitive and effective in achieving high-quality model merging.

Multi-objective alignment from human feedback (MOAHF) in large language models (LLMs) is a challenging problem as human preferences are complex, multifaceted, and often conflicting. Recent works on MOAHF considered a-priori multi-objective optimization (MOO), where human preferences are known at training or inference time. In contrast, when human preferences are unknown or difficult to quantify, a natural approach is to cover the Pareto front by multiple diverse solutions. We propose an algorithm HaM for learning diverse LLM policies that maximizes their hypervolume. This is the first application of a-posteriori MOO to MOAHF. HaM is computationally and space efficient, and empirically superior across objectives such as harmlessness, helpfulness, humor, faithfulness, and hallucination, on various datasets.

Multi-objective reinforcement learning (MORL) excels at handling rapidly changing preferences in tasks that involve multiple criteria, even for unseen preferences. However, previous dominating MORL methods typically generate a fixed policy set or preference-conditioned policy through multiple training iterations exclusively for sampled preference vectors, and cannot ensure the efficient discovery of the Pareto front. Furthermore, integrating preferences into the input of policy or value functions presents scalability challenges, in particular as the dimension of the state and preference space grow, which can complicate the learning process and hinder the algorithm's performance on more complex tasks. To address these issues, we propose a two-stage Pareto front discovery algorithm called Constrained MORL (C-MORL), which serves as a seamless bridge between constrained policy optimization and MORL. Concretely, a set of policies is trained in parallel in the initialization stage, with each optimized towards its individual preference over the multiple objectives. Then, to fill the remaining vacancies in the Pareto front, the constrained optimization steps are employed to maximize one objective while constraining the other objectives to exceed a predefined threshold. Empirically, compared to recent advancements in MORL methods, our algorithm achieves more consistent and superior performances in terms of hypervolume, expected utility, and sparsity on both discrete and continuous control tasks, especially with numerous objectives (up to nine objectives in our experiments).

LLM agents organize behavior through skills - structured natural-language specifications governing how an agent reasons, retrieves, and responds. Unlike monolithic prompts, skills are multi-field artifacts subject to hard platform constraints: description fields are truncated for routing, instruction bodies are compacted via progressive disclosure, and co-resident skills compete for limited context windows. These constraints make skill optimization inherently multi-objective: a skill must simultaneously maximize task performance and satisfy platform limits. Yet existing prompt optimizers either ignore these trade-offs or collapse them into a weighted sum, missing Pareto-optimal variants in non-convex objective regions. We introduce MOCHA (Multi-Objective Chebyshev Annealing), which replaces single-objective selection with Chebyshev scalarization - covering the full Pareto front, including non-convex regions - combined with exponential annealing that transitions from exploration to exploitation. In our experiments across six diverse agent skills - where all methods share the same multi-objective mutation operator and baselines receive identical per-objective textual feedback - existing optimizers fail to improve the seed skill on 4 of 6 tasks: 1000 rollouts yield zero progress. MOCHA breaks through on every task, achieving 7.5% relative improvement in mean correctness over the strongest baseline (up to 14.9% on FEVER and 10.4% on TheoremQA) while discovering twice as many more Pareto-optimal skill variants.

Large language models (LLMs) are increasingly deployed in real-world applications that require careful balancing of multiple, often conflicting, objectives, such as informativeness versus conciseness, or helpfulness versus creativity. However, current alignment methods, primarily based on RLHF, optimize LLMs toward a single reward function, resulting in rigid behavior that fails to capture the complexity and diversity of human preferences. This limitation hinders the adaptability of LLMs to practical scenarios, making multi-objective alignment (MOA) a critical yet underexplored area. To bridge this gap, we propose Pareto Multi-Objective Alignment (PAMA), a principled and computationally efficient algorithm designed explicitly for MOA in LLMs. In contrast to computationally prohibitive multi-objective optimization (MOO) methods, PAMA transforms multi-objective RLHF into a convex optimization with a closed-form solution, significantly enhancing scalability. Traditional MOO approaches suffer from prohibitive O(n^2*d) complexity, where d represents the number of model parameters, typically in the billions for LLMs, rendering direct optimization infeasible. PAMA reduces this complexity to O(n) where n is the number of objectives, enabling optimization to be completed within milliseconds. We provide theoretical guarantees that PAMA converges to a Pareto stationary point, where no objective can be improved without degrading at least one other. Extensive experiments across language models ranging from 125M to 7B parameters demonstrate PAMA's robust and effective MOA capabilities, aligning with its theoretical advantages. PAMA provides a highly efficient solution to the MOA problem that was previously considered intractable, offering a practical and theoretically grounded approach to aligning LLMs with diverse human values, paving the way for versatile and adaptable real-world AI deployments.

Multi-objective reinforcement learning (MORL) seeks to learn policies that balance multiple, often conflicting objectives. Although a single preference-conditioned policy is the most flexible and scalable solution, existing approaches remain brittle in practice, frequently failing to recover complete Pareto fronts. We show that this failure stems from two structural issues in current methods: destructive gradient interference caused by premature scalarization and representational collapse across the preference space. We introduce D^3PO, a PPO-based framework that reorganizes multi-objective policy optimization to address these issues directly. D^3PO preserves per-objective learning signals through a decomposed optimization pipeline and integrates preferences only after stabilization, enabling reliable credit assignment. In addition, a scaled diversity regularizer enforces sensitivity of policy behavior to preference changes, preventing collapse. Across standard MORL benchmarks, including high-dimensional and many-objective control tasks, D^3PO consistently discovers broader and higher-quality Pareto fronts than prior single- and multi-policy methods, matching or exceeding state-of-the-art hypervolume and expected utility while using a single deployable policy.

Multi-objective reinforcement learning (MORL) approaches have emerged to tackle many real-world problems with multiple conflicting objectives by maximizing a joint objective function weighted by a preference vector. These approaches find fixed customized policies corresponding to preference vectors specified during training. However, the design constraints and objectives typically change dynamically in real-life scenarios. Furthermore, storing a policy for each potential preference is not scalable. Hence, obtaining a set of Pareto front solutions for the entire preference space in a given domain with a single training is critical. To this end, we propose a novel MORL algorithm that trains a single universal network to cover the entire preference space scalable to continuous robotic tasks. The proposed approach, Preference-Driven MORL (PD-MORL), utilizes the preferences as guidance to update the network parameters. It also employs a novel parallelization approach to increase sample efficiency. We show that PD-MORL achieves up to 25% larger hypervolume for challenging continuous control tasks and uses an order of magnitude fewer trainable parameters compared to prior approaches.

The goal of this article is to provide an introduction to the desirability function approach to multi-objective optimization (direct and surrogate model-based), and multi-objective hyperparameter tuning. This work is based on the paper by Kuhn (2016). It presents a `Python` implementation of Kuhn's `R` package `desirability`. The `Python` package `spotdesirability` is available as part of the `sequential parameter optimization` framework. After a brief introduction to the desirability function approach is presented, three examples are given that demonstrate how to use the desirability functions for classical optimization, surrogate-model based optimization, and hyperparameter tuning.

Population Based Training (PBT) is an efficient hyperparameter optimization algorithm. PBT is a single-objective algorithm, but many real-world hyperparameter optimization problems involve two or more conflicting objectives. In this work, we therefore introduce a multi-objective version of PBT, MO-PBT. Our experiments on diverse multi-objective hyperparameter optimization problems (Precision/Recall, Accuracy/Fairness, Accuracy/Adversarial Robustness) show that MO-PBT outperforms random search, single-objective PBT, and the state-of-the-art multi-objective hyperparameter optimization algorithm MO-ASHA.

In problem-solving, we humans can come up with multiple novel solutions to the same problem. However, reinforcement learning algorithms can only produce a set of monotonous policies that maximize the cumulative reward but lack diversity and novelty. In this work, we address the problem of generating novel policies in reinforcement learning tasks. Instead of following the multi-objective framework used in existing methods, we propose to rethink the problem under a novel perspective of constrained optimization. We first introduce a new metric to evaluate the difference between policies and then design two practical novel policy generation methods following the new perspective. The two proposed methods, namely the Constrained Task Novel Bisector (CTNB) and the Interior Policy Differentiation (IPD), are derived from the feasible direction method and the interior point method commonly known in the constrained optimization literature. Experimental comparisons on the MuJoCo control suite show our methods can achieve substantial improvement over previous novelty-seeking methods in terms of both the novelty of policies and their performances in the primal task.

Recent advancements in meta-learning have enabled the automatic discovery of novel reinforcement learning algorithms parameterized by surrogate objective functions. To improve upon manually designed algorithms, the parameterization of this learned objective function must be expressive enough to represent novel principles of learning (instead of merely recovering already established ones) while still generalizing to a wide range of settings outside of its meta-training distribution. However, existing methods focus on discovering objective functions that, like many widely used objective functions in reinforcement learning, do not take into account the total number of steps allowed for training, or "training horizon". In contrast, humans use a plethora of different learning objectives across the course of acquiring a new ability. For instance, students may alter their studying techniques based on the proximity to exam deadlines and their self-assessed capabilities. This paper contends that ignoring the optimization time horizon significantly restricts the expressive potential of discovered learning algorithms. We propose a simple augmentation to two existing objective discovery approaches that allows the discovered algorithm to dynamically update its objective function throughout the agent's training procedure, resulting in expressive schedules and increased generalization across different training horizons. In the process, we find that commonly used meta-gradient approaches fail to discover such adaptive objective functions while evolution strategies discover highly dynamic learning rules. We demonstrate the effectiveness of our approach on a wide range of tasks and analyze the resulting learned algorithms, which we find effectively balance exploration and exploitation by modifying the structure of their learning rules throughout the agent's lifetime.

Heuristics are widely used for dealing with complex search and optimization problems. However, manual design of heuristics can be often very labour extensive and requires rich working experience and knowledge. This paper proposes Evolution of Heuristic (EoH), a novel evolutionary paradigm that leverages both Large Language Models (LLMs) and Evolutionary Computation (EC) methods for Automatic Heuristic Design (AHD). EoH represents the ideas of heuristics in natural language, termed thoughts. They are then translated into executable codes by LLMs. The evolution of both thoughts and codes in an evolutionary search framework makes it very effective and efficient for generating high-performance heuristics. Experiments on three widely studied combinatorial optimization benchmark problems demonstrate that EoH outperforms commonly used handcrafted heuristics and other recent AHD methods including FunSearch. Particularly, the heuristic produced by EoH with a low computational budget (in terms of the number of queries to LLMs) significantly outperforms widely-used human hand-crafted baseline algorithms for the online bin packing problem.

