Evolutionary Search

LLM-driven evolutionary search finds programs by launching seeds and iterating each one. Papers report a single budget setting, usually one seed run for a fixed number of iterations, and rank methods from that one point. We show this is not enough. We evaluate three evolutionary search strategies on five optimization tasks, commonly used by papers in the genre to report results. We run the analysis over a full grid of seeds and iterations. Our findings suggest that the best way to split a fixed budget between more seeds (width) and more iterations (depth) changes with the strategy, the task, and the total budget. Furthermore, we observe that the ranking of strategies also changes with the budget. On one task the strategy that looks worst at one seed is best at forty seeds. On another the best number of iterations is well below the value common in practice, so extra depth wastes budget that more seeds would turn into score. We provide a measurement protocol that reports the seeds-by-iterations frontier and practical guidance for using it.

Surrogate-assisted evolutionary algorithms (SAEAs) are effective methods for solving expensive optimization problems (EOPs), where surrogate models replace most expensive evaluations and critically influence the final optimization results. In recent years, tabular foundation models have advanced rapidly, and the Tabular Prior-data Fitted Network (TabPFN) has been adopted as a surrogate model for EOPs due to its strong predictive capability, demonstrating promising performance. Motivated by its potential as a surrogate model in SAEAs, this work conducts a comprehensive study that combines extensive experiments with in-depth theoretical analysis to investigate the effectiveness of TabPFN. Specifically, we perform experiments across both offline and online SAEA settings, covering diverse problem scenarios such as single-objective, multi-objective, constrained, combinatorial, mixed-variable, and engineering optimization problems. In addition, we further analyze the advantages and limitations of TabPFN within SAEAs and provide practical guidelines for its application in different optimization settings. Results show that the effectiveness of TabPFN is highly problem dependent, and it cannot replace conventional surrogates universally. Overall, TabPFN should be adopted selectively according to data availability, landscape complexity, search space characteristics, and its role within the algorithm. Customized model management strategies and role-specific algorithm design are necessary to fully exploit its advantages and avoid its pitfalls.

Indirectly encoded neural networks can assign different activation functions to individual nodes, but the right functions are rarely known in advance. When the available set contains only standard monotonic functions, problems like parity become unsolvable, yet an all-inclusive palette underperforms a curated one. How should evolution discover which functions to use? We address this as a meta-learning problem, designing 13 strategies (11 inspired by biological adaptation mechanisms, plus baseline and oracle controls) that modify the set of available activation functions during evolution. Each strategy translates a biological principle into an evolutionary operator: for example, circadian-inspired oscillatory gating cycles functions in and out of the palette on a fixed schedule, while immune-inspired Clonal Selection permanently protects functions that consistently correlate with fitness. We evaluate all strategies across more than 3,000 runs on parity and non-parity problems, first evolving the activation palette alone, then co-evolving a per-node aggregation palette on harder problems; an independent replication with new seeds confirms a stable high-reliability tier, with Circadian holding its top rank. Bio-inspired strategies match the solve rate of a tuned baseline but converge up to twice as fast, with Circadian halving total compute. Strategy rankings reverse across problem types, with no strategy dominating all domains. Strategy success is largely shaped by timescale compatibility: strategies whose characteristic timescale matches the evolutionary evaluation window consistently outperform those that operate too slowly. The practical guideline: match the mechanism's timescale to the evaluation budget. Rescaling the slowest strategy bypasses the oscillatory barrier entirely: all nine solutions solve parity with non-oscillatory activations paired with min or max aggregation.

This paper presents a novel approach to hexapod locomotion by evolving each leg's gait independently through a decentralized evolutionary algorithm. Using the Webots simulator and the Mantis hexapod robot, we optimize individual leg controllers without centralized coordination, allowing emergent behaviors to drive the development of efficient, coordinated locomotion. Our decentralized method is benchmarked against cooperative coevolution, demonstrating improved efficacy in generating stable and adaptive gaits while showing interesting emergent coordination. By enabling independent evolution of leg controllers, this method reduces the complexity of gait optimization and highlights the potential of decentralized strategies for scalable and adaptive robotic systems.

The Core is a unique competitive co-evolution algorithm that allows agents to evolve autonomous control without utilizing a traditional fitness function. The agents evolve via local interactions through tournament selection, crossover, and mutation, producing offspring by evolving better controllers. Previous works have shown The Core's ability to evolve agents capable of combat and navigation in the Xpilot video game. This research expands upon that premise by niching agents to specific subsets of the original environment The Core was tested in. Our results demonstrate the niched agents capacity for success over agents niched to the entire system and agents niched to different sub-environments.

EGGROLL makes evolution strategies (ES) practical for LLMs by replacing dense Gaussian weight perturbations with low-rank Gaussian products, often of rank one. This choice is computationally attractive but geometrically severe: each rank-one perturbation lies in a zero-volume subset of the ambient matrix space, despite having identity covariance. We characterize the mean EGGROLL update field at finite rank and nonzero perturbation radii, then analyze the error of its finite-population estimator. The population field is obtained by applying an explicit resolvent to the gradient of the objective smoothed by the perturbations. We show that the resolvent can introduce a nonconservative component and can reverse the local stability of an optimum. EGGROLL is nevertheless exact on every quadratic objective at every rank and radius. For smooth objectives, its first local finite-rank correction is $O(\sigma^2/r)$, and nonasymptotic bounds control the resulting field error under smoothness assumptions. Under a local affine model, rank-one perturbations increase the variance of the gradient estimator by only $\frac{2(m+n+1)}{mn+1}$ relative to dense Gaussian ES, or $0.098\%$ for a $4096\times4096$ matrix. We then introduce LOO-ROLL, a leave-one-out estimator that preserves the finite-rank population field while replacing EGGROLL's two antithetic evaluations per direction by one. At equal evaluation cost, LOO-ROLL halves estimator MSE in transformer blocks. At matched wall time across ten post-training settings and models up to 8B parameters, LOO-ROLL improves seven outcomes in individual paired tests, with no significant loss. On the GSM8K test set, accuracy increases from $38.1\%$ to $63.0\%$ at 0.6B and from $65.9\%$ to $80.0\%$ at 8B. Transformer measurements recover the predicted finite-rank variance, while the rank comparisons show no reproducible reward-based advantage for rank eight.

Evolvable-Substrate HyperNEAT (ES-HyperNEAT), a bio-inspired indirect encoding that determines neuron placement and connection weights from spatial coordinates, exhibits a failure mode on MNIST as a diagnostic benchmark. Because input pixels map to a coordinate space centered at the origin, evolved networks converge on a small central cluster of input pixels, a spatial-concentration bias; prior work observed only 21% mean accuracy in this regime. Is this bias an optimization artifact or an architectural ceiling? Inspired by Mixture-of-Experts (MoE) principles, we partition the input into non-overlapping spatial segments, each assigned to a separately evolved specialist network. With 13 such experts, this design reaches 43% mean accuracy, a 106% relative improvement over the baseline. The architectural gain does not depend on data-driven aggregation: equal-weighted averaging, which uses no validation data, already yields a 70% improvement; the gain comes from partitioning, not the weighting. Receptive-field analysis shows the mechanism: partitioning forces evolution to discover features across the entire image, expanding active pixel coverage from 4% to 79%. Absolute accuracy stays below gradient-trained baselines, but the relative gain points to central bias, not the evolutionary search. Two tools are designed to generalize beyond MNIST: a receptive-field diagnostic for silent input-coverage collapse, and a spatial-partitioning remedy that restores coverage.

This paper introduces an evolutionary computation approach for consensus in structural Bayesian Network (BN) fusion under the constraint of limited treewidth. The consensus BN aims to reconcile multiple input BNs into a single one that retains key structural features present in the original networks. Treewidth, a graph-based parameter associated with computationally tractable inference, is utilized to restrict the complexity of the resulting network. A genetic algorithm is proposed to look for a BN that codifies as much information about the unrestricted fusion as possible while ensuring the treewidth restriction. Experimental evaluation demonstrates the genetic algorithm's ability to obtain consensus BNs with limited treewidth, providing a valuable tool for aggregating information from diverse sources while returning a computationally actionable model.

