Evolutionary Search

Evolutionary computation has long promised to deliver both high-performance optimization tools as well as rigorous scientific simulations of Darwinian evolution. However, modern algorithms frequently abandon evolutionary fidelity for physics-inspired heuristics or superficial biological metaphors. This paper derives a suite of advanced gradient-based optimization algorithms directly from evolutionary first principles. We introduce Darwinian Lineage Simulations (DLS) to prove that, in an asexual context, Fisher's and Wright's historically opposed views of evolution are actually formally equivalent; One can partition Fisher's deterministically-evolving total population into Wright's randomly-drifting sub-populations. We prove that proper bookkeeping requires introducing a specific kind of structured noise (the DLS noise relation). Crucially, any bookkeeping choices which satisfy this relation will yield a faithful simulation of evolution. Using this vast representational freedom, we prove that a broad family of battle-tested optimization algorithms are already perfectly compatible with evolutionary dynamics. These include: Stochastic Gradient Descent as well as many regularizations/approximations of Newton's method and Natural Gradient Descent. By simply adding DLS noise (i.e., evolutionarily faithful genetic drift), these algorithms become scientifically valid in silico simulations of Darwinian evolution. Finally, we demonstrate that even the state-of-the-art Adam optimizer can be brought into evolutionary compliance through a minor mathematical surgery.

We present CodeEvolve, an evolutionary framework for improving program performance and code quality with Large Language Models (LLMs). CodeEvolve extends OpenEvolve with runtime-guided target selection, Monte Carlo Tree Search (MCTS), automated code refinement, and language-specific evaluation pipelines for Java and Salesforce Apex. The system uses Java Flight Recorder (JFR) profiles to build weighted component graphs and select optimization targets that account for most execution cost, reducing reliance on manual bottleneck identification. For each target, CodeEvolve generates candidate edits, evaluates them through build validation, unit tests, performance checks, static analysis, and LLM-based review, and retains only variants that preserve functional correctness. Across real-world optimization tasks, CodeEvolve improves performance and code metrics while maintaining correctness. On a large enterprise Java codebase, it achieves an average speedup of 15.22$\times$ across seven hotspot functions and outperforms single-pass LLM optimization on five of them. An ablation study on Apex optimization shows that the full MCTS-augmented configuration produces 19.5 valid programs out of 20 on average, indicating that search, filtering, and refinement each contribute to more reliable optimization.

Interactive multi-objective optimization systems face a budget allocation dilemma: one can spend resources on expensive objective evaluations or on eliciting decision-maker preferences that identify the relevant region of the Pareto set. Moreover, preference elicitation itself spans modalities with different information content and cognitive burden, ranging from cheap, noisy pairwise preference statements (PS) to richer but costlier indifference adjustments (IA). We study cost-aware optimization under an unknown scalarization and introduce QUIVER (Query-Informed Value Estimation for Regret), a surrogate-assisted evolutionary multi-objective optimizer that adaptively chooses between objective evaluations and heterogeneous preference queries. At each step, QUIVER selects the next action by maximizing the expected decision-quality improvement per unit total cost. Across DTLZ and WFG benchmarks under synthetic decision-maker models, QUIVER achieves the lowest final utility regret on challenging WFG problems (utility regret of 2.14 on WFG4, 2.82 on WFG9: a 25% improvement over baselines), outperforming all single-modality baselines. We analyze how the optimal mix of PS and IA adapts to problem difficulty: on easy problems (DTLZ2), QUIVER selects 80% PS queries; on hard problems (WFG9), it shifts to 35% IA queries. This adaptive modality selection demonstrates cost-aware preference learning in action.

We study day-ahead transmission topology control for high-voltage grid operation under $N-1$ security constraints. The operational task is to select, over a 24-hour horizon, a sequence of substation topologies obtained via busbar-coupler switching to relieve line overloads while limiting switching effort and topological complexity. We formulate this task as a sequential multi-objective optimization problem with four objectives used in TSO decision making: worst-case $N-1$ line loading, maximum topological depth, number of topology changes, and time spent outside the reference topology. We propose an exact block algorithm that exploits the temporal structure of topology plans: consecutive hours with the same topology are represented as blocks, enabling enumeration of the complete Pareto front over the admissible set of topologies under fixed operational bounds on depth and switching. We also develop a tailored NSGA-III-based evolutionary heuristic and evaluate it against the exact front. Using real operational data from the Dutch high-voltage transmission grid operated by TenneT, the block algorithm computes the exact front for a highly congested day in under three minutes after topology-level load-flow preprocessing. The exact front reveals low-switching plans with no DC $N-1$ thermal overloads that the tested evolutionary search fails to find. The proposed method, therefore, provides both a practical day-ahead decision-support tool for transmission operators and a benchmark for heuristic and learning-based topology-control methods.