Multi-objective reinforcement learning (MORL) extends traditional RL by seeking policies making different compromises among conflicting objectives. The recent surge of interest in MORL has led to diverse studies and solving methods, often drawing from existing knowledge in multi-objective optimization based on decomposition (MOO/D). Yet, a clear categorization based on both RL and MOO/D is lacking in the existing literature. Consequently, MORL researchers face difficulties when trying to classify contributions within a broader context due to the absence of a standardized taxonomy. To tackle such an issue, this paper introduces multi-objective reinforcement learning based on decomposition (MORL/D), a novel methodology bridging the literature of RL and MOO. A comprehensive taxonomy for MORL/D is presented, providing a structured foundation for categorizing existing and potential MORL works. The introduced taxonomy is then used to scrutinize MORL research, enhancing clarity and conciseness through well-defined categorization. Moreover, a flexible framework derived from the taxonomy is introduced. This framework accommodates diverse instantiations using tools from both RL and MOO/D. Its versatility is demonstrated by implementing it in different configurations and assessing it on contrasting benchmark problems. Results indicate MORL/D instantiations achieve comparable performance to current state-of-the-art approaches on the studied problems. By presenting the taxonomy and framework, this paper offers a comprehensive perspective and a unified vocabulary for MORL. This not only facilitates the identification of algorithmic contributions but also lays the groundwork for novel research avenues in MORL.

Domain adaptation (DA) attempts to transfer the knowledge from a labeled source domain to an unlabeled target domain that follows different distribution from the source. To achieve this, DA methods include a source classification objective to extract the source knowledge and a domain alignment objective to diminish the domain shift, ensuring knowledge transfer. Typically, former DA methods adopt some weight hyper-parameters to linearly combine the training objectives to form an overall objective. However, the gradient directions of these objectives may conflict with each other due to domain shift. Under such circumstances, the linear optimization scheme might decrease the overall objective value at the expense of damaging one of the training objectives, leading to restricted solutions. In this paper, we rethink the optimization scheme for DA from a gradient-based perspective. We propose a Pareto Domain Adaptation (ParetoDA) approach to control the overall optimization direction, aiming to cooperatively optimize all training objectives. Specifically, to reach a desirable solution on the target domain, we design a surrogate loss mimicking target classification. To improve target-prediction accuracy to support the mimicking, we propose a target-prediction refining mechanism which exploits domain labels via Bayes' theorem. On the other hand, since prior knowledge of weighting schemes for objectives is often unavailable to guide optimization to approach the optimal solution on the target domain, we propose a dynamic preference mechanism to dynamically guide our cooperative optimization by the gradient of the surrogate loss on a held-out unlabeled target dataset. Extensive experiments on image classification and semantic segmentation benchmarks demonstrate the effectiveness of ParetoDA

Discovering efficient algorithms for solving complex problems has been an outstanding challenge in mathematics and computer science, requiring substantial human expertise over the years. Recent advancements in evolutionary search with large language models (LLMs) have shown promise in accelerating the discovery of algorithms across various domains, particularly in mathematics and optimization. However, existing approaches treat the LLM as a static generator, missing the opportunity to update the model with the signal obtained from evolutionary exploration. In this work, we propose to augment LLM-based evolutionary search by continuously refining the search operator - the LLM - through reinforcement learning (RL) fine-tuning. Our method leverages evolutionary search as an exploration strategy to discover improved algorithms, while RL optimizes the LLM policy based on these discoveries. Our experiments on three combinatorial optimization tasks - bin packing, traveling salesman, and the flatpack problem - show that combining RL and evolutionary search improves discovery efficiency of improved algorithms, showcasing the potential of RL-enhanced evolutionary strategies to assist computer scientists and mathematicians for more efficient algorithm design.

Neural architecture search (NAS), the study of automating the discovery of optimal deep neural network architectures for tasks in domains such as computer vision and natural language processing, has seen rapid growth in the machine learning research community. While there have been many recent advancements in NAS, there is still a significant focus on reducing the computational cost incurred when validating discovered architectures by making search more efficient. Evolutionary algorithms, specifically genetic algorithms, have a history of usage in NAS and continue to gain popularity versus other optimization approaches as a highly efficient way to explore the architecture objective space. Most NAS research efforts have centered around computer vision tasks and only recently have other modalities, such as the rapidly growing field of natural language processing, been investigated in depth. In this work, we show how genetic algorithms can be paired with lightly trained objective predictors in an iterative cycle to accelerate multi-objective architectural exploration in a way that works in the modalities of both machine translation and image classification.

Recent advances in Neural Architecture Search (NAS) such as one-shot NAS offer the ability to extract specialized hardware-aware sub-network configurations from a task-specific super-network. While considerable effort has been employed towards improving the first stage, namely, the training of the super-network, the search for derivative high-performing sub-networks is still under-explored. Popular methods decouple the super-network training from the sub-network search and use performance predictors to reduce the computational burden of searching on different hardware platforms. We propose a flexible search framework that automatically and efficiently finds optimal sub-networks that are optimized for different performance metrics and hardware configurations. Specifically, we show how evolutionary algorithms can be paired with lightly trained objective predictors in an iterative cycle to accelerate architecture search in a multi-objective setting for various modalities including machine translation and image classification.

Recent research in Cooperative Coevolution~(CC) have achieved promising progress in solving large-scale global optimization problems. However, existing CC paradigms have a primary limitation in that they require deep expertise for selecting or designing effective variable decomposition strategies. Inspired by advancements in Meta-Black-Box Optimization, this paper introduces LCC, a pioneering learning-based cooperative coevolution framework that dynamically schedules decomposition strategies during optimization processes. The decomposition strategy selector is parameterized through a neural network, which processes a meticulously crafted set of optimization status features to determine the optimal strategy for each optimization step. The network is trained via the Proximal Policy Optimization method in a reinforcement learning manner across a collection of representative problems, aiming to maximize the expected optimization performance. Extensive experimental results demonstrate that LCC not only offers certain advantages over state-of-the-art baselines in terms of optimization effectiveness and resource consumption, but it also exhibits promising transferability towards unseen problems.

One-Shot Neural Architecture Search (NAS) algorithms often rely on training a hardware agnostic super-network for a domain specific task. Optimal sub-networks are then extracted from the trained super-network for different hardware platforms. However, training super-networks from scratch can be extremely time consuming and compute intensive especially for large models that rely on a two-stage training process of pre-training and fine-tuning. State of the art pre-trained models are available for a wide range of tasks, but their large sizes significantly limits their applicability on various hardware platforms. We propose InstaTune, a method that leverages off-the-shelf pre-trained weights for large models and generates a super-network during the fine-tuning stage. InstaTune has multiple benefits. Firstly, since the process happens during fine-tuning, it minimizes the overall time and compute resources required for NAS. Secondly, the sub-networks extracted are optimized for the target task, unlike prior work that optimizes on the pre-training objective. Finally, InstaTune is easy to "plug and play" in existing frameworks. By using multi-objective evolutionary search algorithms along with lightly trained predictors, we find Pareto-optimal sub-networks that outperform their respective baselines across different performance objectives such as accuracy and MACs. Specifically, we demonstrate that our approach performs well across both unimodal (ViT and BERT) and multi-modal (BEiT-3) transformer based architectures.

We explore the use of Evolution Strategies (ES), a class of black box optimization algorithms, as an alternative to popular MDP-based RL techniques such as Q-learning and Policy Gradients. Experiments on MuJoCo and Atari show that ES is a viable solution strategy that scales extremely well with the number of CPUs available: By using a novel communication strategy based on common random numbers, our ES implementation only needs to communicate scalars, making it possible to scale to over a thousand parallel workers. This allows us to solve 3D humanoid walking in 10 minutes and obtain competitive results on most Atari games after one hour of training. In addition, we highlight several advantages of ES as a black box optimization technique: it is invariant to action frequency and delayed rewards, tolerant of extremely long horizons, and does not need temporal discounting or value function approximation.

Recent advances in LLM-guided evolutionary computation, particularly AlphaEvolve (Novikov et al., 2025; Georgiev et al., 2025), have demonstrated remarkable success in discovering novel mathematical constructions and solving challenging optimization problems. However, the high-level descriptions in published work leave many implementation details unspecified, hindering reproducibility and further research. In this report we present GigaEvo, an extensible open-source framework that enables researchers to study and experiment with hybrid LLM-evolution approaches inspired by AlphaEvolve. Our system provides modular implementations of key components: MAP-Elites quality-diversity algorithms, asynchronous DAG-based evaluation pipelines, LLM-driven mutation operators with insight generation and bidirectional lineage tracking, and flexible multi-island evolutionary strategies. In order to assess reproducibility and validate our implementation we evaluate GigaEvo on challenging problems from the AlphaEvolve paper: Heilbronn triangle placement, circle packing in squares, and high-dimensional kissing numbers. The framework emphasizes modularity, concurrency, and ease of experimentation, enabling rapid prototyping through declarative configuration. We provide detailed descriptions of system architecture, implementation decisions, and experimental methodology to support further research in LLM driven evolutionary methods. The GigaEvo framework and all experimental code are available at https://github.com/AIRI-Institute/gigaevo-core.

While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing approaches typically formulate AHD around constructive priority rules or parameterized local search guidance, thereby restricting the search space to fixed heuristic forms. Such designs offer limited capacity for structural exploration, making it difficult to escape deep local optima in complex Combinatorial Optimization Problems (COPs). In this work, we propose G-LNS, a generative evolutionary framework that extends LLM-based AHD to the automated design of Large Neighborhood Search (LNS) operators. Unlike prior methods that evolve heuristics in isolation, G-LNS leverages LLMs to co-evolve tightly coupled pairs of destroy and repair operators. A cooperative evaluation mechanism explicitly captures their interaction, enabling the discovery of complementary operator logic that jointly performs effective structural disruption and reconstruction. Extensive experiments on challenging COP benchmarks, such as Traveling Salesman Problems (TSP) and Capacitated Vehicle Routing Problems (CVRP), demonstrate that G-LNS significantly outperforms LLM-based AHD methods as well as strong classical solvers. The discovered heuristics not only achieve near-optimal solutions with reduced computational budgets but also exhibit robust generalization across diverse and unseen instance distributions.