Language model agents increasingly propose actions, observe external feedback, and explain their own behavior. Their confidence and rationales are convenient monitoring signals, but convenience is not verification. We introduce an environment-grounded audit in which every intermediate proposal receives an exact outcome. A language model operates an evolutionary Contexto search whose feedback function assigns every valid guess an exact rank without human annotation. Across 200 runs spanning five configurations and three model families, four reporting configurations produce 12,249 self-reports. We test three assumptions: stated confidence is calibrated, inherited rationales affect later proposals, and fitness-based selection improves report quality. All three fail. Operators overstate top-100 success by factors of 4.8 to 9.3, while calibration and discrimination dissociate across model families. Controlled interventions on 754 inherited rationales bound any measured benefit of the genuine rationale to roughly 250 ranks. Neither fitness-based nor random selection produces a detectable selection differential or parent-to-offspring transmission in report accuracy, despite sharply different search behavior. Agent self-reports should therefore be treated as claims to verify against the environment, not as evidence of their own reliability.

We provide an expository introduction on the importance of higher-arity tensor operations to deep learning. Then, we conduct a novel empirical investigation of higher-arity phenomenon in trained neural networks, introduce a hypergraphical generalization of the multilayer perceptron, and explore connections to evolutionary algorithms. We conclude with a discussion of promising directions for future research.

Large language models are increasingly required to generate responses that satisfy multiple competing objectives. Since optimal trade-offs depend on both user preferences and input prompts, controllable multi-objective generation must dynamically adapt models at inference time without retraining. To address this, we propose Evolutionary Soups, a mixture-of-experts framework for fine-grained generation control, with gating networks trained via an evolutionary algorithm. The per-layer gating networks dynamically produce expert-merging coefficients from hidden-state representations, while the evolutionary algorithm incorporates greedy hypervolume contribution for effective evolution of these gating networks, achieving consistent improvements on large and noisy training datasets and broader coverage of the non-convex Pareto front. Experiments across three tasks demonstrate the effectiveness of Evolutionary Soups over baselines: it achieves the best hypervolume, linear utility, and Tchebyshev utility (~20% improvement) among controllable methods on all tasks.

In evolutionary search, a weak child can be a valuable ancestor that makes high-fitness regions reachable. Immediate-return control is blind to this delayed utility, penalizing mutations through their immediate offspring even when they open productive future lineages. We formalize this hidden dynamic as the time value of evolution within a finite-horizon Markov decision process. To exploit it, we introduce Lineage-Value Policy Gradients (LVPG), a long-horizon actor-critic framework for automated trading policy discovery. Our architecture decouples search control into specialized policy heads over a shared generative backbone: a bootstrapped critic head estimates the value of finite-horizon lineage potential from multi-step mutation trees, while an actor head dynamically modulates mutation intensity over the remaining search budget. We isolate the impact of long-horizon credit assignment against immediate-return optimization across 90 paired runs under matched operators, lineage supervision, folds, seeds, and budgets. Path-based credit assignment substantially accelerates finite-budget search, increasing validation best-so-far AUC by 0.394 Sharpe units. LVPG also produces fewer temporary regressions than immediate-return optimization and recovers from them more often. Finite-horizon lineage value yields more selective non-monotonic search and stronger policies within identical resource constraints.

Large Language Models (LLMs) are increasingly deployed in discovery domains such as math and science. The usual approach is to present the problem to the model and use its answer as the proposed solution. However, beyond this best guess, discovery can be enhanced by increasing test-time compute. In a process called pass@k, the model is allowed to explore the solution space and generate diverse candidate solutions. Unfortunately, the standard approach to post-training LLMs through Reinforcement Learning (RL) may limit pass@k: the model's output distribution narrows around high-reward outputs, causing the solution coverage to collapse. The alternative is to use Evolution Strategies (ES), a population-based, gradient-free post-training method that optimizes directly in weight space through random perturbations. As this paper shows, ES achieves consistently higher pass@k than RL and produces a broader output distribution with greater solution coverage. This coverage in turn makes it possible to achieve better results in e.g. standard math benchmarks. Thus, ES provides a better foundation for post-training in discovery problems and other domains where diverse solution coverage is critical.

Autonomous agent teams deployed in settings such as marine and extraterrestrial outposts must coordinate actions to achieve optimal outcomes across multiple competing objectives. Multi-objective evolutionary algorithms such as NSGA-II optimize for diversity in the objective space, but neglect diversity in the behavior space, possibly leading to premature convergence and a collapse in behaviors that may differentiate policies in different external conditions. To address this, we introduce an entropy-augmented policy evaluation strategy that incorporates an entropy bonus into agent fitness scores, discouraging behavioral homogeneity across the evolving population. By augmenting policy evaluation with a behavior-space diversity signal while preserving the underlying Pareto optimization framework, our method is designed to encourage exploration of behaviorally distinct policies in multiagent domains. We evaluate our approach across rover-domain experiments with qualitatively distinct reward structures and observe hypervolume improvements of up to 48% relative to the NSGA-II baseline, suggesting that behavioral diversity is a promising and underexplored direction for improving multi-objective multiagent evolutionary optimization.

Successful mutation strategies in evolutionary code search may contain reusable knowledge that is useful beyond a single run, and in some cases may transfer across related tasks and domains. However, existing LLM-driven evolutionary frameworks largely discard such knowledge, repeatedly rediscovering similar ideas and limiting opportunities for cross-run and cross-task learning. We introduce EvoMem, a persistent memory architecture for LLM-based evolutionary program search that captures and reuses candidate mutation knowledge. EvoMem converts successful mutation events into structured, task-aware advice for future runs. It operates in two phases: after each run, it extracts and stores promising ideas with provenance, and during subsequent evolution, it retrieves a small set of relevant instructions based on the current task and program context to guide mutation. Across geometric optimization, multi-hop question answering, GPU kernel optimization, and related benchmarks, our experiments show positive average improvements in target metrics or search speed for most evaluated settings, while also revealing variability across tasks. Overall, EvoMem provides evidence that persistent memory can reduce some redundant exploration and improve the reuse and adaptation of successful strategies in LLM-driven evolutionary search.

Evolutionary optimization of LLM prompts and agentic programs (e.g., GEPA) is dominated by fitness evaluation: scoring each candidate runs an answering LLM over a validation set, so the evaluator's price tier dictates total search cost. We restructure that search by decoupling the three roles an LLM plays, running the high-volume answering role on the cheapest tier, reserving a strong model for the rare reflection/variation operator, then exploiting upward cross-tier transfer to deploy the cheaply evolved prompt on a stronger target. We contribute a cost-controlled characterization of when cheap-tier search substitutes for target-tier search, and where it fails. Across four tasks (HotpotQA, IFBench, LiveBench-Math, HoVer) and eleven models in four model families, the resulting prompt matches or exceeds same-tier optimization while placing over 96% of search tokens on the cheapest tier, at 5.6-14x lower search cost, rising to 25-54x where reasoning tiers emit long chains of thought on every fitness call.

In this work, we introduce analytical replay experiments to the evolutionary computing community. Replay experiments originated in the context of laboratory experimental evolution as an empirical approach to identifying potentiating events that increased the likelihood of an observed evolutionary outcome. By restarting a population's evolution from different historical time points, replay experiments sample the distribution of what could have evolved from different points in time, which allows us to quantify how a population's potential for different evolutionary outcomes changed as a result of that population's history. In this work, we give a step-by-step guide to designing replay experiments for evolutionary computing systems. We then provide a demonstrative example replay experiment that measures how potentiation for problem-solving success changed in an evolved genetic programming population, showing that increases in potential for success do not necessarily correspond with increases in a population's fitness. Broadly, we argue that analytical replay experiments can be a powerful tool for expanding the theoretical foundations of evolutionary computing, and we offer suggestions for promising future research directions enabled by replay experiments.