Efficient radar resource allocation is a fundamental yet computationally challenging problem, as optimal solutions typically require iterative optimization with high complexity. Motivated by the need for real-time scheduling, robust generalization, and low data dependency, this paper proposes a novel paradigm that leverages large language model (LLM)-guided evolutionary search (AlphaEvolve) to autonomously discover a closed-form power allocation solution for multi-target tracking. The approach encodes high-dimensional radar states into physically inspired features, then evolves a compact and interpretable scoring function, which is transformed to feasible power allocations via a deterministic constraint-satisfying transformation. Extensive experiments demonstrate that the discovered closed-form solution achieves near-optimal tracking accuracy (average relative performance loss of only $1.51\%$), reliable generalization across diverse scenarios and target counts, and over three orders of magnitude speedup compared to conventional iterative solvers. These results highlight the potential of LLM-guided symbolic search to revolutionize not only radar resource management but also broader classes of engineering optimization problems.

The Zarankiewicz number $\textbf{Z}(m, n, s, t)$ is the maximum number of edges in a bipartite graph $G_{m, n}$ such that there is no complete $K_{s, t}$ bipartite subgraph. We determine for the first time the exact values of three Zarankiewicz numbers: $\textbf{Z}(11, 21, 3, 3)=116$, $\textbf{Z}(11, 22, 3, 3)=121$, and $\textbf{Z}(12, 22, 3, 3)=132$. We further establish lower bounds for 41 more Zarankiewicz numbers, including several that are within one edge of the best known upper bound, and we match the established value in four more closed cases. Our results are obtained using OpenEvolve, an open-source evolutionary algorithm based on Large Language Models (LLMs) that iteratively improves algorithms for generating mathematical constructions by optimizing a reward signal which we tailored for this specific problem. These findings provide new extremal graph constructions and demonstrate the potential of LLM-guided evolutionary search to contribute to mathematical research. In addition to presenting the resulting constructions, we report the generation algorithms produced, describe the relevant implementation details, and provide our computational costs. Our costs are remarkably low, at less than $30 for each Zarankiewicz parameter combination, showing that LLM-guided evolutionary search can be an inexpensive, reproducible, and accessible tool for discovering new combinatorial constructions.

Expensive optimization problems (EOPs) are black-box tasks with costly objective evaluations and no gradient access, making the evaluation budget the key bottleneck. Surrogate-assisted evolutionary algorithms (SAEAs) reduce evaluations via surrogate predictions, but conventional surrogates often require frequent retraining as populations evolve, incurring overhead. This paper proposes R2SAEA, a reinforcement-trained relation-based large language model (LLM) surrogate assisted evolutionary algorithm. We cast relation-based surrogate modeling as an in-context pairwise reasoning task. To enable efficient inference in evolutionary loops, we develop an anchor-based iterative context construction strategy that reduces prompt complexity from quadratic to linear in population size, and a voting-based aggregation scheme that converts predicted relations into scores for offspring selection. We further build an RL pipeline from evolutionary trajectories and fine-tune Qwen2.5 with GRPO. Experiments on single- and multi-objective benchmarks show improved relation prediction and state-of-the-art optimization performance over strong SAEA baselines and general LLMs. Quantization also enables efficient edge deployment, supporting a zero-shot surrogate paradigm without per-generation retraining. Code and models are available at https://github.com/Septend9/R2SAEA.

Technology mapping is a critical yet challenging stage in logic synthesis. While Large Language Models (LLMs) have been applied to generate optimization scripts, their potential for core algorithm enhancement remains untapped. We introduce MappingEvolve, an open-source framework that pioneers the use of LLMs to directly evolve technology mapping code. Our method abstracts the mapping process into distinct optimization operators and employs a hierarchical agent-based architecture, comprising a Planner, Evolver, and Evaluator, to guide the evolutionary search. This structured approach enables strategic and effective code modifications. Experiments show our method significantly outperforms direct evolution and strong baselines, achieving 10.04% area reduction versus ABC and 7.93% versus mockturtle, with 46.6%--96.0% $S_{overall}$ improvement on EPFL benchmarks, while explicitly navigating the area--delay trade-off. Our code and data are available at https://github.com/Flians/MappingEvolve.

Conceptual aircraft design is traditionally an expert-mediated iterative process in which a human designer proposes a configuration, runs low-order physics, inspects the result, and re-proposes. We present AlphaJet, an end-to-end automated synthesis pipeline that closes this loop. From a textual mission specification (mass, range, cruise speed, hard size envelope, engine count, areal density) AlphaJet evolves a feasible 3D aircraft in real time, scored by a transparent multi-disciplinary fitness function covering aerodynamics, structures, weights, stability, packaging, and geometric mount consistency. Three contributions distinguish our approach: (i) an Anatomically-Disentangled Variational Autoencoder (AD-VAE) whose first 25 latent dimensions are supervised to align with named anatomical parameters, providing an interpretable shape prior; (ii) a topology-elitist genetic algorithm that protects the best individual from each of five tail topologies and triggers stagnation restarts, preventing premature collapse to a single configuration; and (iii) mount-aware geometric scoring that computes signed penetration between engines and other structural parts, eliminating the redundant artifacts common in generative aircraft models. The full loop runs interactively on a CPU and streams every generation to a browser viewer, making it a practical real-world automation tool for early-phase design-space exploration.