Optimization can be found in many real-life applications. Designing an effective algorithm for a specific optimization problem typically requires a tedious amount of effort from human experts with domain knowledge and algorithm design skills. In this paper, we propose a novel approach called Algorithm Evolution using Large Language Model (AEL). It utilizes a large language model (LLM) to automatically generate optimization algorithms via an evolutionary framework. AEL does algorithm-level evolution without model training. Human effort and requirements for domain knowledge can be significantly reduced. We take constructive methods for the salesman traveling problem as a test example, we show that the constructive algorithm obtained by AEL outperforms simple hand-crafted and LLM-generated heuristics. Compared with other domain deep learning model-based algorithms, these methods exhibit excellent scalability across different problem sizes. AEL is also very different from previous attempts that utilize LLMs as search operators in algorithms.

This paper presents a reinforced genetic approach to a defined d-resource system optimization problem. The classical evolution schema was ineffective due to a very strict feasibility function in the studied problem. Hence, the presented strategy has introduced several modifications and adaptations to standard genetic routines, e.g.: a migration operator which is an analogy to the biological random genetic drift.

We consider function optimization as a sequential decision making problem under budget constraint. This constraint limits the number of objective function evaluations allowed during the optimization. We consider an algorithm inspired by a continuous version of a multi-armed bandit problem which attacks this optimization problem by solving the tradeoff between exploration (initial quasi-uniform search of the domain) and exploitation (local optimization around the potentially global maxima). We introduce the so-called Simultaneous Optimistic Optimization (SOO), a deterministic algorithm that works by domain partitioning. The benefit of such approach are the guarantees on the returned solution and the numerical efficiency of the algorithm. We present this machine learning approach to optimization, and provide the empirical assessment of SOO on the CEC'2014 competition on single objective real-parameter numerical optimization test-suite.

Reinforcement learning (RL) has emerged as a powerful approach for tackling complex problems. The recent introduction of multi-objective reinforcement learning (MORL) has further expanded the scope of RL by enabling agents to make trade-offs among multiple objectives. This advancement not only has broadened the range of problems that can be tackled but also created numerous opportunities for exploration and advancement. Yet, the effectiveness of RL agents heavily relies on appropriately setting their hyperparameters. In practice, this task often proves to be challenging, leading to unsuccessful deployments of these techniques in various instances. Hence, prior research has explored hyperparameter optimization in RL to address this concern. This paper presents an initial investigation into the challenge of hyperparameter optimization specifically for MORL. We formalize the problem, highlight its distinctive challenges, and propose a systematic methodology to address it. The proposed methodology is applied to a well-known environment using a state-of-the-art MORL algorithm, and preliminary results are reported. Our findings indicate that the proposed methodology can effectively provide hyperparameter configurations that significantly enhance the performance of MORL agents. Furthermore, this study identifies various future research opportunities to further advance the field of hyperparameter optimization for MORL.

Many sequential decision-making tasks involve optimizing multiple conflicting objectives, requiring policies that adapt to different user preferences. In multi-objective reinforcement learning (MORL), one widely studied approach} addresses this by training a single policy network conditioned on preference-weighted rewards. In this paper, we explore a novel algorithmic perspective: leveraging reward-free reinforcement learning (RFRL) for MORL. While RFRL has historically been studied independently of MORL, it learns optimal policies for any possible reward function, making it a natural fit for MORL's challenge of handling unknown user preferences. We propose using the RFRL's training objective as an auxiliary task to enhance MORL, enabling more effective knowledge sharing beyond the multi-objective reward function given at training time. To this end, we adapt a state-of-the-art RFRL algorithm to the MORL setting and introduce a preference-guided exploration strategy that focuses learning on relevant parts of the environment. Through extensive experiments and ablation studies, we demonstrate that our approach significantly outperforms the state-of-the-art MORL methods across diverse MO-Gymnasium tasks, achieving superior performance and data efficiency. This work provides the first systematic adaptation of RFRL to MORL, demonstrating its potential as a scalable and empirically effective solution to multi-objective policy learning.

We study the problem of black-box optimization of a function f of any dimension, given function evaluations perturbed by noise. The function is assumed to be locally smooth around one of its global optima, but this smoothness is unknown. Our contribution is an adaptive optimization algorithm, POO or parallel optimistic optimization, that is able to deal with this setting. POO performs almost as well as the best known algorithms requiring the knowledge of the smoothness. Furthermore, POO works for a larger class of functions than what was previously considered, especially for functions that are difficult to optimize, in a very precise sense. We provide a finite-time analysis of POO's performance, which shows that its error after n evaluations is at most a factor of sqrt(ln n) away from the error of the best known optimization algorithms using the knowledge of the smoothness.

A single language model (LM), despite aligning well with an average labeler through reinforcement learning from human feedback (RLHF), may not universally suit diverse human preferences. Recent approaches therefore opt for customization by collecting multi-dimensional feedback and creating distinct reward models (RMs) for each dimension (e.g., helpfulness, harmlessness, or honesty). Different LMs can then be optimized for different preferences using multi-objective RLHF (MORLHF) with different reward weightings. Yet, RL fine-tuning is unstable and resource-heavy, especially for MORLHF with diverse and usually conflicting objectives. In this paper, we present Multi-Objective Direct Preference Optimization (MODPO), an RL-free algorithm that extends Direct Preference Optimization (DPO) for multiple alignment objectives with minimal overheads. Essentially, MODPO folds language modeling directly into reward modeling, training LMs as implicit collective reward models (cRMs) that combine all objectives with specific weightings. While theoretically guaranteed to produce the same optimal solutions as MORLHF, MODPO is practically more stable and computationally efficient. Empirical results from safety alignment and long-form question answering confirm that MODPO matches or outperforms existing methods, consistently producing a Pareto front of LMs that cater to diverse preferences with 3 times less computational resources compared to MORLHF.

Evolutionary program synthesis systems such as AlphaEvolve, OpenEvolve, and ShinkaEvolve offer a new approach to AI-assisted mathematical discovery. These systems utilize teams of large language models (LLMs) to generate candidate solutions to a problem as human readable code. These candidate solutions are then 'evolved' with the goal of improving them beyond what an LLM can produce in a single shot. While existing mathematical applications have mostly focused on problems of establishing bounds (e.g., sphere packing), the program synthesis approach is well suited to any problem where the solution takes the form of an explicit construction. With this in mind, in this paper we explore the use of OpenEvolve for combinatorial bijection discovery. We describe the results of applying OpenEvolve to three bijection construction problems involving Dyck paths, two of which are known and one of which is open. We find that while systems like OpenEvolve show promise as a valuable tool for combinatorialists, the problem of finding novel, research-level bijections remains a challenging task for current frontier systems, reinforcing the need for human mathematicians in the loop. We describe some lessons learned for others in the field interested in exploring the use of these systems.

Choosing automatically the right algorithm using problem descriptors is a classical component of combinatorial optimization. It is also a good tool for making evolutionary algorithms fast, robust and versatile. We present Shiwa, an algorithm good at both discrete and continuous, noisy and noise-free, sequential and parallel, black-box optimization. Our algorithm is experimentally compared to competitors on YABBOB, a BBOB comparable testbed, and on some variants of it, and then validated on several real world testbeds.

Normalization layers and activation functions are fundamental components in deep networks and typically co-locate with each other. Here we propose to design them using an automated approach. Instead of designing them separately, we unify them into a single tensor-to-tensor computation graph, and evolve its structure starting from basic mathematical functions. Examples of such mathematical functions are addition, multiplication and statistical moments. The use of low-level mathematical functions, in contrast to the use of high-level modules in mainstream NAS, leads to a highly sparse and large search space which can be challenging for search methods. To address the challenge, we develop efficient rejection protocols to quickly filter out candidate layers that do not work well. We also use multi-objective evolution to optimize each layer's performance across many architectures to prevent overfitting. Our method leads to the discovery of EvoNorms, a set of new normalization-activation layers with novel, and sometimes surprising structures that go beyond existing design patterns. For example, some EvoNorms do not assume that normalization and activation functions must be applied sequentially, nor need to center the feature maps, nor require explicit activation functions. Our experiments show that EvoNorms work well on image classification models including ResNets, MobileNets and EfficientNets but also transfer well to Mask R-CNN with FPN/SpineNet for instance segmentation and to BigGAN for image synthesis, outperforming BatchNorm and GroupNorm based layers in many cases.

In Multi-Task Learning (MTL), tasks may compete and limit the performance achieved on each other, rather than guiding the optimization to a solution, superior to all its single-task trained counterparts. Since there is often not a unique solution optimal for all tasks, practitioners have to balance tradeoffs between tasks' performance, and resort to optimality in the Pareto sense. Most MTL methodologies either completely neglect this aspect, and instead of aiming at learning a Pareto Front, produce one solution predefined by their optimization schemes, or produce diverse but discrete solutions. Recent approaches parameterize the Pareto Front via neural networks, leading to complex mappings from tradeoff to objective space. In this paper, we conjecture that the Pareto Front admits a linear parameterization in parameter space, which leads us to propose Pareto Manifold Learning, an ensembling method in weight space. Our approach produces a continuous Pareto Front in a single training run, that allows to modulate the performance on each task during inference. Experiments on multi-task learning benchmarks, ranging from image classification to tabular datasets and scene understanding, show that Pareto Manifold Learning outperforms state-of-the-art single-point algorithms, while learning a better Pareto parameterization than multi-point baselines.

This paper presents a strategy to allocate services on a Cloud system without overloading nodes and maintaining the system stability with minimum cost. We specify an abstract model of cloud resources utilization, including multiple types of resources as well as considerations for the service migration costs. A prototype meta-heuristic load balancer is demonstrated and experimental results are presented and discussed. We also propose a novel genetic algorithm, where population is seeded with the outputs of other meta-heuristic algorithms.

Resided at the intersection of multi-fidelity optimization (MFO) and Bayesian optimization (BO), MF BO has found a niche in solving expensive engineering design optimization problems, thanks to its advantages in incorporating physical and mathematical understandings of the problems, saving resources, addressing exploitation-exploration trade-off, considering uncertainty, and processing parallel computing. The increasing number of works dedicated to MF BO suggests the need for a comprehensive review of this advanced optimization technique. In this paper, we survey recent developments of two essential ingredients of MF BO: Gaussian process (GP) based MF surrogates and acquisition functions. We first categorize the existing MF modeling methods and MFO strategies to locate MF BO in a large family of surrogate-based optimization and MFO algorithms. We then exploit the common properties shared between the methods from each ingredient of MF BO to describe important GP-based MF surrogate models and review various acquisition functions. By doing so, we expect to provide a structured understanding of MF BO. Finally, we attempt to reveal important aspects that require further research for applications of MF BO in solving intricate yet important design optimization problems, including constrained optimization, high-dimensional optimization, optimization under uncertainty, and multi-objective optimization.