Large Language Model (LLM)-based automated algorithm design typically evolves algorithms as complete, indivisible programs. While this whole-program perspective simplifies the search space, it fundamentally couples the useful local logic to its host program. Consequently, valuable code snippets vanish when the overall program is discarded, making it highly difficult to assess the contribution of individual algorithmic components.To address this, we propose Primitive-Aware Code Evolution (PACE), which decouples local logic from complete programs by representing it as persistent units called Executable Algorithmic Primitives (EAPs). To enable code-level transfer, PACE maintains a dynamic set of EAPs. Algorithm evolution is driven by primitive-aware operators that structurally guarantee the retention and cross-program transfer of these components. To evaluate them effectively, PACE leverages Thompson sampling based on parent-relative performance improvements, guiding primitive selection from the set without requiring extra evaluation datasets. Experiments on four tasks demonstrate that PACE effectively discovers competitive algorithms while structurally preserving valuable algorithmic components.

Training controllers that are safe and robust in simulation, and systematically assessing their readiness for real-world deployment, remain key challenges in sim-to-real transfer. To address this, we propose LyEvO, a physics-grounded framework that combines constrained Evolutionary Optimization and Statistical Model Checking (SMC)-based verification with Lyapunov-based stability analysis. Leveraging prior knowledge of the system dynamics, LyEvO uses Lyapunov analysis to compute an initial candidate stability region. An iterative loop then uses operational scenarios drawn from this region to jointly optimize and statistically verify a policy, and subsequently expands the region's boundaries based on the verification outcome. This integrated procedure provides a practical criterion for assessing deployment readiness. We evaluate LyEvO on Cartpole and 3D Quadrotor benchmarks through extensive simulations and targeted real-world experiments, demonstrating safe and robust sim-to-real transfer.

Microarchitecture design space exploration suffers from expansive search spaces and expensive PPA evaluation, leaving only a small simulation budget for design decision-making. Existing methods perform blind search without considering microarchitectural dependencies and fail to learn from the iterative search effectively, leading to wasted evaluations and weak Pareto convergence. In this paper, we propose MicroEvo, a knowledge-guided framework that couples off-the-shelf LLMs with Monte Carlo Tree Search (MCTS) for multi-objective microarchitecture optimization. MicroEvo combines LLM-driven evolutionary operators, a Pareto-aware tree policy that balances Pareto contribution and diversity, an active knowledge accumulation mechanism that extracts and reuses optimization insights, and state-aware directives that adapt the search behavior online. Experiments show that MicroEvo improves Pareto-front quality by up to 36.2% over NSGA-II and achieves 10.6x higher search efficiency, and also demonstrates strong scalability to a complex industrial-scale core. The code repository is available at: https://github.com/GEAR-SEU/MicroEvo-ICCAD-26.

To address the issue that existing dynamic multi-objective optimization algorithms mainly rely on individual migration or independent special point sampling after environmental changes, while failing to fully exploit the structural relationships among representative solutions, a Special Point Skeleton Reconstruction based Dynamic Multi-Objective Evolutionary Algorithm (SPSR-DMOEA) is proposed. First, the centroid, knee points, and extreme points are extracted from the Pareto optimal solution set of the current environment, and their positions in the new environment are adaptively predicted according to their movement velocities across consecutive environments. Subsequently, in the decision space, the centroid is connected with other anchor points, and a minimum spanning tree is constructed among the non-centroid anchor points, thereby establishing a prediction skeleton capable of describing the overall population structure. According to the lengths of the skeleton edges, the number of individuals allocated to each edge is determined proportionally. Candidate solutions are uniformly generated along each edge, and random orthogonal perturbations are introduced to expand the search region around the skeleton. Experimental results on the DF dynamic multi-objective benchmark suite demonstrate the effectiveness of the proposed method in dynamic tracking capability.

Evolution Strategy (ES) is a promising alternative to gradient-based fine-tuning for resource-constrained Large Language Model (LLM) reasoning. However, directly applying ES to billion-parameter LLMs is highly ineffective. In such high-dimensional parameter spaces, most random perturbations are nearly orthogonal to useful update directions, leading to unstable optimization. We propose Hyper-ES, a subspace-based ES framework that avoids the weakness of ES in full-parameter search while exploiting its strength in low-dimensional optimization. Instead of asking ES to discover useful directions from random perturbations in the LLM parameter space, Hyper-ES first performs a small number of inexpensive gradient-based fine-tuning runs to obtain descent directions. Although each direction may provide only a limited improvement on its own, their span forms a compact adaptation subspace that captures useful reasoning updates. Hyper-ES then applies CMA-ES to optimize layer-wise DARE-TIES merging coefficients within this subspace, allowing ES to search over combinations of meaningful descent directions rather than over arbitrary full-model perturbations. We evaluate Hyper-ES on three Qwen2.5-Instruct and DeepSeek-R1-Distill backbones across six mathematical reasoning datasets. Results show that Hyper-ES consistently outperforms GRPO-LoRA by 1% while requiring 10% fewer space-consuming gradient updates. Code at https://github.com/kuangrepi/Hyper-ES.

Large Language Model-assisted Evolutionary Search (LES) has emerged as a powerful paradigm for automated algorithm design. However, existing LES methods primarily optimize for average performance, inherently directing search effort toward instances that contribute most to this metric while leaving others poorly served, resulting in weak tail robustness and limited real-world reliability. To address this limitation, we propose Dynamic Instance Clustering and Specialized Algorithm Design (DyCA), an LES framework with a feature-free, structure-aware mechanism for constructing reliable algorithm portfolios under heterogeneous instance distributions. DyCA treats instance clustering as a co-evolving component within the search process, reusing accumulated evaluation data as feature-free signals to progressively partition instances with similar algorithmic response patterns. The uncovered clusters decompose the mixed objective into a set of structure-aware sub-objectives, thereby enabling finer-grained and more adaptive guidance for specialized algorithm design. Experimental results across four algorithm design tasks with heterogeneous instances demonstrate that DyCA outperforms state-of-the-art LES baselines, improving tail robustness by an average of 15.2% and overall performance by 7.1% while maintaining competitive head performance.

Tool-using large language model (LLM) agents produce long, multi-turn trajectories, making gradient-based post-training memory-intensive. Evolution strategies (ES) enable memory-efficient full-parameter post-training without backpropagation and can eventually match the performance of gradient-based reinforcement learning (RL). However, resource-constrained settings typically offer only a few GPUs, so the high GPU-hour requirements of ES translate into prohibitively long training times. To address this, we introduce Cooperative Parameter-subspace Evolution Strategy (CoPES), a cooperative coevolutionary method that decomposes the full parameter space into lower-dimensional subspaces and searches over them cooperatively to improve optimization efficiency. We post-train a Qwen3.5-4B tool-using agent for the math task and evaluate it on five benchmarks of varying difficulty. Under the GPU-hour budget of full-parameter GRPO's best validation checkpoint, CoPES recovers 92% of GRPO's validation-accuracy gain, versus 67% for standard ES, while its theoretical GPU memory requirement is less than one-eighth that of full-parameter GRPO. It consistently outperforms standard ES and LoRA-based GRPO on all evaluated pass@k metrics across the five benchmarks. Additional experiments further show the advantage of CoPES on the question-answering task. These results demonstrate an improved trade-off between memory requirements and training time for agentic LLM post-training under resource constraints. The code is open-sourced in https://github.com/MetaronWang/CoPES

We investigate Optimization under Input Uncertainty (OIU), in which the input to the objective function, rather than the objective function itself, is subject to uncertainty. OIU appears in manufacturing processes with production tolerance, control of physical systems with actuation noise, Mixture of Experts, and Reinforcement Learning (RL). Most of the existing approaches solve OIU by using the value of the objective function but discard the information of the realized input, even though the realized input is observable in various applications. The question here is whether the discarded information of the realized input is useful to accelerate the optimization process. We affirmatively answer this question for Evolutionary Strategy (ES) by theoretically showing that the information of the realized input can reduce the variance of the gradient estimator via Rao-Blackwellization. Using the Rao-Blackwellized gradient estimator, we propose Phenotype-Accelerated Evolutionary Strategy (PAES), which is a refinement of ES for OIU. Numerical experiments show that PAES converges faster than the usual ES from simple continuous optimization problems to RL benchmarks.