Stopping criteria automatically determine when to stop an evolutionary algorithm, so as not to waste function evaluations on a stagnant population. Although stopping criteria play an important role in real-world applications, they have attracted little attention in the evolutionary multi-objective optimization (EMO) community. In fact, new stopping criteria for EMO have been rarely developed in recent years. One reason for the stagnation in developing stopping criteria for EMO is a lack of effective benchmarking methodologies. To address this issue, this paper proposes (i) a performance measure of stopping criteria for EMO and (ii) a file-based benchmarking approach. This paper also proposes (iii) a data representation method that effectively stores population states in text files. (i) The proposed measure represents the performance of stopping criteria as a single scalar value, making comparison easy. (ii) The proposed file-based approach not only simplifies the benchmarking process but also facilitates reproducibility. (iii) The proposed data representation method addresses the issue of file size in (ii). We demonstrate the effectiveness of our three contributions (i)--(iii) by benchmarking five representative stopping criteria for EMO.

Evolutionary methods have long been useful for analysis and explanation in genetics, biology, ecology, and related fields. In this work, we extend these methods to neural networks, specifically large language models (LLMs), to better analyze and explain relationships among models. We show how relating weights to genotypes and output text to phenotypes can improve our understanding of model lineage, important datasets, the roles of different model layers, and visualization of model relationships. We demonstrate this in a controlled experiment, where our estimated evolutionary trees reliably recover the topology of the ground-truth training tree. We further identify the most important weight layers according to weight differences and show through phenotypic experiments that one training dataset appears to contribute more useful information than the others. Finally, we generate an unsupervised evolutionary tree of black-box foundation models. Throughout, we provide visualizations that support a clearer understanding of evolutionary relationships among LLMs.

Large Language Model (LLM)-guided evolutionary search is increasingly used for automated algorithm discovery, yet most current methods track search progress primarily through executable programs and scalar fitness. Even when natural-language reasoning is used through heuristic descriptions or reflection, it typically remains transient mutation context or unstructured memory, rather than organized as persistent population-level state over strategic directions. As a result, evolutionary search can struggle to distinguish syntactically different implementations of the same idea, preserve lower-fitness but strategically promising directions, or detect when an entire family of strategies has saturated. We introduce \model, a modular strategy-space layer that turns language-level strategic reasoning into first-class population-level evolutionary state in LLM-driven program search. \model represents each candidate program with an explicit natural-language strategy, clusters the archive by strategy semantics, retrieves behaviorally complementary inspirations, and periodically navigates the strategy landscape to avoid saturated directions. Without modifying the underlying evolutionary algorithms, \model improves existing evolutionary backbones across algorithm discovery, systems optimization, and agent-scaffold design tasks in most settings. Across four systems benchmarks, \model achieves a 20.6% average relative improvement, with the best single run on Prism scoring 3$\times$ higher. These results suggest that persistent strategy representations provide a practical mechanism for improving the effectiveness and cost-efficiency of LLM-guided evolutionary search, pointing toward compound AI systems whose search capabilities benefit from the structured accumulation and reuse of algorithmic strategies.

Designing heuristics for combinatorial optimization problems (COPs) is a fundamental yet challenging task that traditionally requires extensive domain expertise. Recently, Large Language Model (LLM)-based Automated Heuristic Design (AHD) has shown promise in autonomously generating heuristic components with minimal human intervention. However, most existing LLM-based AHD methods enforce fixed algorithmic templates to ensure executability, which confines the search to component-level tuning and limits system-level algorithmic expressiveness. To enable open-ended solver synthesis beyond rigid templates, we propose Automated Algorithm Design via Evolutionary Program Trees (A2DEPT), which treats LLMs as system-level algorithm architects. A2DEPT explores the vast program space via a tree-structured evolutionary search with hybrid selection and hierarchical operators, enabling iterative refinement of complete algorithms. To make open-ended generation practical, we enforce executability with a lightweight program-maintenance loop that performs feedback-driven repair. In experiments, A2DEPT consistently outperforms representative LLM-based baselines on both standard and highly constrained benchmarks. On the standard benchmarks, it reduces the mean normalized optimality gap by 9.8% relative to the strongest competing AHD baseline.