The core challenge of high-dimensional and expensive black-box optimization (BBO) is how to obtain better performance faster with little function evaluation cost. The essence of the problem is how to design an efficient optimization strategy tailored to the target task. This paper designs a powerful optimization framework to automatically learn the optimization strategies from the target or cheap surrogate task without human intervention. However, current methods are weak for this due to poor representation of optimization strategy. To achieve this, 1) drawing on the mechanism of genetic algorithm, we propose a deep neural network framework called B2Opt, which has a stronger representation of optimization strategies based on survival of the fittest; 2) B2Opt can utilize the cheap surrogate functions of the target task to guide the design of the efficient optimization strategies. Compared to the state-of-the-art BBO baselines, B2Opt can achieve multiple orders of magnitude performance improvement with less function evaluation cost. We validate our proposal on high-dimensional synthetic functions and two real-world applications. We also find that deep B2Opt performs better than shallow ones.

Vehicle Routing Problems (VRP) are an extension of the Traveling Salesperson Problem and are a fundamental NP-hard challenge in combinatorial optimization. Solving VRP in real-time at large scale has become critical in numerous applications, from growing markets like last-mile delivery to emerging use-cases like interactive logistics planning. Such applications involve solving similar problem instances repeatedly, yet current state-of-the-art solvers treat each instance on its own without leveraging previous examples. We introduce a novel optimization framework that uses a reinforcement learning agent - trained on prior instances - to quickly generate initial solutions, which are then further optimized by genetic algorithms. Our framework, Evolutionary Algorithm with Reinforcement Learning Initialization (EARLI), consistently outperforms current state-of-the-art solvers across various time scales. For example, EARLI handles vehicle routing with 500 locations within 1s, 10x faster than current solvers for the same solution quality, enabling applications like real-time and interactive routing. EARLI can generalize to new data, as demonstrated on real e-commerce delivery data of a previously unseen city. Our hybrid framework presents a new way to combine reinforcement learning and genetic algorithms, paving the road for closer interdisciplinary collaboration between AI and optimization communities towards real-time optimization in diverse domains.

The study of hardest and easiest fitness landscapes is an active area of research. Recently, Kaufmann, Larcher, Lengler and Zou conjectured that for the self-adjusting (1,lambda)-EA, Adversarial Dynamic BinVal (ADBV) is the hardest dynamic monotone function to optimize. We introduce the function Switching Dynamic BinVal (SDBV) which coincides with ADBV whenever the number of remaining zeros in the search point is strictly less than n/2, where n denotes the dimension of the search space. We show, using a combinatorial argument, that for the (1+1)-EA with any mutation rate p in [0,1], SDBV is drift-minimizing among the class of dynamic monotone functions. Our construction provides the first explicit example of an instance of the partially-ordered evolutionary algorithm (PO-EA) model with parameterized pessimism introduced by Colin, Doerr and F\'erey, building on work of Jansen. We further show that the (1+1)-EA optimizes SDBV in Theta(n^{3/2}) generations. Our simulations demonstrate matching runtimes for both static and self-adjusting (1,lambda) and (1+lambda)-EA. We further show, using an example of fixed dimension, that drift-minimization does not equal maximal runtime.

We study Pareto optimality in multi-objective multi-armed bandit by providing a formulation of adversarial multi-objective multi-armed bandit and defining its Pareto regrets that can be applied to both stochastic and adversarial settings. The regrets do not rely on any scalarization functions and reflect Pareto optimality compared to scalarized regrets. We also present new algorithms assuming both with and without prior information of the multi-objective multi-armed bandit setting. The algorithms are shown optimal in adversarial settings and nearly optimal up to a logarithmic factor in stochastic settings simultaneously by our established upper bounds and lower bounds on Pareto regrets. Moreover, the lower bound analyses show that the new regrets are consistent with the existing Pareto regret for stochastic settings and extend an adversarial attack mechanism from bandit to the multi-objective one.

Optimizing multiple competing black-box objectives is a challenging problem in many fields, including science, engineering, and machine learning. Multi-objective Bayesian optimization (MOBO) is a sample-efficient approach for identifying the optimal trade-offs between the objectives. However, many existing methods perform poorly when the observations are corrupted by noise. We propose a novel acquisition function, NEHVI, that overcomes this important practical limitation by applying a Bayesian treatment to the popular expected hypervolume improvement (EHVI) criterion and integrating over this uncertainty in the Pareto frontier. We argue that, even in the noiseless setting, generating multiple candidates in parallel is an incarnation of EHVI with uncertainty in the Pareto frontier and therefore can be addressed using the same underlying technique. Through this lens, we derive a natural parallel variant, qNEHVI, that reduces computational complexity of parallel EHVI from exponential to polynomial with respect to the batch size. qNEHVI is one-step Bayes-optimal for hypervolume maximization in both noisy and noiseless environments, and we show that it can be optimized effectively with gradient-based methods via sample average approximation. Empirically, we demonstrate not only that qNEHVI is substantially more robust to observation noise than existing MOBO approaches, but also that it achieves state-of-the-art optimization performance and competitive wall-times in large-batch environments.

This paper presents a distributed algorithm applicable to a wide range of practical multi-robot applications. In such multi-robot applications, the user-defined objectives of the mission can be cast as a general optimization problem, without explicit guidelines of the subtasks per different robot. Owing to the unknown environment, unknown robot dynamics, sensor nonlinearities, etc., the analytic form of the optimization cost function is not available a priori. Therefore, standard gradient-descent-like algorithms are not applicable to these problems. To tackle this, we introduce a new algorithm that carefully designs each robot's subcost function, the optimization of which can accomplish the overall team objective. Upon this transformation, we propose a distributed methodology based on the cognitive-based adaptive optimization (CAO) algorithm, that is able to approximate the evolution of each robot's cost function and to adequately optimize its decision variables (robot actions). The latter can be achieved by online learning only the problem-specific characteristics that affect the accomplishment of mission objectives. The overall, low-complexity algorithm can straightforwardly incorporate any kind of operational constraint, is fault-tolerant, and can appropriately tackle time-varying cost functions. A cornerstone of this approach is that it shares the same convergence characteristics as those of block coordinate descent algorithms. The proposed algorithm is evaluated in three heterogeneous simulation set-ups under multiple scenarios, against both general-purpose and problem-specific algorithms. Source code is available at https://github.com/athakapo/A-distributed-plug-n-play-algorithm-for-multi-robot-applications.

This article reviews modern optimization methods for training neural networks with an emphasis on efficiency and scale. We present state-of-the-art optimization algorithms under a unified algorithmic template that highlights the importance of adapting to the structures in the problem. We then cover how to make these algorithms agnostic to the scale of the problem. Our exposition is intended as an introduction for both practitioners and researchers who wish to be involved in these exciting new developments.

Solving NP-hard problems traditionally relies on heuristics, yet manually designing effective heuristics for complex problems remains a significant challenge. While recent advancements like FunSearch have shown that large language models (LLMs) can be integrated into evolutionary algorithms (EAs) for heuristic design, their potential is hindered by limitations in balancing exploitation and exploration. We introduce Quality-Uncertainty Balanced Evolution (QUBE), a novel approach that enhances LLM+EA methods by redefining the priority criterion within the FunSearch framework. QUBE employs the Quality-Uncertainty Trade-off Criterion (QUTC), based on our proposed Uncertainty-Inclusive Quality metric, to evaluate and guide the evolutionary process. Through extensive experiments on challenging NP-complete problems, QUBE demonstrates significant performance improvements over FunSearch and baseline methods. Our code are available at https://github.com/zzjchen/QUBE\_code.

Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates with probabilities proportional to a given reward. However, GFlowNets can only be used with a predefined scalar reward, which can be either computationally expensive or not directly accessible, in the case of multi-objective optimization (MOO) tasks for example. Moreover, to prioritize identifying high-reward candidates, the conventional practice is to raise the reward to a higher exponent, the optimal choice of which may vary across different environments. To address these issues, we propose Order-Preserving GFlowNets (OP-GFNs), which sample with probabilities in proportion to a learned reward function that is consistent with a provided (partial) order on the candidates, thus eliminating the need for an explicit formulation of the reward function. We theoretically prove that the training process of OP-GFNs gradually sparsifies the learned reward landscape in single-objective maximization tasks. The sparsification concentrates on candidates of a higher hierarchy in the ordering, ensuring exploration at the beginning and exploitation towards the end of the training. We demonstrate OP-GFN's state-of-the-art performance in single-objective maximization (totally ordered) and multi-objective Pareto front approximation (partially ordered) tasks, including synthetic datasets, molecule generation, and neural architecture search.

We present new algorithms for optimizing non-smooth, non-convex stochastic objectives based on a novel analysis technique. This improves the current best-known complexity for finding a (delta,epsilon)-stationary point from O(epsilon^{-4}delta^{-1}) stochastic gradient queries to O(epsilon^{-3}delta^{-1}), which we also show to be optimal. Our primary technique is a reduction from non-smooth non-convex optimization to online learning, after which our results follow from standard regret bounds in online learning. For deterministic and second-order smooth objectives, applying more advanced optimistic online learning techniques enables a new complexity of O(epsilon^{-1.5}delta^{-0.5}). Our techniques also recover all optimal or best-known results for finding epsilon stationary points of smooth or second-order smooth objectives in both stochastic and deterministic settings.

Communications satellite network (CSN), as an integral component of the next generation of communication systems, has the capability to offer services globally. Data transmission in this network primarily relies on two modes: inter-satellite communication and satellite-to-ground station communication. The latter directly impacts the successful reception of data by users. However, due to resource and task limitations, finding a satisfactory solution poses a significant challenge. The communication satellite-ground station network scheduling problem (CS-GSNSP) aims to optimize CSN effectiveness by devising a plan that maximizes link construction time while considering constraints associated with satellite operation modes. The large number of tasks and numerous constraints in the problem result in a time-consuming evaluation of fitness function values. To address this issue, we propose a fuzzy fitness evaluation method (FFEM) that employs fuzzy or real evaluation methods based on individual similarity degrees. Additionally, we introduce an evolutionary algorithm based on FFEM, called evolutionary algorithm based on FFEM (FFEEA), for iteratively searching high-quality network construction schemes. In FFEEA, an adaptive crossover approach is used for efficient population search. Finally, extensive experiments are conducted to demonstrate that our proposed fuzzy fitness evaluation method and other improvement strategies significantly enhance satellite network service time. The study introduces a novel approach to enhance the efficiency of solving combinatorial optimization problems, such as CS-GSNSP, by mitigating the complexity associated with fitness evaluation.