Automated formulaic alpha discovery aims to generate predictive and interpretable trading signals from large symbolic factor spaces. Its effectiveness is constrained by noisy fitness estimates, market nonstationarity, costly backtesting, semantic redundancy, and conflicting practical objectives. Existing studies employ diverse techniques, including genetic programming (GP), evolutionary algorithms (EAs), reinforcement learning (RL), generative flow networks (GFlowNets), Monte Carlo tree search (MCTS), large language models (LLMs), and agentic workflows, but generally examine them as separate algorithmic families. This article introduces, for the first time, a unified evolutionary computation (EC) perspective on automated formulaic alpha discovery, formulating it as a noisy, dynamic, and multiobjective symbolic evolutionary optimization problem. A six-component analytical framework is developed to characterize existing methods through representation, variation, fitness evaluation, selection, memory, and adaptation. Furthermore, an eight-dimensional, autonomy-oriented evaluation framework is proposed, covering search efficiency, fitness reliability, residual alpha quality, economic diversity, tradability, evolutionary autonomy, robustness to nonstationarity, and reproducibility. Together, these frameworks provide a systematic foundation for unifying heterogeneous approaches, diagnosing component-level limitations, and guiding the development of reliable, adaptive, interpretable, and reproducible autonomous alpha discovery systems.

An ensemble of surrogate models helps improve the prediction quality and robustness of surrogate models, and in turn, the search performance of surrogate-assisted evolutionary algorithms (SAEAs). Although different degrees of smoothness of the approximated fitness landscapes need to be carefully designed for an effective ensemble, little attention has been paid to the explicit tuning of the degree of smoothness derived by surrogate models. This study proposes an adaptive ensemble SAEA, which automatically constructs plausible ensemble models by optimizing their parameter settings. Unlike existing adaptive/ensemble SAEAs, which consider prediction accuracy alone, the proposed algorithm optimizes the structure of radial basis function networks (RBFNs) by solving bi-objective minimization problems of approximation error and model complexity, resulting in robust ensemble models of accurate surrogate models with different degrees of smoothness of the approximated fitness landscapes. As a result, the over/under-fittings are reduced. Additionally, an infill criterion is designed so that surrogate models with different degrees of smoothness can contribute to the solution prescreening. The experimental results demonstrated the statistical superiority of our algorithm over state-of-the-art SAEAs on a single-objective benchmark and real-world problem sets under an expensive optimization scenario. The source code of the proposed algorithm is available at https://github.com/haranychan/EPOS

Recursive self-improvement (RSI) requires AI systems that improve the process of building AI (i.e., AI4AI); machine learning engineering (MLE) offers a concrete, executable testbed for studying this capability. We introduce OpenMLE, an open full-stack system for RSI research in MLE, spanning verifiable task environments with execution feedback (OpenMLE-Gym), operator learning (OpenMLE-RL), and long-horizon search (OpenMLE-Evo). On this stack we post-train Frontis-MA1 (35B) as a meta-evolution agent for MLE, aligning post-training and inference around four atomic program-evolution operators (Draft, Improve, Debug, Crossover): the same operators are trained via execution-grounded SFT and RL on data deduplicated against all evaluation benchmarks, then composed into long-horizon search, coupling learning and evolution in a single loop. On MLE-Bench Lite under a 12-hour per-task budget on one RTX 4090 capped at 12 GB VRAM, Frontis-MA1 (35B) improves Medal Average from 39.39% to 60.61% over its base model with OpenMLE-Evo, and reaches 71.21% with OpenMLE-Evo-Max (benchmark-independent experience priors and asynchronous search), exceeding GPT-5.5 + Codex and approaching GPT-5.6 Sol and the 2.8T Kimi K3. On held-out NatureBench Lite, both components transfer: with the framework fixed, swapping in the trained model raises Match-SOTA from 50% to 70%; with the model fixed, swapping in OpenMLE-Evo raises it from 20% to 50%. We release the model weights and the full OpenMLE stack to enable reproducible research on executable AI4AI toward RSI. Code: https://github.com/FrontisAI/OpenRSI

Combinatorial problems appear in numerous industrial applications. A common approach is to formulate these problems as declarative constraint models that can subsequently be compiled to and solved by a range of back-end solvers. Recent work shows that Large Language Models (LLMs) can produce correct models from natural language, but even a correct model can be expensive to solve because performance remains sensitive to modelling choices. In this work, we investigate whether LLMs can automate performance-oriented model reformulation. Inspired by Automatic Heuristic Design (AHD), we use an evolutionary framework in which an LLM proposes candidate reformulations that are verified and benchmarked against the user-defined baseline model. We compare AHD-adapted search strategies that control which prior attempts, instructions, and measured feedback enter each prompt. Existing retention strategies prioritize recency or performance, but do not explicitly diversify the context. To cover this gap, we introduce Profile-Diverse Retention (PDR), which applies Maximal Marginal Relevance (MMR) to instance-level runtime vectors to retain behaviourally diverse attempts. We systematically evaluate the strategies on eight CSPLib problems using validation-based final model selection. The results show that: (i) iterative reformulation can produce substantial held-out speedups; (ii) strategies that keep the retained context diverse outperform those that retain only recent or the fastest attempts; and (iii) validation-based selection improves the held-out speedup of every strategy.

Artificial life systems are typically defined by a set of dynamical rules over an environment, an agent, or both, from which lifelike patterns may emerge. Gifbreeder is an animated version of the interactive evolutionary computation (IEC) platform Picbreeder, and was initially created to generate visual art. Instead of encoding the agent or the environment, Gifbreeder genomes encode a spatiotemporal field and evolve through the user's aesthetic selection. The evolved expressions can sometimes resemble motile lifelike creatures that we term Limbomorphs, given that they exist in a deterministic three-second looping "limbo". We assess their behavior via input-space perturbations and find species-specific reactions to different kinds of perturbations. We discuss whether these reactions may reflect goal-directed behavior like navigation, or merely the appearance of it, and more broadly how agent-like dynamics may emerge in a system with no explicitly defined agent, environment, or interaction rules.

This paper investigates the role of dynamic population sizes in evolutionary multi-objective optimization. Although such approaches are widely used in practice, their benefits remain poorly understood, and rigorous runtime analyses explaining when and why they help are still scarce. To address this, we introduce the bi-objective problem class CLIMB and analyze the runtime of GSEMO and the widely used NSGA-II on this problem. Our results show that allowing a dynamic population size for NSGA-II can lead to a moderate improvement, yielding a speedup of order $Ω(\sqrt{n}/\log n)$. In particular, we prove that GSEMO and NSGA-II-DYN, a version of NSGA-II with dynamic population sizes we propose in this paper, can find the Pareto front of CLIMB in expected $O(n \log n)$ fitness evaluations, whereas NSGA-II with a fixed population size requires $Ω(n^{1.5})$ fitness evaluations in expectation. To the best of our knowledge, this is the first rigorous runtime analysis in multi-objective optimization demonstrating a super-constant speedup of GSEMO over NSGA-II. Our analysis builds on concepts from single-objective optimization, like the evolution of population diversity over time, and employs the well-known family-three method to prove the lower bound.