Local Optima Networks (LONs) represent the global structure of search spaces as graphs, but their construction requires iterative execution of a search algorithm to find local optima and approximate transitions between Basins of Attraction (BoAs). In continuous optimization, this high computational cost prevents systematic investigation of the relationship between LON features and evolutionary algorithm performance. To address this issue, we propose an alternative definition of BoAs for Max-Set of Gaussians (MSG) landscapes with explicitly tunable multimodality. This bypasses search-based BoA identification, enabling low-cost LON construction. Moreover, we leverage Novelty Search (NS) to explore the parameter space of the MSG landscape generator, producing instances with diverse graph topologies. Our experiments show that the proposed BoAs closely align with gradient-based BoAs, and that NS successfully generates instances with varied search difficulty and connectivity patterns among optima. Finally, over the instances generated by NS, we predict the success rate of two well-established evolutionary algorithms from LON features. While our LON construction is specific to MSG landscapes, the proposed framework provides a dataset that serves as a foundation for landscape-aware optimization.

Recent work has demonstrated the promise of orchestrating large language models (LLMs) within evolutionary and agentic optimization systems. However, the mechanisms driving these optimization gains remain poorly understood. In this work, we present a large-scale study of LLM-guided evolutionary search, collecting optimization trajectories for 15 LLMs across 8 tasks. Although zero-shot problem-solving ability correlates with final optimization outcomes, it explains only part of the variance: models with similar initial capability often induce dramatically different search trajectories and outcomes. By analyzing these trajectories, we find that strong LLM optimizers behave as local refiners, producing frequent incremental improvements while progressively localizing the search in semantic space. Conversely, weaker optimizers exhibit large semantic drift, with sporadic breakthroughs followed by stagnation. Notably, various measures of solution novelty do not predict final performance; novelty is beneficial only when the search remains sufficiently localized around high-performing regions of the solution space. Our results highlight the importance of trajectory analysis for understanding and improving LLM-based optimization systems and provide actionable insights for their design and training.

Scalability of evolutionary algorithms refers to assessing how their performance changes as problem size increases. In the area of multi-objective optimisation, research on the scalability of multi-objective evolutionary algorithms (MOEAs) has predominantly focussed on continuous problems. However, multi-objective combinatorial optimisation problems (MOCOPs) differ from continuous ones. Their discrete and rigid structure often brings rugged landscape, numerous local optimal solutions and disjoint global optimal regions. This leads to different behaviour of MOEAs. For example, SEMO, a simple MOEA without mating selection and diversity maintenance mechanisms, has been shown to be highly competitive, and in many cases to outperform more sophisticated MOEAs on MOCOPs. Yet, it remains unclear whether such findings hold for large-scale cases. In this paper, we conduct an empirical investigation into the scalability of MOEAs on combinatorial problems, with problem size from 50 to 5,000. Our results show that SEMO experiences a decline in convergence speed as dimensionality increases, compared to other MOEAs such as NSGA-II, SMS-EMOA and MOEA/D. We further demonstrate that the absence of crossover is a major contributor to SEMO's underperformance in large-scale problems, and that incorporating crossover into SEMO can substantially accelerate convergence in general, despite being detrimental in spreading solutions over the Pareto front.

Deep learning models are the most efficient models in many machine learning tasks. The main disadvantage when using them in IoT, mobile devices, independent autonomous or real-time systems is their complexity and memory size. Therefore, much research has concentrated on compression techniques of deep learning architectures. One of the most popular technique is quantization. In most of the works, the quantization is done based on the nearest neighbour quantization technique. This work focuses on improving the quantization efficiency in pretrained and quantized models. This approach has the potential to improve the final accuracy of quantized models. The main postulate of the work is that final quantization states of the network based on nearest neighbour rounding does not guarantee optimal accuracy. In the presented work, the evolution strategy is used as an optimization approach. The evolution in each iteration changes the values of the small percentage of weights. It shifts theirs values to different quantization states. The work shows that proposed evolution with an appropriate set of operators and parameters can fast improve the accuracy of the quantized models. The results are presented for popular architectures such as VGG and Resnet for image classification and detection. Additionally, simulations were carried out for the autoencoder architecture.

Monotone Boolean functions are a structurally important class of Boolean functions, but their restricted form imposes strong limitations on achievable nonlinearity. In this paper, we investigate whether evolutionary computation can evolve monotone Boolean functions with high nonlinearity, both in the balanced and imbalanced settings. We consider three solution encodings: the standard truth table representation, a balanced truth table encoding that preserves Hamming weight, and a symbolic tree-based genetic programming representation. To guide the search toward monotone increasing functions, we introduce a non-monotonicity penalty and combine it with fitness functions targeting balancedness and nonlinearity. Experimental results are reported for dimensions from $n=5$ to $n=14$. The results show that evolutionary search can discover monotone Boolean functions with nonlinearities clearly exceeding those of majority functions, and in several cases approaching the best currently known values for monotone functions. At the same time, the experiments reveal substantial differences between encodings: the balanced truth table encoding performs poorly for larger dimensions, while the standard truth table and genetic programming encodings remain competitive, with genetic programming becoming especially relevant in the largest tested dimensions.

Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately. We introduce multitasking formulations of these problems that are an effective way to solve multiple related problems with a single run. In our setting the given problems share a monotone submodular function $f$ but have different knapsack constraints. We examine the case where elements within a constraint have the same cost and show that our multitasking formulations result in small Pareto fronts. This allows the population to share solutions between all problems leading to significant improvements compared to running several classical approaches independently. Using rigorous runtime analysis, we analyze the expected time until the introduced multitasking approaches obtain a $(1-1/e)$-approximation for each of the given problems. Our experimental investigations for the maximum coverage problem give further insight into the dynamics behind how the approach works and doesn't work in practice for problems where elements within a constraint also have varied costs.

Interactive Evolutionary Computation (IEC) provides a powerful framework for optimizing subjective criteria such as human preferences and aesthetics, yet it suffers from a fundamental limitation: in high-dimensional generative representations, defining crossover in a semantically consistent manner is difficult, often leading to a mutation-dominated search. In this work, we explicitly define crossover in diffusion models. We propose Diffusion crossover, which formulates evolutionary recombination as step-wise interpolation of noise sequences in the reverse process of Denoising Diffusion Probabilistic Models (DDPMs). By applying spherical linear interpolation (Slerp) to the noise sequences associated with selected parent images, the proposed method generates offspring that inherit characteristics from both parents while preserving the geometric structure of the diffusion process. Furthermore, controlling the time-step range of interpolation enables a principled trade-off between diversity (exploration) and convergence (exploitation). Experimental results using PCA analysis and perceptual similarity metrics (LPIPS) demonstrate that Diffusion crossover produces perceptually smooth and semantically consistent transitions between parent images. Qualitative interactive evolution experiments further confirm that the proposed method effectively supports human-in-the-loop image exploration. These findings suggest a new perspective: diffusion models are not only powerful generators, but also structured evolutionary search spaces in which recombination can be explicitly defined and controlled.

The generation of sustained, open-ended complexity from local interactions remains a fundamental challenge in artificial life. Differentiable multi-agent systems, such as Petri Dish Neural Cellular Automata (PD-NCA), exhibit rich self-organization driven purely by spatial competition; however, they are highly sensitive to hyperparameters and frequently collapse into uninteresting patterns and dynamics, such as frozen equilibria or structureless noise. In this paper, we introduce PBT-NCA, a meta-evolutionary algorithm that evolves a population of PD-NCAs subject to a composite objective that rewards both historical behavioral novelty and contemporary visual diversity. Driven by this continuous evolutionary pressure, PBT-NCA spontaneously generates a plethora of emergent lifelike phenomena over extended horizons-a hallmark of true open-endedness. Strikingly, the substrate autonomously discovers diverse morphological survival and self-organization strategies. We observe highly regular, coordinated periodic waves; spore-like scattering where homogeneous groups eject cell-like clusters to colonize distant territories; and fluid, shape-shifting macro-structures that migrate across the substrate, maintaining stable outer boundaries that enclose highly active interiors. By actively penalizing monocultures and dead states, PBT-NCA sustains a state of effective complexity that is neither globally ordered nor globally random, operating persistently at the "edge of chaos".

We present a new solution concept called evolutionarily stable Stackelberg equilibrium (SESS). We study the Stackelberg evolutionary game setting in which there is a single leading player and a symmetric population of followers. The leader selects an optimal mixed strategy, anticipating that the follower population plays an evolutionarily stable strategy (ESS) in the induced subgame and may satisfy additional ecological conditions. We consider both leader-optimal and leader-pessimal selection among ESSs, which arise as special cases of our framework. Prior approaches to Stackelberg evolutionary games either define the follower response via evolutionary dynamics or assume rational best-response behavior, without explicitly enforcing stability against invasion by mutations. We present algorithms for computing SESS in discrete and continuous games, and validate the latter empirically. Our model applies naturally to biological settings; for example, in cancer treatment the leader represents the physician and the followers correspond to competing cancer cell phenotypes.

Accurate and efficient tracking of surgical instruments is fundamental for Robot-Assisted Minimally Invasive Surgery. Although vision-based robot pose estimation has enabled markerless calibration without tedious physical setups, reliable tool tracking for surgical robots still remains challenging due to partial visibility and specialized articulation design of surgical instruments. Previous works in the field are usually prone to unreliable feature detections under degraded visual quality and data scarcity, whereas rendering-based methods often struggle with computational costs and suboptimal convergence. In this work, we incorporate CMA-ES, an evolutionary optimization strategy, into a versatile tracking pipeline that jointly estimates surgical instrument pose and joint configurations. Using batch rendering to efficiently evaluate multiple pose candidates in parallel, the method significantly reduces inference time and improves convergence robustness. The proposed framework further generalizes to joint angle-free and bi-manual tracking settings, making it suitable for both vision feedback control and online surgery video calibration. Extensive experiments on synthetic and real-world datasets demonstrate that the proposed method significantly outperforms prior approaches in both accuracy and runtime. Source code and data are available at https://github.com/hanyang-hu/online_dvrk_tracking.