In the realm of multi-objective alignment for large language models, balancing disparate human preferences often manifests as a zero-sum conflict. Specifically, the intrinsic tension between competing goals dictates that aggressively optimizing for one metric (e.g., helpfulness) frequently incurs a substantial penalty on another (e.g., harmlessness). While prior work mainly focuses on data selection, parameter merging, or algorithmic balancing during training, these approaches merely force compromises between divergent preferences along a fixed Pareto frontier, failing to fundamentally resolve the inherent trade-off. In this work, we approach this problem from a novel perspective of multi-dimensional rewards. By scaling up the model's rollouts and analyzing the outputs across different reward dimensions, we arrive at a critical conclusion: the conflict among multiple objectives stems from the fact that the prompt itself inherently restricts the achievable multi-dimensional rewards. Based on this core observation, we propose MORA: Multi-Objective Reward Assimilation. Specifically, MORA isolates single-reward prompts through pre-sampling and expands their reward diversity by rewriting the original questions to incorporate multi-dimensional intents. Extensive experiments demonstrate that: (1) in sequential alignment, MORA achieves single-preference improvements ranging from 5% to 12.4%, with exceptional gains in harmlessness, after multiple-preference alignment across helpful, harmless, and truthful dimensions. (2) In simultaneous alignment, MORA achieves an average overall reward improvement of 4.6%. Our codes are available at https://github.com/Shiying-Huang/MORA-MPA.

Deep reinforcement learning (RL) has been applied extensively to solve complex decision-making problems. In many real-world scenarios, tasks often have several conflicting objectives and may require multiple agents to cooperate, which are the multi-objective multi-agent decision-making problems. However, only few works have been conducted on this intersection. Existing approaches are limited to separate fields and can only handle multi-agent decision-making with a single objective, or multi-objective decision-making with a single agent. In this paper, we propose MO-MIX to solve the multi-objective multi-agent reinforcement learning (MOMARL) problem. Our approach is based on the centralized training with decentralized execution (CTDE) framework. A weight vector representing preference over the objectives is fed into the decentralized agent network as a condition for local action-value function estimation, while a mixing network with parallel architecture is used to estimate the joint action-value function. In addition, an exploration guide approach is applied to improve the uniformity of the final non-dominated solutions. Experiments demonstrate that the proposed method can effectively solve the multi-objective multi-agent cooperative decision-making problem and generate an approximation of the Pareto set. Our approach not only significantly outperforms the baseline method in all four kinds of evaluation metrics, but also requires less computational cost.

AlphaEvolve is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines algorithmic solutions to challenging scientific and practical problems. In this paper we showcase AlphaEvolve as a tool for autonomously discovering novel mathematical constructions and advancing our understanding of long-standing open problems. To demonstrate its breadth, we considered a list of 67 problems spanning mathematical analysis, combinatorics, geometry, and number theory. The system rediscovered the best known solutions in most of the cases and discovered improved solutions in several. In some instances, AlphaEvolve is also able to generalize results for a finite number of input values into a formula valid for all input values. Furthermore, we are able to combine this methodology with Deep Think and AlphaProof in a broader framework where the additional proof-assistants and reasoning systems provide automated proof generation and further mathematical insights. These results demonstrate that large language model-guided evolutionary search can autonomously discover mathematical constructions that complement human intuition, at times matching or even improving the best known results, highlighting the potential for significant new ways of interaction between mathematicians and AI systems. We present AlphaEvolve as a powerful new tool for mathematical discovery, capable of exploring vast search spaces to solve complex optimization problems at scale, often with significantly reduced requirements on preparation and computation time.

There often is a dilemma between ease of optimization and robust out-of-distribution (OoD) generalization. For instance, many OoD methods rely on penalty terms whose optimization is challenging. They are either too strong to optimize reliably or too weak to achieve their goals. We propose to initialize the networks with a rich representation containing a palette of potentially useful features, ready to be used by even simple models. On the one hand, a rich representation provides a good initialization for the optimizer. On the other hand, it also provides an inductive bias that helps OoD generalization. Such a representation is constructed with the Rich Feature Construction (RFC) algorithm, also called the Bonsai algorithm, which consists of a succession of training episodes. During discovery episodes, we craft a multi-objective optimization criterion and its associated datasets in a manner that prevents the network from using the features constructed in the previous iterations. During synthesis episodes, we use knowledge distillation to force the network to simultaneously represent all the previously discovered features. Initializing the networks with Bonsai representations consistently helps six OoD methods achieve top performance on ColoredMNIST benchmark. The same technique substantially outperforms comparable results on the Wilds Camelyon17 task, eliminates the high result variance that plagues other methods, and makes hyperparameter tuning and model selection more reliable.

Simulation optimization (SO) is frequently challenged by noisy evaluations, high computational costs, and complex, multimodal search landscapes. This paper introduces Tabu-Enhanced Simulation Optimization (TESO), a novel metaheuristic framework integrating adaptive search with memory-based strategies. TESO leverages a short-term Tabu List to prevent cycling and encourage diversification, and a long-term Elite Memory to guide intensification by perturbing high-performing solutions. An aspiration criterion allows overriding tabu restrictions for exceptional candidates. This combination facilitates a dynamic balance between exploration and exploitation in stochastic environments. We demonstrate TESO's effectiveness and reliability using an queue optimization problem, showing improved performance compared to benchmarks and validating the contribution of its memory components. Source code and data are available at: https://github.com/bulentsoykan/TESO.

Agentic AI systems built on large language models (LLMs) offer significant potential for automating complex workflows, from software development to customer support. However, LLM agents often underperform due to suboptimal configurations; poorly tuned prompts, tool descriptions, and parameters that typically require weeks of manual refinement. Existing optimization methods either are too complex for general use or treat components in isolation, missing critical interdependencies. We present ARTEMIS, a no-code evolutionary optimization platform that jointly optimizes agent configurations through semantically-aware genetic operators. Given only a benchmark script and natural language goals, ARTEMIS automatically discovers configurable components, extracts performance signals from execution logs, and evolves configurations without requiring architectural modifications. We evaluate ARTEMIS on four representative agent systems: the ALE Agent for competitive programming on AtCoder Heuristic Contest, achieving a 13.6% improvement in acceptance rate; the Mini-SWE Agent for code optimization on SWE-Perf, with a statistically significant 10.1\% performance gain; and the CrewAI Agent for cost and mathematical reasoning on Math Odyssey, achieving a statistically significant 36.9% reduction in the number of tokens required for evaluation. We also evaluate the MathTales-Teacher Agent powered by a smaller open-source model (Qwen2.5-7B) on GSM8K primary-level mathematics problems, achieving a 22\% accuracy improvement and demonstrating that ARTEMIS can optimize agents based on both commercial and local models.

The omnipresence of NP-hard combinatorial optimization problems (COPs) compels domain experts to engage in trial-and-error heuristic design. The long-standing endeavor of design automation has gained new momentum with the rise of large language models (LLMs). This paper introduces Language Hyper-Heuristics (LHHs), an emerging variant of Hyper-Heuristics that leverages LLMs for heuristic generation, featuring minimal manual intervention and open-ended heuristic spaces. To empower LHHs, we present Reflective Evolution (ReEvo), a novel integration of evolutionary search for efficiently exploring the heuristic space, and LLM reflections to provide verbal gradients within the space. Across five heterogeneous algorithmic types, six different COPs, and both white-box and black-box views of COPs, ReEvo yields state-of-the-art and competitive meta-heuristics, evolutionary algorithms, heuristics, and neural solvers, while being more sample-efficient than prior LHHs.

Multi-agent systems (MAS) have emerged as a powerful paradigm for orchestrating large language models (LLMs) and specialized tools to collaboratively address complex tasks. However, existing MAS frameworks often require manual workflow configuration and lack native support for dynamic evolution and performance optimization. In addition, many MAS optimization algorithms are not integrated into a unified framework. In this paper, we present EvoAgentX, an open-source platform that automates the generation, execution, and evolutionary optimization of multi-agent workflows. EvoAgentX employs a modular architecture consisting of five core layers: the basic components, agent, workflow, evolving, and evaluation layers. Specifically, within the evolving layer, EvoAgentX integrates three MAS optimization algorithms, TextGrad, AFlow, and MIPRO, to iteratively refine agent prompts, tool configurations, and workflow topologies. We evaluate EvoAgentX on HotPotQA, MBPP, and MATH for multi-hop reasoning, code generation, and mathematical problem solving, respectively, and further assess it on real-world tasks using GAIA. Experimental results show that EvoAgentX consistently achieves significant performance improvements, including a 7.44% increase in HotPotQA F1, a 10.00% improvement in MBPP pass@1, a 10.00% gain in MATH solve accuracy, and an overall accuracy improvement of up to 20.00% on GAIA. The source code is available at: https://github.com/EvoAgentX/EvoAgentX

Is the lottery ticket phenomenon an idiosyncrasy of gradient-based training or does it generalize to evolutionary optimization? In this paper we establish the existence of highly sparse trainable initializations for evolution strategies (ES) and characterize qualitative differences compared to gradient descent (GD)-based sparse training. We introduce a novel signal-to-noise iterative pruning procedure, which incorporates loss curvature information into the network pruning step. This can enable the discovery of even sparser trainable network initializations when using black-box evolution as compared to GD-based optimization. Furthermore, we find that these initializations encode an inductive bias, which transfers across different ES, related tasks and even to GD-based training. Finally, we compare the local optima resulting from the different optimization paradigms and sparsity levels. In contrast to GD, ES explore diverse and flat local optima and do not preserve linear mode connectivity across sparsity levels and independent runs. The results highlight qualitative differences between evolution and gradient-based learning dynamics, which can be uncovered by the study of iterative pruning procedures.

Handcrafting heuristics for solving complex planning tasks (e.g., NP-hard combinatorial optimization (CO) problems) is a common practice but requires extensive domain knowledge. Recently, Large Language Model (LLM)-based automatic heuristics design (AHD) methods have shown promise in generating high-quality heuristics without manual intervention. Existing LLM-based AHD methods employ a population to maintain a fixed number of top-performing LLM-generated heuristics and introduce evolutionary computation (EC) to enhance the population iteratively. However, the population-based procedure brings greedy properties, often resulting in convergence to local optima. Instead, to more comprehensively explore the space of heuristics, we propose using Monte Carlo Tree Search (MCTS) for LLM-based heuristic evolution while preserving all LLM-generated heuristics in a tree structure. With a novel thought-alignment process and an exploration-decay technique, the proposed MCTS-AHD method delivers significantly higher-quality heuristics on various complex tasks. Our code is available at https://github.com/zz1358m/MCTS-AHD-master.