Long-horizon embodied tasks require policies that execute many dependent actions before task success can be observed. Representing policies as executable control pro- grams (code-as-policy) enables their decision logic to be inspected and revised after rollout evaluation. Revised programs can then be executed and compared by rollout performance, framing policy improvement as execution-guided program search. Evo- lutionary methods driven by large language models (LLMs) provide a natural mecha- nism for this search by generating variants and selecting high-performing candidates. However, existing approaches primarily select among independently generated vari- ants and lack a sequential local improvement phase. We introduce MEMENTO, a memory-guided single-elite memetic framework for code-as-policy evolution. ME- MENTO first evolves a rollout evaluator that maps policy rollouts to scalar fitness and structured feedback metrics. Fitness selects accepted candidates and the next elite, while feedback metrics condition policy proposals generated by memory-guided hill-climbing, macro-mutation, and crossover. We evaluate MEMENTO on two long- horizon embodied domains: Robosuite Franka Tower-of-Hanoi manipulation and AI2- THOR household interaction. MEMENTO outperforms Eureka and REvolve, adapted as code-as-policy evolutionary baselines, in task success and generalization to held- out Robosuite object configurations and unseen AI2-THOR scenes. Ablations show that zero-shot generation and unevolved evaluators fail to solve either domain, and that removing policy-search branches reduces performance. Finally, we deploy the best-evolved Robosuite policy on a physical Franka robot, demonstrating the feasibil- ity of sim-to-real transfer of the evolved code-as-policy. Code, prompts, and videos are available at: https://github.com/sygkounas/MEMENTO.

Closed-loop generative selection has become a workhorse of computational drug discovery: a learned generative model proposes candidate molecules, a fitness oracle scores them, the best are kept, and the model is retrained on this elite set before the next round. Despite its wide use, the method has lacked a rigorous convergence theory, largely because retraining the model each round breaks the Markov property on which classical evolutionary-algorithm analysis relies. We develop a self-contained theory of convergence and expected running time for this class of algorithms. By recovering a Markov structure on an enlarged state space, we show that elitism makes the search absorbing, and we prove almost-sure convergence together with a runtime bound that decomposes the search into the time spent escaping each fitness level. We then analyse the role of the model's memory---how much of the past it is trained on. When learning improves steadily with more data, deeper memory never hurts; when it does not, an exit-time analysis pinpoints the optimal memory depth and shows that excess memory can actually slow convergence. The theory extends to multi-objective search and to noisy oracles: we quantify how many repeated evaluations certify progress under light-tailed noise, and how robust estimators restore guarantees under heavy tails. Recast in terms of oracle evaluations - the true bottleneck in drug design - the analysis yields a concrete, evaluation-minimal strategy. Areproducible study confirms the predictions, including the surprising cost of excess memory. We close with three open problems.

Autonomous discovery systems such as OpenEvolve and TTT-Discover are often used as general-purpose harnesses. However, in practice these are composite systems combining several design choices about archives, parent selection, exploration, and budget allocation into a single recipe. Because discovery runs are expensive and inherently stochastic, existing harnesses are often compared using too few independent trials to distinguish key methodological improvements from run-to-run variance. We systematically decompose OpenEvolve-style evolutionary search and the TTT-Discover search harness into its constituent components and systematically evaluate 30 budget-matched harnesses across 12 model-problem pairs using more than 3.1 million LLM rollouts and repeated-trial statistical analysis. Our results show that discovery harnesses have a generalization problem: No fixed harness is reliably superior across the evaluated model-problem pairs, and variants of OpenEvolve generally underperform simpler alternatives. Thus, harness choice is better viewed as a hyperparameter rather than as a universal recipe, and should be tailored to the specific problem and underlying model. We also find that early discovery progress predicts final performance, and use this property to present a budget-matched adaptive-allocation experiment that starts multiple harnesses, prunes weak partial runs, and reallocates compute to stronger survivors, outperforming both commitment to a randomly sampled fixed harness and a non-adaptive harness ensemble. Together, these results motivate shifting from fixed harness selection to online adaptation guided by early performance. We release all run pools including baseline null distributions for every model-problem pair as reusable statistical infrastructure against for future harness proposals.

Large language model (LLM)-driven evolutionary search is an emerging algorithm-discovery paradigm that has already produced novel results in several scientific fields. Yet its application to wireless communications remains largely unexplored. To bridge this gap, we introduce The AI Telco Engineer (AITE), a framework to autonomously design algorithms for complex communication problems, while navigating performance-complexity tradeoffs. We showcase AITE on two challenging physical-layer problems: designing an equalizer for an orthogonal time-frequency space (OTFS) system, and constructing a receiver algorithm for an orthogonal frequency-division multiplexing (OFDM) system using a custom constellation and operating without pilots. For the first task, AITE develops algorithms that outperform the best-known solutions while reducing computational latency by a factor of 3.6 compared to the strongest baseline. For the second task, it discovers the first explicit, explainable algorithms that achieve performance parity with state-of-the-art neural receivers. These results demonstrate the strong potential of LLM-driven evolutionary search for the autonomous discovery of next-generation wireless communications algorithms.

Constrained Optimization Problems are crucial in fields such as engineering, economics, and robotics, where high-dimensional search spaces and complex objectives and constraints are common. Numerical optimization methods, including Feasible Direction, Interior Point, and Sequential Quadratic Programming, have shown strong performance in finding feasible local optima, but require accurate analytical gradients and effective initialization, which can be challenging in real-world settings. Evolutionary Algorithms, on the other hand, offer gradient-free search and robustness to noisy landscapes, managing to detect global optima more often than numerical methods, but they often suffer from high computational costs and slow convergence. In this work, we propose a Hybrid Augmented Lagrangian (HyAL) method that integrates the AL framework's constraint-handling strengths with the exploratory power of population-based search. Our approach employs evolutionary techniques to solve subproblems within the AL iterations, promoting exploration and aiding in the escape from local optima. We conduct extensive experiments on benchmark optimization problems, comparing our method against state-of-the-art optimizers, including IPOPT and CMA-ES, and a standalone evolutionary optimization baseline (with constraint enforcement via penalties). In addition, we evaluate four population-based methods integrated within the AL framework to study the effect of different evolutionary solvers. Our results show that HyAL consistently produces high-quality solutions across the benchmark suite. It outperforms purely evolutionary approaches and scales more effectively to high-dimensional constrained problems, where evolutionary-only methods often struggle. HyAL also surpasses state-of-the-art numerical optimization algorithms on complex landscapes containing numerous local minima and saddle points.

Real-world optimization problems often involve black-box functions and uncertainties in their evaluation, widely referred to as noisy optimization problems (NOPs). Evolutionary algorithms (EA), including Evolutionary Strategies (ES) and genetic algorithms (GA) have been commonly adopted to solve these problems in the contemporary literature. An ongoing challenge is the computational expense involved, given the number of evaluations required for good fitness estimation and ranking. Two fundamental methods commonly used for fitness estimation for NOPs are implicit averaging and explicit averaging. Explicit averaging uses resampling of solutions to improve the estimates, while implicit averaging typically uses a large population size with low resampling. Implicit averaging has been shown to have theoretical advantages for certain cases, which has motivated some recent approaches to use them. However, a recent study demonstrated that its performance is highly dependent on certain assumptions about the function, such as steepness and constant noise level, which may not apply for majority of the real world problems. Moreover, most existing algorithms have only considered homoscedastic noise, where the amplitude of variation is uniform across the entire search space, as opposed to more generic case of heteroscedastic noise. To address these issues, we introduce a set of heteroscedastic test problems and propose a novel confidence ranking method that employs a computationally efficient explicit averaging strategy with sampling budget adaptation. It is implemented within the Covariance Matrix Adaptation ES (CMA-ES) and GA frameworks to demonstrate its effectiveness and versatility. The resulting algorithm is evaluated on a range of problems with both homoscedastic and heteroscedastic noise, and it demonstrates superior performance compared to state-of-the-art approaches.

Many-objective optimization has been a field of interest over the past two decades and several evolutionary optimization algorithms have been introduced to tackle these problems; yet two fundamental questions remain underexplored: (i) What happens when the number of objectives grows beyond the typical many-objective regime of about fifteen and becomes massive? (ii) How do problem characteristics, such as the nature of interactions between objectives, influence algorithmic performance? To answer these questions we employ a diagnostic benchmark suite that allows control over problem characteristics and can be scaled to extremely high objective counts. Using this framework we evaluate several state-of-the-art evolutionary algorithms including NSGA-II, NSGA-III, MOEA/D and lexicase selection across a range of dimensionalities and diagnostic problem landscapes. Our experiments reveal that problem characteristics significantly affect algorithm performance. In particular, the nature of interactions between objectives appears important. These results highlight the importance of understanding these properties before selecting an algorithm for a specific problem. We also show that lexicase selection, an algorithm originally designed for genetic programming, compares favorably with state-of-the-art many-objective optimization algorithms while avoiding the dependence on predefined reference directions.