LLM-guided evolutionary computation, most notably AlphaEvolve, has been remarkably successful in discovering novel mathematical constructions by solving challenging optimization problems. The standard approach is to evolve a monolithic program that directly outputs a candidate solution. We present ImprovEvolve, an algorithmic alternative that drastically reduces cognitive load on the LLM. Instead of prompting the model for an end-to-end optimizer, we evolve a program with three specialized operators of initialization, local improvement, and perturbation. We then approach the optimum by iteratively applying local improvements and intensity-scheduled perturbations, effectively driving a basin-hopping search with LLM-evolved subroutines. For hexagon in hexagon packing, ImprovEvolve discovers new state-of-the-art packings of 11, 12, 15, and 16 hexagons, and additionally for 14, 17, and 23 hexagons after minimal expert tuning of the generated code. For the second autocorrelation inequality, the evolved and human-scaled program pushes the lower bound from 0.96102 to 0.96258. For spherical codes, the ImprovEvolve program lowers the best-known maximum cosine for the majority of 90 randomly chosen diverse state-of-the-art spherical codes, achieving relative improvements of up to 2.4%.

Over the past two decades, research in evolutionary multi-objective optimization has predominantly focused on continuous domains, with comparatively limited attention given to multi-objective combinatorial optimization problems (MOCOPs). Combinatorial problems differ significantly from continuous ones in terms of problem structure and landscape. Recent studies have shown that on MOCOPs multi-objective evolutionary algorithms (MOEAs) can even be outperformed by simple randomised local search. Starting with a randomly sampled solution in search space, randomised local search iteratively draws a random solution (from an archive) to perform local variation within its neighbourhood. However, in most existing methods, the local variation relies on a fixed neighbourhood, which limits exploration and makes the search easy to get trapped in local optima. In this paper, we present a simple yet effective local search method, called variable stepsize randomized local search (VS-RLS), which adjusts the stepsize during the search. VS-RLS transitions gradually from a broad, exploratory search in the early phases to a more focused, fine-grained search as the search progresses. We demonstrate the effectiveness and generalizability of VS-RLS through extensive evaluations against local search and MOEAs methods on diverse MOCOPs.

Evolutionary dynamic optimization (EDO) commonly assumes that environmental changes can be detected from fitness variations and handled through random re-initialization, historical solutions, or learned transition patterns. Online calibration of black-box simulators introduces a different setting, where the dynamic objective is induced by sequential observations and a changing calibration window, rather than being controlled by explicit variables. Fitness variations therefore cannot be directly attributed to regime changes, while the unknown relationship between successive regimes limits conventional adaptation. We formulate this setting as an observation-driven dynamic optimization problem and propose PosEDO, which augments fitness-based EDO with an observation-conditioned parameter-space signal. PosEDO learns this signal online as a posterior distribution over simulator parameters from parameter-trajectory pairs generated during evolutionary evaluation, using posterior shifts for change detection and posterior samples for population adaptation. The new evaluation records are further utilized for online posterior updating without additional simulator calls. Experiments on nonstationary economic and financial simulators show that PosEDO improves calibration accuracy, optimization performance, and change-detection quality over representative EDO baselines.

Optimization benchmarks play a fundamental role in assessing algorithm performance; however, existing artificial benchmarks often fail to capture the diversity and irregularity of real-world problem structures, while benchmarks derived from real-world problems are costly and difficult to construct. To address these challenges, we propose an evolutionary automatic benchmark generation framework that leverages a large language model (LLM) as a generative operator, termed the LLM-driven evolutionary benchmark generator (LLM-EBG). In this framework, the LLM serves as an evolutionary operator that generates and evolves benchmark problems within a flexible, expressive representation space. As a case study, we generate unconstrained single-objective continuous minimization problems represented as mathematical expressions designed to induce significant performance differences between a genetic algorithm (GA) and differential evolution (DE). Experimental results show that LLM-EBG successfully produces benchmark problems in which the designated target algorithm consistently outperforms the comparative algorithm in more than 80% of trials. Furthermore, exploratory landscape analysis reveals that benchmarks favoring GA are highly sensitive to variable scaling, demonstrating that the proposed framework can generate problems with distinct geometric characteristics that reflect the intrinsic search behaviors of different optimization algorithms.

We present an algorithm for computing evolutionarily stable strategies (ESSs) in symmetric perfect-recall extensive-form games of imperfect information. Our main algorithm is for two-player games, and we describe how it can be extended to multiplayer games. The algorithm is sound and computes all ESSs in nondegenerate games and a subset of them in degenerate games which contain an infinite continuum of symmetric Nash equilibria. The algorithm is anytime and can be stopped early to find one or more ESSs. We experiment on an imperfect-information cancer signaling game as well as random games to demonstrate scalability.