One of the biggest missing capabilities in current AI systems is the ability to learn continuously after deployment. Implementing such continually learning systems have several challenges, one of which is the large memory requirement of gradient-based algorithms that are used to train state-of-the-art LLMs. Evolutionary Strategies (ES) have recently re-emerged as a gradient-free alternative to traditional learning algorithms and have shown encouraging performance on specific tasks in LLMs. In this paper, we perform a comprehensive analysis of ES and specifically evaluate its forgetting curves when training for an increasing number of update steps. We first find that ES is able to reach performance numbers close to GRPO for math and reasoning tasks with a comparable compute budget. However, and most importantly for continual learning, the performance gains in ES is accompanied by significant forgetting of prior abilities, limiting its applicability for training models online. We also explore the reason behind this behavior and show that the updates made using ES are much less sparse and have orders of magnitude larger ell_2 norm compared to corresponding GRPO updates, explaining the contrasting forgetting curves between the two algorithms. With this study, we aim to highlight the issue of forgetting in gradient-free algorithms like ES and hope to inspire future work to mitigate these issues.

We propose a sparsity-aware evolutionary (SAE) framework for model merging that involves iterative pruning-merging cycles to act as a novel mutation operator. We incorporate the sparsity constraints into the score function, which steers the evolutionary process to favor more sparse models, in addition to other conventional performance scores. Interestingly, the by-product of competition for sparsity introduces an extra local attraction and interplay into the evolutionary process: if one competitor has more zero elements, the other competitor's non-zero elements will occupy those positions, even though the less sparse competitor loses to the more sparse competitor in other positions. The proposed pipeline is evaluated on a variety of large-scale LLM benchmarks. Experiments demonstrate that our approach can improve model merging reliability across multiple benchmarks, and is easy to incorporate due to its simplicity and being orthogonal to most existing approaches.

Model merging constructs versatile models by integrating task-specific models without requiring labeled data or expensive joint retraining. Although recent methods improve adaptability to heterogeneous tasks by generating customized merged models for each instance, they face two critical limitations. First, the instance-specific merged models lack reusability, restricting the exploitation of high-quality merging configurations and efficient batch inference. Second, these methods treat each task-specific model as a monolithic whole, overlooking the diverse mergeability of homologous components such as attention and multilayer perceptron layers, and the differing merging sensitivities across components. To address these limitations, we propose MERGE (Modular Expert Recombination for fine-Grained mErging), a method that enables component-wise model merging and input-aware, on-demand module recombination at inference. MERGE formulates component-wise merging as a bi-objective optimization problem that balances cross-task performance and storage efficiency, and develops a surrogate-assisted evolutionary algorithm to efficiently identify Pareto-optimal merging configurations. These high-quality configurations underpin a reusable modular expert library, from which a lightweight routing network dynamically activates and recombines modular experts to assemble input-specific models and enable efficient inference under storage constraints. Extensive experiments across various model scales, task types, and fine-tuning strategies demonstrate that MERGE consistently outperforms strong baselines and generalizes effectively.

We introduce Evolution Guided General Optimization via Low-rank Learning (EGGROLL), an evolution strategies (ES) algorithm designed to scale backprop-free optimization to large population sizes for modern large neural network architectures with billions of parameters. ES is a set of powerful blackbox optimisation methods that can handle non-differentiable or noisy objectives with excellent scaling potential through parallelisation. Na{ï}ve ES becomes prohibitively expensive at scale due to the computational and memory costs associated with generating matrix perturbations EinR^{mtimes n} and the batched matrix multiplications needed to compute per-member forward passes. EGGROLL overcomes these bottlenecks by generating random matrices Ain R^{mtimes r}, Bin R^{ntimes r} with rll min(m,n) to form a low-rank matrix perturbation A B^top that are used in place of the full-rank perturbation E. As the overall update is an average across a population of N workers, this still results in a high-rank update but with significant memory and computation savings, reducing the auxiliary storage from mn to r(m+n) per layer and the cost of a forward pass from O(mn) to O(r(m+n)) when compared to full-rank ES. A theoretical analysis reveals our low-rank update converges to the full-rank update at a fast Oleft(1{r}right) rate. Our experiments show that (1) EGGROLL does not compromise the performance of ES in tabula-rasa RL settings, despite being faster, (2) it is competitive with GRPO as a technique for improving LLM reasoning, and (3) EGGROLL enables stable pre-training of nonlinear recurrent language models that operate purely in integer datatypes.

Neural architecture search (NAS) methods rely on a search strategy for deciding which architectures to evaluate next and a performance estimation strategy for assessing their performance (e.g., using full evaluations, multi-fidelity evaluations, or the one-shot model). In this paper, we focus on the search strategy. We introduce the simple yet powerful evolutionary algorithm of differential evolution to the NAS community. Using the simplest performance evaluation strategy of full evaluations, we comprehensively compare this search strategy to regularized evolution and Bayesian optimization and demonstrate that it yields improved and more robust results for 13 tabular NAS benchmarks based on NAS-Bench-101, NAS-Bench-1Shot1, NAS-Bench-201 and NAS-HPO bench.

The FOX optimizer, inspired by red fox hunting behavior, is a powerful algorithm for solving real-world and engineering problems. However, despite balancing exploration and exploitation, it can prematurely converge to local optima, as agent positions are updated solely based on the current best-known position, causing all agents to converge on one location. This study proposes the modified FOX optimizer (mFOX) to enhance exploration and balance exploration and exploitation in three steps. First, the Oppositional-Based Learning (OBL) strategy is used to improve the initial population. Second, control parameters are refined to achieve a better balance between exploration and exploitation. Third, a new update equation is introduced, allowing agents to adjust their positions relative to one another rather than relying solely on the best-known position. This approach improves exploration efficiency without adding complexity. The mFOX algorithm's performance is evaluated against 12 well-known algorithms on 23 classical benchmark functions, 10 CEC2019 functions, and 12 CEC2022 functions. It outperforms competitors in 74% of the classical benchmarks, 60% of the CEC2019 benchmarks, and 58% of the CEC2022 benchmarks. Additionally, mFOX effectively addresses four engineering problems. These results demonstrate mFOX's strong competitiveness in solving complex optimization tasks, including unimodal, constrained, and high-dimensional problems.

Deep artificial neural networks (DNNs) are typically trained via gradient-based learning algorithms, namely backpropagation. Evolution strategies (ES) can rival backprop-based algorithms such as Q-learning and policy gradients on challenging deep reinforcement learning (RL) problems. However, ES can be considered a gradient-based algorithm because it performs stochastic gradient descent via an operation similar to a finite-difference approximation of the gradient. That raises the question of whether non-gradient-based evolutionary algorithms can work at DNN scales. Here we demonstrate they can: we evolve the weights of a DNN with a simple, gradient-free, population-based genetic algorithm (GA) and it performs well on hard deep RL problems, including Atari and humanoid locomotion. The Deep GA successfully evolves networks with over four million free parameters, the largest neural networks ever evolved with a traditional evolutionary algorithm. These results (1) expand our sense of the scale at which GAs can operate, (2) suggest intriguingly that in some cases following the gradient is not the best choice for optimizing performance, and (3) make immediately available the multitude of neuroevolution techniques that improve performance. We demonstrate the latter by showing that combining DNNs with novelty search, which encourages exploration on tasks with deceptive or sparse reward functions, can solve a high-dimensional problem on which reward-maximizing algorithms (e.g.\ DQN, A3C, ES, and the GA) fail. Additionally, the Deep GA is faster than ES, A3C, and DQN (it can train Atari in {raise.17ex\scriptstyle\sim}4 hours on one desktop or {raise.17ex\scriptstyle\sim}1 hour distributed on 720 cores), and enables a state-of-the-art, up to 10,000-fold compact encoding technique.

Mixed Integer Linear Programming (MILP) is essential for modeling complex decision-making problems but faces challenges in computational tractability and requires expert formulation. Current deep learning approaches for MILP focus on specific problem classes and do not generalize to unseen classes. To address this shortcoming, we take a foundation model training approach, where we train a single deep learning model on a diverse set of MILP problems to generalize across problem classes. As existing datasets for MILP lack diversity and volume, we introduce MILP-Evolve, a novel LLM-based evolutionary framework that is capable of generating a large set of diverse MILP classes with an unlimited amount of instances. We study our methodology on three key learning tasks that capture diverse aspects of MILP: (1) integrality gap prediction, (2) learning to branch, and (3) a new task of aligning MILP instances with natural language descriptions. Our empirical results show that models trained on the data generated by MILP-Evolve achieve significant improvements on unseen problems, including MIPLIB benchmarks. Our work highlights the potential of moving towards a foundation model approach for MILP that can generalize to a broad range of MILP applications. Our code and data are publicly available at https://github.com/microsoft/OptiGuide.

Group Relative Policy Optimization (GRPO) has been shown to be an effective algorithm when an accurate reward model is available. However, such a highly reliable reward model is not available in many real-world tasks. In this paper, we particularly focus on multi-objective settings, in which we identify that GRPO is vulnerable to reward hacking, optimizing only one of the objectives at the cost of the others. To address this issue, we propose MO-GRPO, an extension of GRPO with a simple normalization method to reweight the reward functions automatically according to the variances of their values. We first show analytically that MO-GRPO ensures that all reward functions contribute evenly to the loss function while preserving the order of preferences, eliminating the need for manual tuning of the reward functions' scales. Then, we evaluate MO-GRPO experimentally in four domains: (i) the multi-armed bandits problem, (ii) simulated control task (Mo-Gymnasium), (iii) machine translation tasks on the WMT benchmark (En-Ja, En-Zh), and (iv) instruction following task. MO-GRPO achieves stable learning by evenly distributing correlations among the components of rewards, outperforming GRPO, showing MO-GRPO to be a promising algorithm for multi-objective reinforcement learning problems.