This paper addresses multi-objective service placement in computing continuum environments through a collaborative hybrid island-model MOEA. The key innovation is not the design of a new general hybrid algorithm, but the systematic application and analysis of heterogeneous hybridization for this specific optimization domain through two independent experimental campaigns: a first one with four state-of-the-art MOEAs (NSGA-II, NSGA-III, U-NSGA-III, and SMS-EMOA), and a second one with a complementary hybrid configuration based on NSGA-II, MOEA/TS, and MOCPO, both co-evolving and periodically exchanging solutions. These designs enable complementary search behaviors across islands and are naturally aligned with the distributed edge-fog-cloud architecture of the computing continuum, facilitating scalable parallel execution. To evaluate the approach, we define two research hypotheses: (i) whether hybrid cooperation yields significant performance gains over standalone algorithms, and (ii) whether all constituent algorithms contribute equally to the final outcomes. We combine standard Pareto-front quality indicators (GD, IGD, HV, S, and STE) with a traceability-oriented analysis based on genetic load, which quantifies the contribution of each island to the evolved solutions. Across 30 independent runs, the hybrid method outperforms most of the standalone baselines, and statistical tests confirm significant improvements. Results also show non-uniform contributions among islands, providing interpretable evidence of effective hybrid cooperation.

Structural optimization problems often involve a large number of decision variables and highly non-convex feasible regions, making convergence to the true Pareto front extremely challenging. Even when convergence is achievable, it typically requires thousands of function evaluations, resulting in significant computational cost. This highlights the need for efficient and robust optimization algorithms for real-world engineering applications. In this study, we introduce a novel constrained multi-objective evolutionary algorithm, termed DPCME. The algorithm employs two interacting populations that exchange information, enabling effective global exploration and reducing the risk of convergence to local optima. To further enhance performance, a recent repair-based constraint-handling technique is incorporated, and alternative repair approaches are proposed and systematically evaluated. The proposed algorithm is tested on three engineering problems: the 72-bar truss, the 120-bar truss, and a chemical tanker structure, each involving hundreds of nonlinear failure constraints. Its performance is evaluated against state-of-the-art constrained multi-objective optimization algorithms from the latest PlatEMO package. A total of 43 algorithms are initially tested, from which the 12 best-performing methods are selected for detailed comparison. The results demonstrate that DPCME achieves superior or competitive convergence and diversity across all test cases, and that the inclusion of repair-based constraint handling further improves its performance.

Automatic Heuristic Design (AHD) has emerged as a transformative approach for solving combinatorial optimization problems. While recent Large Language Model (LLM)-based methods have shown promise, they predominantly rely on fixed evolutionary operators and struggle to effectively accumulate and reuse historical search experience. This paper proposes RefineEvo, a novel evolutionary framework that transforms AHD from a static trial-and-error process into a planning-guided, experience-driven system. RefineEvo introduces a Planner to dynamically schedule evolutionary operators and trigger refinement based on the current search state, and a Reflector to distill valuable lessons into a Bidirectional Experience Pool containing both positive insights and negative pitfalls. This synergistic framework enables the system to adapt its search tools to the evolving complexity of the problem and leverage trajectory-aware, situation-conditioned insights to guide generation. Experiments on several classic combinatorial optimization benchmarks demonstrate that RefineEvo consistently outperforms strong baselines. In particular, RefineEvo delivers superior solution quality while improving token efficiency, enabling more efficient and autonomous heuristic design.

Evolutionary program search guided by Large Language Models (LLMs) has emerged as a powerful paradigm for automated scientific discovery. However, current approaches are fundamentally constrained by three bottlenecks: structurally blind parent selection, sparse whole-program evaluation rewards, and static mutation operators that fail to adapt during search. We present GAE (Graph-Augmented Evolution), a framework that resolves these limitations through a tightly coupled, three-pillar architecture. First, a relational graph neural network (GNN) parses programs into typed computation graphs, producing structure-aware embeddings. Second, an RL-optimized meta-controller leverages these embeddings to replace blind evolutionary sampling with a directed policy, dynamically selecting optimal parents and mutation directions based on reward history. Third, an online GRPO fine-tuning loop continuously updates the LLM mutation operator at test-time using group-normalized evaluation rewards, directly aligning the model's generation distribution with high-fitness structural edits. We evaluate GAE on a challenging scientific discovery task: symbolic regression for complex nonlinear oscillator systems. By transforming stochastic search into a directed, self-improving trajectory, GAE efficiently discovers closed-form physical equations, consistently matching or outperforming static LLM-driven baselines and achieving state-of-the-art out-of-distribution performance.

We study a symbolic search space for the Collatz conjecture based on finite exponent codes of the accelerated map. Each code records the number of divisions by two after every 3n + 1 step and determines three quantities: real drift, a 2-adic start representative, and a 3-adic endpoint representative. Their combination defines the 2-3-infinity diagnostic. Counterexample-like codes should exhibit near-critical drift, small 2-adic start representatives, and endpoints compatible with growth on the scale of (3/2)^k. We prove that every infinite code generated by a fixed positive integer has asymptotically vanishing 2-adic and 3-adic residue rates. Experiments with random critical codes, mechanical critical codes, and adaptive evolutionary search at lengths 100, 200, and 400 show that adaptive search improves finite-length trade-offs, while all methods retain clearly positive residue rates. The proposed framework is not a verification method for the Collatz conjecture, but a symbolic diagnostic approach for investigating obstruction structures in exponent-code space.

Decision-making is posing an increasingly formidable challenge to investors because of the growing number of alternatives available in financial markets. A hot area of research over the past few decades has been portfolio optimization that seeks to determine how much an investor should invest in which asset. Introducing real-world conditions to the optimization model turns the problem into an NP-hard one for whose solution exact methods become inefficient; hence, researchers have turned to evolutionary algorithms to approximate solutions. In this paper, strengthening strategies are presented for multi-objective evolutionary algorithms that can provide a faster convergence rate and extensive search ability in the portfolio optimization problem under the cardinality constraint. To implement those features, a unique solution representation, a novel operator, and new repair mechanisms are introduced for solving the aforementioned problem in which lower and upper limits are set on the number of assets in the portfolio. For this purpose, new mating strategies along with the aforesaid package are implemented in well-known multi-objective evolutionary algorithms to solve the problem. The customized algorithms are subsequently tested against traditional ones using well-known market indices as benchmarks. Results indicate that the proposed strategy not only provides better approximations but also converges faster as well at no loss of performance with an increasing number of assets in the market.

While traditional evolutionary algorithms hard-code reproduction, self-replication can emerge spontaneously within digital ``primordial soups''. This paper investigates the coevolution of such emergent self-replication alongside problem-solving capabilities. We initialize a population of random 32-byte Z80 assembly programs, requiring self-replication to arise purely through random assembly-level mutations and pairwise program interactions. To couple computation with reproduction, we introduce a task-based validation step: correctly evaluating a polynomial raises a program's interaction probability above a baseline rate. Our experiments yield four primary findings. First, self-replication and mathematical problem-solving successfully coevolve from initial randomness. Second, the pressure to compute accelerates the emergence of compact, robust reproductive architectures that preserve memory for task execution. Third, applying metabolic constraints that penalize runtime promotes the emergence of sophisticated conditional execution patterns that reduce energy use. Finally, partitioning programs into interconnected task niches generates an emergent learning curriculum that utilizes simple solutions as stepping stones toward more complex tasks. Altogether, these results demonstrate an interactive feedback loop: environmental task demands actively shape the physical architecture of self-replication, while spontaneous replication alters the evolutionary trajectory of functional problem-solving.