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 \emph{ALE Agent} for competitive programming on AtCoder Heuristic Contest, achieving a \textbf{$13.6\%$ improvement} in acceptance rate; the \emph{Mini-SWE Agent} for code optimization on SWE-Perf, with a statistically significant \textbf{10.1% performance gain}; and the \emph{CrewAI Agent} for cost and mathematical reasoning on Math Odyssey, achieving a statistically significant \textbf{$36.9\%$ reduction} in the number of tokens required for evaluation. We also evaluate the \emph{MathTales-Teacher Agent} powered by a smaller open-source model (Qwen2.5-7B) on GSM8K primary-level mathematics problems, achieving a \textbf{22% accuracy improvement} and demonstrating that ARTEMIS can optimize agents based on both commercial and local models.

Progress in computational science depends on complex numerical workflows that must faithfully encode physical laws, yet translating conceptual insight into reliable code remains a major bottleneck. Although large language models can generate isolated code fragments, they lack the structured reasoning required to design, verify, and iteratively refine complete scientific pipelines. Here we introduce ATHENA, an agentic framework explicitly designed to emulate scientific research modeled as a knowledge-driven contextual bandit process. Its core loop separates conceptual policy from numerical realization through expert-derived conceptual scaffolding, enabling principled diagnosis, reformulation, and repair of computational strategies. Across scientific computing and scientific machine learning tasks, ATHENA autonomously derives and correctly applies exact analytical solutions, constructs stable numerical solvers, diagnoses ill-posed formulations, and orchestrates hybrid symbolic-numeric workflows. Quantitatively, ATHENA matches and frequently surpasses the accuracy of expert-authored reference solutions reported in the literature on canonical benchmarks. By reframing computation as an object of agentic reasoning, our framework enables autonomous orchestration of heterogeneous algorithms across scientific domains.

We present an algorithm for computing all evolutionarily stable strategies in nondegenerate normal-form games with three or more players.

Fine-tuning large language models (LLMs) for downstream tasks is an essential stage of modern AI deployment. Reinforcement learning (RL) has emerged as the dominant fine-tuning paradigm, underpinning many state-of-the-art LLMs. In contrast, evolution strategies (ES) has largely been overlooked due to the widespread belief that it does not scale to modern model sizes. This paper overturns this assumption by demonstrating the first successful application of ES to full-parameter fine-tuning of LLMs at the billion-parameter scale, without dimensionality reduction. ES can indeed search over extremely high-dimensional parameter spaces and outperform established RL implementations across multiple axes, including improved tolerance to long-horizon and delayed rewards, robustness across diverse base LLMs, reduced susceptibility to reward hacking, and improved training stability. These findings suggest that ES is not merely a viable alternative to RL, but a fundamentally different and powerful backpropagation-free post-training paradigm that opens a new direction for LLM fine-tuning beyond current RL-based approaches.

Large language models (LLMs) are increasingly integrated with evolutionary computation to support optimization tasks. This survey primarily focuses on evolutionary optimization, i.e., optimization based on evolutionary computation. For brevity, we use the term optimization throughout to denote this scope. However, existing surveys typically examine isolated roles of LLMs and do not provide a unified view that connects optimization modeling with optimization solving. To address this gap, we systematically review recent developments through a workflow-oriented framework. First, we organize the literature into two primary stages: LLMs for optimization modeling and LLMs for optimization solving (in this survey, the terms optimization modeling and optimization solving are used as concise forms of optimization problem modeling and optimization problem solving, respectively). Second, we divide the solving stage into three paradigms according to the role of the LLM: stand-alone optimizers, low-level components embedded in optimization algorithms, and high-level managers for algorithm selection and generation. Third, we analyze representative methods, identify their technical limitations, and clarify their relationships with traditional optimization approaches. We further substantiate this taxonomy through benchmark systematization, baseline comparisons, and practitioner-oriented guidance, and we review interdisciplinary applications across the natural sciences, engineering, and machine learning. Based on the resulting analysis, we identify research directions toward dynamic, self-evolving, and agentic optimization ecosystems. An up-to-date collection of related literature is maintained at https://github.com/ishmael233/LLM4OPT.

Large Language Models have achieved remarkable performance across a large number of tasks, but face critical deployment and usage barriers due to substantial computational requirements. Model compression methods, which aim to reduce model size while preserving its capacity, are an important means to mitigate these issues. Promising approaches along these lines, such as structured pruning, typically require costly manual hyperparameter exploration or rely on local heuristics that may run the risk of ignoring better solutions. In this work we introduce GeLaCo, an evolutionary approach to LLM compression via layer collapse. Our approach supports an efficient exploration of the compression solution space via population-based search and a novel layer collapse formulation based on parametrized weight merging, with a fitness function based on similarity over residual updates and language modeling KL divergence. GeLaCo also supports both single and multi-objective evolutionary compression search, establishing the first Pareto front estimation along compression and quality axes. We evaluate GeLaCo solutions via both perplexity-based and generative evaluations over foundational and instruction-tuned models, outperforming state-of-the-art alternatives.