LLM-based agents depend on effective tool-use policies to solve complex tasks, yet optimizing these policies remains challenging due to delayed supervision and the difficulty of credit assignment in long-horizon trajectories. Existing optimization approaches tend to be either monolithic, which are prone to entangling behaviors, or single-aspect, which ignore cross-module error propagation. To address these limitations, we propose EvoTool, a self-evolving framework that optimizes a modular tool-use policy via a gradient-free evolutionary paradigm. EvoTool decomposes agent's tool-use policy into four modules, including Planner, Selector, Caller, and Synthesizer, and iteratively improves them in a self-improving loop through three novel mechanisms. Trajectory-Grounded Blame Attribution uses diagnostic traces to localize failures to a specific module. Feedback-Guided Targeted Mutation then edits only that module via natural-language critique. Diversity-Aware Population Selection preserves complementary candidates to ensure solution diversity. Across four benchmarks, EvoTool outperforms strong baselines by over 5 points on both GPT-4.1 and Qwen3-8B, while achieving superior efficiency and transferability. The code will be released once paper is accepted.

In recent years, large language models (LLMs) have made remarkable progress, with model optimization primarily relying on gradient-based optimizers such as Adam. However, these gradient-based methods impose stringent hardware requirements, demanding high-concurrency, high-memory GPUs. Moreover, they require all neural network operations to be differentiable, thereby excluding many promising non-differentiable architectures from practical use. To address these limitations, we propose EA4LLM, an evolutionary algorithm for optimizing LLMs, and, for the first time, empirically verify full-parameter optimization from the pretraining stage across model sizes ranging from 0.5B to 32B. We conduct extensive experiments and provide key insights into how evolutionary algorithms can effectively optimize neural networks. Our work challenges the prevailing assumption that gradient-based optimization is the only viable approach for training neural networks. It also holds significant potential to reduce the computational cost of training large language models, thereby enabling groups with limited computational resources to participate in deep learning research.

The paradigm of automated program generation is shifting from one-shot generation to inference-time search, where Large Language Models (LLMs) function as semantic mutation operators within evolutionary loops. While effective, these systems are currently governed by static schedules that fail to account for the non-stationary dynamics of the search process. This rigidity results in substantial computational waste, as resources are indiscriminately allocated to stagnating populations while promising frontiers remain under-exploited. We introduce AdaEvolve, a framework that reformulates LLM-driven evolution as a hierarchical adaptive optimization problem. AdaEvolve uses an "accumulated improvement signal" to unify decisions across three levels: Local Adaptation, which dynamically modulates the exploration intensity within a population of solution candidates; Global Adaptation, which routes the global resource budget via bandit-based scheduling across different solution candidate populations; and Meta-Guidance which generates novel solution tactics based on the previously generated solutions and their corresponding improvements when the progress stalls. We demonstrate that AdaEvolve consistently outperforms the open-sourced baselines across 185 different open-ended optimization problems including combinatorial, systems optimization and algorithm design problems.

Prior works in multi-objective reinforcement learning typically use linear reward scalarization with fixed weights, which provably fail to capture non-convex Pareto fronts and thus yield suboptimal results. This limitation becomes especially critical in online preference alignment for large language models. Here, stochastic trajectories generated by parameterized policies create highly non-linear and non-convex mappings from parameters to objectives that no single static weighting scheme can find optimal trade-offs. We address this limitation by introducing dynamic reward weighting, which adaptively adjusts reward weights during the online reinforcement learning process. Unlike existing approaches that rely on fixed-weight interpolation, our dynamic weighting continuously balances and prioritizes objectives in training, facilitating effective exploration of Pareto fronts in objective space. We introduce two approaches of increasing sophistication and generalizability: (1) hypervolume-guided weight adaptation and (2) gradient-based weight optimization, offering a versatile toolkit for online multi-objective alignment. Our extensive experiments demonstrate their compatibility with commonly used online reinforcement learning algorithms (including GRPO, REINFORCE, and RLOO), effectiveness across multiple mathematical reasoning datasets, and applicability to different model families, consistently achieving Pareto dominant solutions with fewer training steps than fixed-weight linear scalarization baselines.

Learned optimization has emerged as a promising alternative to hand-crafted optimizers, with the potential to discover stronger learned update rules that enable faster, hyperparameter-free training of neural networks. A critical element for practically useful learned optimizers, that can be used off-the-shelf after meta-training, is strong meta-generalization: the ability to apply the optimizers to new tasks. Recent state-of-the-art work in learned optimizers, VeLO (Metz et al., 2022), requires a large number of highly diverse meta-training tasks along with massive computational resources, 4000 TPU months, to achieve meta-generalization. This makes further improvements to such learned optimizers impractical. In this work, we identify several key elements in learned optimizer architectures and meta-training procedures that can lead to strong meta-generalization. We also propose evaluation metrics to reliably assess quantitative performance of an optimizer at scale on a set of evaluation tasks. Our proposed approach, Celo, makes a significant leap in improving the meta-generalization performance of learned optimizers and also outperforms tuned state-of-the-art optimizers on a diverse set of out-of-distribution tasks, despite being meta-trained for just 24 GPU hours.

When a robot autonomously performs a complex task, it frequently must balance competing objectives while maintaining safety. This becomes more difficult in uncertain environments with stochastic outcomes. Enhancing transparency in the robot's behavior and aligning with user preferences are also crucial. This paper introduces a novel framework for multi-objective reinforcement learning that ensures safe task execution, optimizes trade-offs between objectives, and adheres to user preferences. The framework has two main layers: a multi-objective task planner and a high-level selector. The planning layer generates a set of optimal trade-off plans that guarantee satisfaction of a temporal logic task. The selector uses active inference to decide which generated plan best complies with user preferences and aids learning. Operating iteratively, the framework updates a parameterized learning model based on collected data. Case studies and benchmarks on both manipulation and mobile robots show that our framework outperforms other methods and (i) learns multiple optimal trade-offs, (ii) adheres to a user preference, and (iii) allows the user to adjust the balance between (i) and (ii).

As a cornerstone in the Evolutionary Computation (EC) domain, Differential Evolution (DE) is known for its simplicity and effectiveness in handling challenging black-box optimization problems. While the advantages of DE are well-recognized, achieving peak performance heavily depends on its hyperparameters such as the mutation factor, crossover probability, and the selection of specific DE strategies. Traditional approaches to this hyperparameter dilemma have leaned towards parameter tuning or adaptive mechanisms. However, identifying the optimal settings tailored for specific problems remains a persistent challenge. In response, we introduce MetaDE, an approach that evolves DE's intrinsic hyperparameters and strategies using DE itself at a meta-level. A pivotal aspect of MetaDE is a specialized parameterization technique, which endows it with the capability to dynamically modify DE's parameters and strategies throughout the evolutionary process. To augment computational efficiency, MetaDE incorporates a design that leverages parallel processing through a GPU-accelerated computing framework. Within such a framework, DE is not just a solver but also an optimizer for its own configurations, thus streamlining the process of hyperparameter optimization and problem-solving into a cohesive and automated workflow. Extensive evaluations on the CEC2022 benchmark suite demonstrate MetaDE's promising performance. Moreover, when applied to robot control via evolutionary reinforcement learning, MetaDE also demonstrates promising performance. The source code of MetaDE is publicly accessible at: https://github.com/EMI-Group/metade.

Optimization plays a vital role in scientific research and practical applications. However, formulating a concrete optimization problem described in natural language into a mathematical form and selecting a suitable solver to solve the problem requires substantial domain expertise. We introduce OptimAI, a framework for solving Optimization problems described in natural language by leveraging LLM-powered AI agents, and achieve superior performance over current state-of-the-art methods. Our framework is built upon the following key roles: (1) a formulator that translates natural language problem descriptions into precise mathematical formulations; (2) a planner that constructs a high-level solution strategy prior to execution; and (3) a coder and a code critic capable of interacting with the environment and reflecting on outcomes to refine future actions. Ablation studies confirm that all roles are essential; removing the planner or code critic results in 5.8times and 3.1times drops in productivity, respectively. Furthermore, we introduce UCB-based debug scheduling to dynamically switch between alternative plans, yielding an additional 3.3times productivity gain. Our design emphasizes multi-agent collaboration, and our experiments confirm that combining diverse models leads to performance gains. Our approach attains 88.1% accuracy on the NLP4LP dataset and 82.3% on the Optibench dataset, reducing error rates by 58% and 52%, respectively, over prior best results.

While Retrieval Augmented Generation (RAG) has emerged as a popular technique for improving Large Language Model (LLM) systems, it introduces a large number of choices, parameters and hyperparameters that must be made or tuned. This includes the LLM, embedding, and ranker models themselves, as well as hyperparameters governing individual RAG components. Yet, collectively optimizing the entire configuration in a RAG or LLM system remains under-explored - especially in multi-objective settings - due to intractably large solution spaces, noisy objective evaluations, and the high cost of evaluations. In this work, we introduce the first approach for multi-objective parameter optimization of cost, latency, safety and alignment over entire LLM and RAG systems. We find that Bayesian optimization methods significantly outperform baseline approaches, obtaining a superior Pareto front on two new RAG benchmark tasks. We conclude our work with important considerations for practitioners who are designing multi-objective RAG systems, highlighting nuances such as how optimal configurations may not generalize across tasks and objectives.

We study multi-agent reinforcement learning (MARL) for the general-sum Markov Games (MGs) under the general function approximation. In order to find the minimum assumption for sample-efficient learning, we introduce a novel complexity measure called the Multi-Agent Decoupling Coefficient (MADC) for general-sum MGs. Using this measure, we propose the first unified algorithmic framework that ensures sample efficiency in learning Nash Equilibrium, Coarse Correlated Equilibrium, and Correlated Equilibrium for both model-based and model-free MARL problems with low MADC. We also show that our algorithm provides comparable sublinear regret to the existing works. Moreover, our algorithm combines an equilibrium-solving oracle with a single objective optimization subprocedure that solves for the regularized payoff of each deterministic joint policy, which avoids solving constrained optimization problems within data-dependent constraints (Jin et al. 2020; Wang et al. 2023) or executing sampling procedures with complex multi-objective optimization problems (Foster et al. 2023), thus being more amenable to empirical implementation.

In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion models inherently perform evolutionary algorithms, naturally encompassing selection, mutation, and reproductive isolation. Building on this equivalence, we propose the Diffusion Evolution method: an evolutionary algorithm utilizing iterative denoising -- as originally introduced in the context of diffusion models -- to heuristically refine solutions in parameter spaces. Unlike traditional approaches, Diffusion Evolution efficiently identifies multiple optimal solutions and outperforms prominent mainstream evolutionary algorithms. Furthermore, leveraging advanced concepts from diffusion models, namely latent space diffusion and accelerated sampling, we introduce Latent Space Diffusion Evolution, which finds solutions for evolutionary tasks in high-dimensional complex parameter space while significantly reducing computational steps. This parallel between diffusion and evolution not only bridges two different fields but also opens new avenues for mutual enhancement, raising questions about open-ended evolution and potentially utilizing non-Gaussian or discrete diffusion models in the context of Diffusion Evolution.