Artificial intelligence (AI) is shifting scientific discovery from task-specific workflows towards autonomous systems that organize exploration with experimental and human feedback in open-ended candidate spaces. Evolutionary computation (EC) provides a computational basis for feedback-driven discovery because population-based search can maintain diverse scientific candidates while steering exploration through accumulated evidence. However, EC predominantly focuses on candidate refinement for predefined problems, whereas cumulative discovery requires experience retention. To bridge this gap, this review introduces evolutionary intelligence (EI) for scientific discovery. EI characterizes scientific AI systems that sustain exploration by linking candidate refinement with experience retention across evolutionary cycles. We introduce a five-dimensional analytical framework that asks what evolves, how candidates change, why candidates are selected, where feedback originates, and when evolution occurs. This framework clarifies how EI transforms isolated search trajectories into cumulative scientific insight. We further demonstrate this paradigm across diverse discovery modes, from evolving concrete scientific entities to orchestrating automated research workflows. Finally, we identify critical bottlenecks regarding evaluation, process traceability, and shared infrastructure, providing a concrete roadmap for advancing the transition from EC to EI in scientific discovery.

The inverse design of physical systems governed by partial differential equations is computationally demanding due to the high dimensionality and non-convexity of design spaces. Generative models for inverse design often lack robustness and transferability, whereas evolutionary strategies are robust but struggle in high-dimensional spaces. This paper introduces a Neural Operator-enabled Topology-informed Evolutionary Strategy (NOTES) that integrates dimensionality reduction, representation learning, and evolutionary optimization for efficient and transferable inverse design. NOTES couples a DeepONet-based neural operator with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) to perform global optimization in a compact latent space that encodes topology-aware priors while discovering high-performance designs for unseen operating conditions. Applied to nanophotonic beam-deflector inverse design governed by Maxwell's equations, NOTES reduces the design dimensionality from 256 to 25 and consistently achieves over 95 percent efficiency, outperforming CMA-ES, topology optimization, and other baselines. Applied to structural optimization, NOTES discovers designs that achieve compliance down to 246. By decoupling topology learning of a DeepONet from the governing physics in a PDE solver, NOTES provides a flexible and transferable framework for the inverse design of physical systems.

Designing effective multi-objective Bayesian optimization (MOBO) algorithms requires balancing many interdependent design choices whose optimal configuration is problem-dependent and typically demands deep expertise. We extend the LLaMEA framework to MOBO, using large language models as mutation and crossover operators within evolutionary strategies to generate complete algorithm implementations, with SMAC hyperparameter optimization integrated into the evolutionary loop. Across nine evolutionary runs we generated approximately 900 algorithms and benchmarked them on twelve synthetic problems (ZDT, DTLZ, WFG) and three real-world engineering problems (RE), using a BoFire qParEGO implementation as a state-of-the-art Bayesian-optimization baseline. On the synthetic suite the strongest generated algorithm attains the highest mean normalized hypervolume (0.971, vs. 0.869 for qParEGO) while requiring roughly 60x less wall-clock time; a Friedman test with post-hoc analysis places the two in a single top-performing group, and per-problem tests find the generated algorithm significantly better than qParEGO on 7 of the 12 problems and never worse, matching state-of-the-art accuracy at an order-of-magnitude lower cost. On the three unseen real-world engineering problems a generated algorithm attains the best mean normalized hypervolume (0.985, vs. 0.971 for qParEGO)--significantly better than qParEGO on two of the three problems--at roughly 3.4x lower wall-clock cost, confirming that the gains transfer beyond the synthetic regime. LLM-driven evolutionary search can thus discover algorithm designs that achieve Pareto-efficient trade-offs difficult to reach through manual design.

The integration of Large Language Models (LLMs) with evolutionary computation has emerged as a powerful paradigm for automated heuristic design in combinatorial optimization. However, existing approaches suffer from mode collapse, converging to homogeneous populations that lack semantic diversity and fail to explore the full algorithmic space. We propose Quality-Diversity Evolution (QDEvo), a multi-objective framework that integrates Quality-Diversity optimization with LLM-driven heuristic search, maintaining an unbounded archive of semantically diverse algorithms using pre-trained code embeddings and incorporating hierarchical self-reflection to guide the evolutionary process. Extensive experiments across standard benchmarks and real-world industrial applications demonstrate that QDEvo significantly outperforms state-of-the-art methods in both Hypervolume and Inverted Generational Distance metrics. Our framework enables the discovery of heuristics that are simultaneously high-performing, computationally efficient, and semantically diverse, providing practitioners with a rich portfolio of solutions for complex optimization problems.

Before fixing an issue, it is useful to first reproduce it by generating a bug reproduction test (BRT). However, generating a BRT is itself a challenging task, because issue descriptions tend to be informal, making it difficult to determine whether a candidate BRT indeed fails for the reason in the issue. Prior work has attempted to tackle this problem via inference scaling, using large language models to generate many BRTs and patches, then using execution feedback to select and improve them. Unfortunately, this is expensive and the feedback is unreliable. This paper explores evolutionary programming for BRT generation to sharpen the feedback, while enhancing evolutionary programming to keep costs in check. Our new approach, EvoOtter, controls test execution costs via successive halving. Furthermore, it controls LLM costs via batched crossover for an entire generation in a single LLM call, as well as via rule-based code mutations, with a new fitness score tailored for BRTs. As a result, EvoOtter generates state-of-the-art quality BRTs at the fraction of the cost of prior inference-scaling approaches to this problem. More broadly, this paper points at how to efficiently and effectively combine evolutionary programming with large language models for software engineering.

Wave Function Collapse (WFC) is a widely used procedural content generation method that learns local adjacency constraints from example inputs to generate larger outputs. In this paper, we explore combining WFC with evolutionary search by evolving the small input examples used by WFC rather than directly evolving complete levels. In this approach, WFC acts as a genotype-to-phenotype mapping. The generated levels are then evaluated through domain-specific fitness functions. We evaluate the method in two domains with different relationships between local and global structure: Maze connectivity maps and Zelda-style dungeon layouts. Our results show that evolutionary optimization over WFC inputs improves generation quality in domains where properties emerge from local relationships, while domains requiring global constraints remain challenging. These findings suggest that evolutionary search can effectively guide WFC generation when target objectives align with local structure.

Evolutionary multitasking (EMT) has shown strong capability in solving multiple optimization problems simultaneously by exploiting latent inter-task consistency, such as similarities in promising solutions or search directions. However, most existing EMT studies remain focused on objective-driven optimization, where such consistency is mainly used to accelerate convergence toward predefined optima. In this paper, we move EMT from consistency to collaborative discovery and propose a multifactorial evolutionary algorithm with collaborative discovery (MFEA-CoD) for multitask novelty search. Unlike conventional EMT, MFEA-CoD coordinates multiple novelty search tasks to collaboratively discover behaviorally novel solutions rather than merely transferring consistent search information for faster convergence. Specifically, a multitask repulsion operator encourages different tasks to explore distinct regions of the unified search space, thereby reducing redundant behavioral discoveries. Meanwhile, an adaptive inter-task transfer mechanism exploits shared discovery opportunities in overlapping novelty-improving regions by adjusting the transfer probability according to the online contribution of transferred information. Furthermore, MFEA-CoD is extended to multitask novelty-augmented optimization, where behavioral novelty is jointly considered with objective information to alleviate premature convergence caused by deceptive objectives. Experiments on synthetic basin-type problems, deceptive maze navigation problems, MuJoCo policy optimization problems, and generative novelty search problems demonstrate that MFEA-CoD improves the efficiency of discovering diverse novel solutions and shows clear advantages in deceptive objective landscapes.