Online alignment of large language models (LLMs) is dominated by reinforcement learning from human feedback (RLHF) with gradient-based optimizers such as PPO or GRPO. While effective, these pipelines require backpropagation through long rollouts, gradient synchronization across devices, and careful hyperparameter tuning, all of which become increasingly costly at scale. We present ESSA (Evolutionary Strategies for Scalable Alignment), a gradient-free online alignment stage that follows supervised fine-tuning (SFT) and replaces the gradient loop with inference-only black-box search. ESSA optimizes only the singular values of low-rank adaptation (LoRA) factors after a short SFT warm-start, restricting the search to a compact, task-aligned subspace where evolutionary search is practical even for 72B-parameter models. Because the loop is inference-only, ESSA is compatible with INT4/INT8 weight quantization and reduces inter-GPU communication to a few bytes per iteration. Across instruction following (IFEval), preference-based assistant tuning (HelpSteer2, HH-RLHF), and mathematical reasoning (GSM8K, MATH500), ESSA matches or exceeds LoRA-GRPO in the reported LoRA comparisons; on GSM8K it also outperforms Online DPO and PPO, while remaining competitive with both methods on IFEval. At scale, ESSA reaches a fixed MATH500 accuracy on Qwen2.5-32B/PRM800K up to 7.8x faster than LoRA-GRPO on 128 GPUs.

Consensus-based optimization (CBO) has established itself as an efficient gradient-free optimization scheme, with attractive mathematical properties, such as mean-field convergence results for non-convex loss functions. In this work, we study CBO in the context of closed-box adversarial attacks, which are imperceptible input perturbations that aim to fool a classifier, without accessing its gradient. Our contribution is to establish a connection between the so-called consensus hopping as introduced by Riedl et al. and natural evolution strategies (NES) commonly applied in the context of adversarial attacks and to rigorously relate both methods to gradient-based optimization schemes. Beyond that, we provide a comprehensive experimental study that shows that despite the conceptual similarities, CBO can outperform NES and other evolutionary strategies in certain scenarios.

Multi-task optimization is typically characterized by a fixed and finite set of tasks. The present paper relaxes this condition by considering a non-fixed and potentially infinite set of optimization tasks defined in a parameterized, continuous and bounded task space. We refer to this unique problem setting as parametric multi-task optimization (PMTO). Assuming the bounds of the task parameters to be ($\boldsymbolθ_l$, $\boldsymbolθ_u$), a novel ($\boldsymbolθ_l$, $\boldsymbolθ_u$)-PMTO algorithm is crafted to operate in two complementary modes. In an offline optimization mode, a joint search over solution and task spaces is carried out with the creation of two approximation models: (1) for mapping points in a unified solution space to the objective spaces of all tasks, which provably accelerates convergence by acting as a conduit for inter-task knowledge transfers, and (2) for probabilistically mapping tasks to their corresponding solutions, which facilitates evolutionary exploration of under-explored regions of the task space. In the online mode, the derived models enable direct optimization of any task within the bounds without the need to search from scratch. This outcome is validated on both synthetic test problems and practical case studies, with the significant real-world applicability of PMTO shown towards fast reconfiguration of robot controllers under changing task conditions. The potential of PMTO to vastly speedup the search for solutions to minimax optimization problems is also demonstrated through an example in robust engineering design.

Molecular optimization, the process of designing molecules with desirable properties, represents a critical challenge in drug discovery. The recent advancements in large language models (LLMs) have opened new opportunities for their integration with traditional molecular optimization algorithms to improve performance. In this work, we propose Molecular Language Model powered Evolutionary Algorithm (Mol-E), an evolutionary algorithm that relies on the generative capabilities of LLMs trained on molecules and molecular properties. Scientific Contribution. Mol-E obtains the highest aggregate Top-10 AUC among the comparable full-23-task results considered here, scoring 17.500 in the task-agnostic regime, in which the oracle is treated strictly as a black box, and 20.551 in the task-informed regime, in which the optimizer receives a fixed semantic description of the objective. Mol-E also improves over the evaluated baselines on multi-property optimization with docking against DRD2, MK2, and AChE.

Neuroevolution of Augmenting Topologies (NEAT) and its advanced version, Evolvable-Substrate HyperNEAT (ES-HyperNEAT), have shown great potential in developing neural networks. However, their effectiveness heavily depends on the selection of hyperparameters. This study investigates the optimization of ES-HyperNEAT hyperparameters using the Tree-structured Parzen Estimator (TPE) on the MNIST classification task, exploring a search space of over 3 billion potential combinations. TPE effectively navigates this vast space, significantly outperforming random search in terms of mean, median, and best accuracy. During the validation process, the best hyperparameter configuration found by TPE achieves an accuracy of 29.00% on MNIST, surpassing previous studies while using a smaller population size and fewer generations. The transferability of the optimized hyperparameters is explored in logic operations and Fashion-MNIST tasks, revealing successful transfer to the more complex Fashion-MNIST problem but limited to simpler logic operations. This study emphasizes a method to unlock the full potential of neuroevolutionary algorithms and provides insights into the hyperparameters' transferability across tasks of varying complexity.