Decision trees are a crucial class of models offering robust predictive performance and inherent interpretability across various domains, including healthcare, finance, and logistics. However, current tree induction methods often face limitations such as suboptimal solutions from greedy methods or prohibitive computational costs and limited applicability of exact optimization approaches. To address these challenges, we propose an evolutionary optimization method for decision tree induction based on genetic programming (GP). Our key innovation is the integration of semantic priors and domain-specific knowledge about the search space into the optimization algorithm. To this end, we introduce LLEGO, a framework that incorporates semantic priors into genetic search operators through the use of Large Language Models (LLMs), thereby enhancing search efficiency and targeting regions of the search space that yield decision trees with superior generalization performance. This is operationalized through novel genetic operators that work with structured natural language prompts, effectively utilizing LLMs as conditional generative models and sources of semantic knowledge. Specifically, we introduce fitness-guided crossover to exploit high-performing regions, and diversity-guided mutation for efficient global exploration of the search space. These operators are controlled by corresponding hyperparameters that enable a more nuanced balance between exploration and exploitation across the search space. Empirically, we demonstrate across various benchmarks that LLEGO evolves superior-performing trees compared to existing tree induction methods, and exhibits significantly more efficient search performance compared to conventional GP approaches.

Reinforcement Learning (RL) post-training has become the standard for aligning generative models with human preferences, yet most methods rely on a single scalar reward. When multiple criteria matter, the prevailing practice of ``early scalarization'' collapses rewards into a fixed weighted sum. This commits the model to a single trade-off point at training time, providing no inference-time control over inherently conflicting goals -- such as prompt adherence versus source fidelity in image editing. We introduce ParetoSlider, a multi-objective RL (MORL) framework that trains a single diffusion model to approximate the entire Pareto front. By training the model with continuously varying preference weights as a conditioning signal, we enable users to navigate optimal trade-offs at inference time without retraining or maintaining multiple checkpoints. We evaluate ParetoSlider across three state-of-the-art flow-matching backbones: SD3.5, FluxKontext, and LTX-2. Our single preference-conditioned model matches or exceeds the performance of baselines trained separately for fixed reward trade-offs, while uniquely providing fine-grained control over competing generative goals.

We consider the problem of multi-objective alignment of foundation models with human preferences, which is a critical step towards helpful and harmless AI systems. However, it is generally costly and unstable to fine-tune large foundation models using reinforcement learning (RL), and the multi-dimensionality, heterogeneity, and conflicting nature of human preferences further complicate the alignment process. In this paper, we introduce Rewards-in-Context (RiC), which conditions the response of a foundation model on multiple rewards in its prompt context and applies supervised fine-tuning for alignment. The salient features of RiC are simplicity and adaptivity, as it only requires supervised fine-tuning of a single foundation model and supports dynamic adjustment for user preferences during inference time. Inspired by the analytical solution of an abstracted convex optimization problem, our dynamic inference-time adjustment method approaches the Pareto-optimal solution for multiple objectives. Empirical evidence demonstrates the efficacy of our method in aligning both Large Language Models (LLMs) and diffusion models to accommodate diverse rewards with only around 10% GPU hours compared with multi-objective RL baseline.

In multi-fidelity optimization, biased approximations of varying costs of the target function are available. This paper studies the problem of optimizing a locally smooth function with a limited budget, where the learner has to make a tradeoff between the cost and the bias of these approximations. We first prove lower bounds for the simple regret under different assumptions on the fidelities, based on a cost-to-bias function. We then present the Kometo algorithm which achieves, with additional logarithmic factors, the same rates without any knowledge of the function smoothness and fidelity assumptions, and improves previously proven guarantees. We finally empirically show that our algorithm outperforms previous multi-fidelity optimization methods without the knowledge of problem-dependent parameters.

Large language model (LLM)-based multi-agent systems (MAS) show strong promise for complex reasoning, planning, and tool-augmented tasks, but designing effective MAS architectures remains labor-intensive, brittle, and hard to generalize. Existing automatic MAS generation methods either rely on code generation, which often leads to executability and robustness failures, or impose rigid architectural templates that limit expressiveness and adaptability. We propose Evolutionary Generation of Multi-Agent Systems (EvoMAS), which formulates MAS generation as structured configuration generation. EvoMAS performs evolutionary generation in configuration space. Specifically, EvoMAS selects initial configurations from a pool, applies feedback-conditioned mutation and crossover guided by execution traces, and iteratively refines both the candidate pool and an experience memory. We evaluate EvoMAS on diverse benchmarks, including BBEH, SWE-Bench, and WorkBench, covering reasoning, software engineering, and tool-use tasks. EvoMAS consistently improves task performance over both human-designed MAS and prior automatic MAS generation methods, while producing generated systems with higher executability and runtime robustness. EvoMAS outperforms the agent evolution method EvoAgent by +10.5 points on BBEH reasoning and +7.1 points on WorkBench. With Claude-4.5-Sonnet, EvoMAS also reaches 79.1% on SWE-Bench-Verified, matching the top of the leaderboard.

Recent Meta-learning for Black-Box Optimization (MetaBBO) methods harness neural networks to meta-learn configurations of traditional black-box optimizers. Despite their success, they are inevitably restricted by the limitations of predefined hand-crafted optimizers. In this paper, we present Symbol, a novel framework that promotes the automated discovery of black-box optimizers through symbolic equation learning. Specifically, we propose a Symbolic Equation Generator (SEG) that allows closed-form optimization rules to be dynamically generated for specific tasks and optimization steps. Within Symbol, we then develop three distinct strategies based on reinforcement learning, so as to meta-learn the SEG efficiently. Extensive experiments reveal that the optimizers generated by Symbol not only surpass the state-of-the-art BBO and MetaBBO baselines, but also exhibit exceptional zero-shot generalization abilities across entirely unseen tasks with different problem dimensions, population sizes, and optimization horizons. Furthermore, we conduct in-depth analyses of our Symbol framework and the optimization rules that it generates, underscoring its desirable flexibility and interpretability.

Although Large Language Models have advanced Automated Heuristic Design, treating algorithm evolution as a monolithic text generation task overlooks the coupling between discrete algorithmic structures and continuous numerical parameters. Consequently, existing methods often discard promising algorithms due to uncalibrated constants and suffer from premature convergence resulting from simple similarity metrics. To address these limitations, we propose TIDE, a Tuning-Integrated Dynamic Evolution framework designed to decouple structural reasoning from parameter optimization. TIDE features a nested architecture where an outer parallel island model utilizes Tree Similarity Edit Distance to drive structural diversity, while an inner loop integrates LLM-based logic generation with a differential mutation operator for parameter tuning. Additionally, a UCB-based scheduler dynamically prioritizes high-yield prompt strategies to optimize resource allocation. Extensive experiments across nine combinatorial optimization problems demonstrate that TIDE discovers heuristics that significantly outperform state-of-the-art baselines in solution quality while achieving improved search efficiency and reduced computational costs.

Although Deep Reinforcement Learning (DRL) methods can learn effective policies for challenging problems such as Atari games and robotics tasks, algorithms are complex and training times are often long. This study investigates how evolution strategies (ES) perform compared to gradient-based deep reinforcement learning methods. We use ES to optimize the weights of a neural network via neuroevolution, performing direct policy search. We benchmark both regular networks and policy networks consisting of a single linear layer from observations to actions; for three classical ES methods and for three gradient-based methods such as PPO. Our results reveal that ES can find effective linear policies for many RL benchmark tasks, in contrast to DRL methods that can only find successful policies using much larger networks, suggesting that current benchmarks are easier to solve than previously assumed. Interestingly, also for higher complexity tasks, ES achieves results comparable to gradient-based DRL algorithms. Furthermore, we find that by directly accessing the memory state of the game, ES are able to find successful policies in Atari, outperforming DQN. While gradient-based methods have dominated the field in recent years, ES offers an alternative that is easy to implement, parallelize, understand, and tune.

Like generic multi-task learning, continual learning has the nature of multi-objective optimization, and therefore faces a trade-off between the performance of different tasks. That is, to optimize for the current task distribution, it may need to compromise performance on some previous tasks. This means that there exist multiple models that are Pareto-optimal at different times, each addressing a distinct task performance trade-off. Researchers have discussed how to train particular models to address specific trade-off preferences. However, existing algorithms require training overheads proportional to the number of preferences -- a large burden when there are multiple, possibly infinitely many, preferences. As a response, we propose Imprecise Bayesian Continual Learning (IBCL). Upon a new task, IBCL (1) updates a knowledge base in the form of a convex hull of model parameter distributions and (2) obtains particular models to address task trade-off preferences with zero-shot. That is, IBCL does not require any additional training overhead to generate preference-addressing models from its knowledge base. We show that models obtained by IBCL have guarantees in identifying the Pareto optimal parameters. Moreover, experiments on standard image classification and NLP tasks support this guarantee. Statistically, IBCL improves average per-task accuracy by at most 23% and peak per-task accuracy by at most 15% with respect to the baseline methods, with steadily near-zero or positive backward transfer. Most importantly, IBCL significantly reduces the training overhead from training 1 model per preference to at most 3 models for all preferences.

The effort devoted to hand-crafting neural network image classifiers has motivated the use of architecture search to discover them automatically. Although evolutionary algorithms have been repeatedly applied to neural network topologies, the image classifiers thus discovered have remained inferior to human-crafted ones. Here, we evolve an image classifier---AmoebaNet-A---that surpasses hand-designs for the first time. To do this, we modify the tournament selection evolutionary algorithm by introducing an age property to favor the younger genotypes. Matching size, AmoebaNet-A has comparable accuracy to current state-of-the-art ImageNet models discovered with more complex architecture-search methods. Scaled to larger size, AmoebaNet-A sets a new state-of-the-art 83.9% / 96.6% top-5 ImageNet accuracy. In a controlled comparison against a well known reinforcement learning algorithm, we give evidence that evolution can obtain results faster with the same hardware, especially at the earlier stages of the search. This is relevant when fewer compute resources are available. Evolution is, thus, a simple method to effectively discover high-quality architectures.