Evolutionary neural architecture design for multivariate time-series forecasting remains underexplored, with most approaches relying on fixed Transformer architectures despite substantial variation across tasks and forecasting settings. This paper introduces an evolutionary neural architecture search framework for discovering task-adaptive Transformer-like models for time-series forecasting (EVOTS). Architectures are encoded using a modular genome representation that enables flexible composition of attention, feed-forward, and projection components, while a repair mechanism enforces structural validity throughout the evolutionary process. This formulation allows effective exploration of a diverse architecture space without relying on hand-crafted design rules. The proposed approach is evaluated on four benchmark datasets from the ETT family (ETTh1, ETTh2, ETTm1, and ETTm2) under multiple forecasting settings, including univariate-to-univariate, multivariate-to-univariate, and multivariate-to-multivariate prediction, with horizons of 96, 192, 336, and 720. In the multivariate-to-multivariate setting, the evolved architectures achieve competitive and, in several cases, improved mean squared error relative to a strong Transformer-based baseline. Additional analyses examine performance differences across forecasting settings and report wall-clock training time to provide a coarse indication of computational cost. Overall, the results demonstrate that evolutionary search can effectively discover flexible and high-performing Transformer-like architectures for multivariate time-series forecasting within practical runtime constraints.

We analyze the effect of optimizing the initial population of genetic programming (GP) for symbolic regression (SR) on the accuracy and complexity of solutions. We compare three well-established random initialization methods as well as initialization with small optimized solutions from exhaustive symbolic regression (ESR) using a GP/SR implementation which is based on the multi-objective evolutionary algorithm NSGA-II. We compare the final Pareto fronts found with each initialization method on twelve synthetic problems of varying complexity and one real-world dataset. We find no significant differences in accuracy or model complexity among the initialization methods. The initial advantage of initialization with ESR disappears after only a few generations. Our results show that, given similar diversity in the initial population, the effect of the initialization method in GP-based symbolic regression on the final Pareto front is negligible.

Automated Heuristic Design (AHD) with Large Language Models (LLMs) has shown remarkable progress in discovering high-quality heuristics. However, existing LLM-based AHD methods optimize heuristics for a fixed training instance set and may fail catastrophically when deployed under real-world distributional shifts. We propose Robust Adversary Instance Search (RAISE), a framework that integrates constrained worst-case instance search within a principled neighborhood of the training distribution into the LLM-based evolutionary search loop. RAISE treats robust AHD as a constrained adversarial instance search problem: the outer loop evolves heuristics via LLM operators, while an LLM-free inner loop efficiently identifies hard instances within an epsilon-ball around the training instance set using a basis distribution parameterization with boundary projection. Comprehensive experiments on Online Bin Packing (OBP), Online Job Shop Scheduling (OJSP), and Online Vehicle Routing (OVRP) across five distribution families demonstrate that existing LLM-based AHD methods degrade by up to 19 times under distribution shift, while RAISE consistently maintains strong performance across all tested distributions and problem scales

LLM-assisted evolutionary search (LES) has emerged as a promising paradigm for automated algorithm design. However, existing methods usually suffer from two inherent limitations when facing the automated design of real-world complex algorithms that usually consist of multiple components. The first limitation is that they either focus on modifying entire algorithms, making it difficult to reuse high-quality components, or concentrate on component refinement within a limited set of predefined multicomponent configurations. The second limitation is the insufficient explicit modeling and exploitation of algorithm semantics. These limitations severely degrade search efficiency and hinder effective exploration of complex design spaces. Therefore, this paper proposes STABLE (Semantics-Aware Bilevel Co-Evolution), an LES method purpose-built for automated multicomponent algorithm design that introduces structural algorithm formulation and semantics-driven evolution. In STABLE, complex algorithms are organized into hierarchical and modular architectures rooted in domain knowledge, aligning the search space with their intrinsic compositional traits. Based on this structured algorithm formulation, STABLE simultaneously optimizes high-level multicomponent configurations and low-level functional components, enabling coordinated cross-level updates while maintaining suitable granularities for design space exploration. At each level, STABLE establishes a multi-faceted semantic model to assist LLMs in capturing structural correlations, functional compatibilities, and inherent rationalities among algorithm components. This semantic model serves as the core guidance for evolutionary search, enabling principled algorithm generation and algorithm evaluation. Extensive experiments demonstrate that STABLE outperform both human-designed baselines and those from advanced LES methods.

This research investigates the optimization of Convolutional and Dense Neural Networks (CNNs and DNNs) for autonomous steering using the (N+M) Evolution Strategy (ES) with the 1/5th success rule. The primary objective is to develop a lightweight CNN based model capable of real-time steering angle prediction, mimicking human driving behavior on predefined paths. The ES algorithm automates hyperparameter tuning, dynamically adjusting parameters such as filter sizes and layer configurations. Data collection encompasses driving scenarios recorded via the LTU ACTor autonomous driving platform, including variations in path direction and driving style. The very small dataset consists of timestamped images labeled with steering angles and pre-processed to focus on relevant visual information. Initial experiments involve training a baseline CNN model, which is then refined using ES to significantly reduce the size of the model while maintaining competitive predictive accuracy. The results highlight the viability of lightweight neural network architectures for real-time autonomous systems, striking a balance between computational efficiency and performance. This study not only advances research initiatives on the use of evolutionary algorithms for autonomous driving applications but also lays the foundation for the deployment of cost-effective and scalable solutions in self-driving technology.

Would experience designing faster GPU kernels also help close in on a long-standing open mathematical conjecture? Large Language Models (LLMs) integrated into evolutionary search have recently produced state-of-the-art solutions on optimization tasks, including open mathematical conjectures, GPU kernel design, scientific law discovery, and combinatorial puzzles. To achieve this, prior work applied search scaffolds to one target task at a time, so every new problem is approached from scratch and the experience accumulated during search is discarded once the model finishes its attempt. This leaves the capability of iteratively evolving a solution (e.g., knowing which part to mutate and how, deciding when to backtrack) entirely in the scaffold rather than in the model itself. Whether the model itself could acquire this capability and reuse it across different tasks has been largely unexamined. To address this, we introduce Evolution Fine-Tuning (EFT), a mid-training paradigm that teaches LLMs to evolve solutions across tasks by converting evolutionary search trajectories into supervision. We construct Finch Collection, a 156K-trajectory dataset spanning 10 domains and 371 optimization tasks, and fine-tune open-source LLMs from 2B to 9B parameters. Empirically, EFT confers cross-task generalization: across 22 held-out tasks, our models surpass their base counterparts by 10.22% on average. Furthermore, when paired with test-time RL, our model matches state-of-the-art performance on two circle-packing tasks and outperforms its base-model counterpart on the Erdős minimum-overlap problem. EFT thus serves as a "practice phase" for general-purpose discovery agents that do not solve new problems from scratch.

Parameter settings in evolutionary algorithms and metaheuristics are important because such parameter values can influence the performance of algorithms under evaluation. For a given algorithm, there are many different numerical experiments to show that the algorithm can work well in practice; however, in most cases there is no theoretical analysis of parameter settings. In this work, we show that theoretical analysis using the theory of dynamical systems and evolution of population variance can give some good results in terms of parameter ranges for the bat algorithm. We also show that results from numerical experiments are consistent with theoretical bounds. Such analyses can provide good insights from different perspectives about the algorithmic characteristics such as variance evolution, transition between exploration and exploitation as well as convergence behaviour.

When gradient information is unavailable, black-box optimization (BBO) methods provide a practical alternative. While Evolution Strategies (ES), Consensus-Based Optimization (CBO), Optimization via Integration (OVI), and related methods have each been studied independently, their connections remain underexplored. We unify these approaches within a common theoretical framework, revealing that they differ primarily in two design choices: fitness aggregation (controlling sharpness preference) and consensus scope (controlling modality). Leveraging these insights, we introduce hybrid optimizers that interpolate between existing methods. Our ES-OVI hybrid allows explicit control over the preference for flat minima, enabling a trade-off between performance and robustness in continuous control tasks. Our CBO-OVI hybrids combine the higher-dimensional efficiency of parametric methods with the multimodal capabilities of particle-based approaches, achieving competitive results on language model merging under limited evaluation budgets. We validate our methods on standard BBO benchmarks and higher-dimensional locomotion tasks, demonstrating that the hybrid methods can outperform their constituent algorithms.