Evolutionary Optimization

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.

We extend our gauge-covariant stochastic neural-field framework by promoting architecture-level parameters to slow stochastic variables evolving in function space. Our effective theory is formulated in terms of classical commuting fields and provides symmetry-constrained diagnostics of marginality and finite-width effects through the maximal Lyapunov exponent, the amplification factor, and dressed spectral kernels. On top of this dynamics, we introduce a Markovian evolutionary scheme compatible with the local $U(1)$ structure of the effective model. By using a minimal implementation, the genotype is reduced to the weight-variance parameter $σ_w^2$, and the fitness functional combines spectral agreement, marginal stability, and a symmetry-constrained critical anchor. Comparing three evolutionary models, we find that only the fully symmetry-constrained Ginibre $U(1)$ version robustly approaches a narrow near-marginal regime and reproduces the predicted low-frequency finite-width spectral behavior. These results support the use of symmetry-guided effective stability diagnostics as practical principles for stochastic architecture search in controlled settings.

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.

Automating operations research (OR) with large language models (LLMs) remains limited by hand-crafted reasoning--execution workflows. Complex OR tasks require adaptive coordination among problem interpretation, mathematical formulation, solver selection, code generation, and iterative debugging. To address this limitation, we propose EvoOR-Agent, a co-evolutionary framework for automated optimization. The framework represents agent workflows as activity-on-edge (AOE)-style networks, making workflow topology, execution dependencies, and alternative reasoning paths explicit. On this representation, the framework maintains an architecture graph and evolves a population of reasoning individuals through graph-mediated path-conditioned recombination, multi-granularity semantic mutation, and elitist population update. A knowledge-base-assisted experience-acquisition module further injects reusable OR practices into initialization and semantic variation. Empirical results on heterogeneous OR benchmarks show that the proposed framework consistently improves over zero-shot LLMs, fixed-pipeline OR agents, and representative evolutionary agent frameworks. Case studies and ablation analyses further indicate that explicit architecture evolution and graph-supported reasoning-trajectory search contribute to both performance improvement and structural interpretability. These results suggest that treating agent architectures and reasoning trajectories as evolvable objects provides an effective route toward adaptive and interpretable automated optimization.

Automated simulator construction requires distributional fidelity, distinguishing it from generic code generation. We identify two failure modes in long-horizon LLM agents: contextual drift and optimization instability arising from conflating structural and parametric errors. We propose SOCIA-EVO, a dual-anchored evolutionary framework. SOCIA-EVO introduces: (1) a static blueprint to enforce empirical constraints; (2) a bi-level optimization to decouple structural refinement from parameter calibration; and (3) a self-curating Strategy Playbook that manages remedial hypotheses via Bayesian-weighted retrieval. By falsifying ineffective strategies through execution feedback, SOCIA-EVO achieves robust convergence, generating simulators that are statistically consistent with observational data. The code and data of SOCIA-EVO are available here: https://github.com/cruiseresearchgroup/SOCIA/tree/evo.

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.

This beta technical report asks how reusable experience should be represented so that it can function as effective test-time control and as a substrate for iterative evolution. We study this question in 4.590 controlled trials across 45 scientific code-solving scenarios. We find that documentation-oriented Skill packages provide unstable control: their useful signal is sparse, and expanding a compact experience object into a fuller documentation package often fails to help and can degrade the overall average. We further show that representation itself is a first-order factor. A compact Gene representation yields the strongest overall average, remains competitive under substantial structural perturbations, and outperforms matched-budget Skill fragments, while reattaching documentation-oriented material usually weakens rather than improves it. Beyond one-shot control, we show that Gene is also a better carrier for iterative experience accumulation: attached failure history is more effective in Gene than in Skill or freeform text, editable structure matters beyond content alone, and failure information is most useful when distilled into compact warnings rather than naively appended. On CritPt, gene-evolved systems improve over their paired base models from 9.1% to 18.57% and from 17.7% to 27.14%. These results suggest that the core problem in experience reuse is not how to supply more experience, but how to encode experience as a compact, control-oriented, evolution-ready object.

To navigate a space, the brain makes an internal representation of the environment using different cells such as place cells, grid cells, head direction cells, border cells, and speed cells. All these cells, along with sensory inputs, enable an organism to explore the space around it. Inspired by these biological principles, we developed NEATNC, a Neuro-Evolution of Augmenting Topology guided Navigation Cells. The goal of the paper is to improve NEAT algorithm performance in path planning in dynamic environments using spatial cognitive cells. This approach uses navigation cells as inputs and evolves recurrent neural networks, representing the hippocampus part of the brain. The performance of the proposed algorithm is evaluated in different static and dynamic scenarios. This study highlights NEAT's adaptability to complex and different environments, showcasing the utility of biological theories. This suggests that our approach is well-suited for real-time dynamic path planning for robotics and games.

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.

Large Language Models (LLMs) exhibit strong mathematical reasoning when trained on high-quality Chain-of-Thought (CoT) that articulates intermediate steps, yet costly CoT curation hinders further progress. While existing remedies such as distillation from stronger LLMs and self-synthesis based on test-time search alleviate this issue, they often suffer from diminishing returns or high computing overhead.In this work, we propose CoTEvol, a genetic evolutionary framework that casts CoT generation as a population-based search over reasoning trajectories.Candidate trajectories are iteratively evolved through reflective global crossover at the trajectory level and local mutation guided by uncertainty at the step level, enabling holistic recombination and fine-grained refinement. Lightweight, task-aware fitness functions are designed to guide the evolutionary process toward accurate and diverse reasoning. Empirically, CoTEvol improves correct-CoT synthesis success by over 30% and enhances structural diversity, with markedly improved efficiency. LLMs trained on these evolutionary CoT data achieve an average gain of 6.6% across eight math benchmarks, outperforming previous distillation and self-synthesis approaches. These results underscore the promise of evolutionary CoT synthesis as a scalable and effective method for mathematical reasoning tasks.

Antibody lead optimization is inherently a multi-objective challenge in drug discovery. Achieving a balance between different drug-like properties is crucial for the development of viable candidates, and this search becomes exponentially challenging as desired properties grow. The ever-growing zoo of sophisticated in silico tools for predicting antibody properties calls for an efficient joint optimization procedure to overcome resource-intensive sequential filtering pipelines. We present BOAT, a versatile Bayesian optimization framework for multi-property antibody engineering. Our `plug-and-play' framework couples uncertainty-aware surrogate modeling with a genetic algorithm to jointly optimize various predicted antibody traits while enabling efficient exploration of sequence space. Through systematic benchmarking against genetic algorithms and newer generative learning approaches, we demonstrate competitive performance with state-of-the-art methods for multi-objective protein optimization. We identify clear regimes where surrogate-driven optimization outperforms expensive generative approaches and establish practical limits imposed by sequence dimensionality and oracle costs.

At the fundamental conceptual level, two alternatives have traditionally been considered for how mutations arise and how evolution happens: 1) random mutation and natural selection, and 2) Lamarckism. Recently, the theory of Interaction-based Evolution (IBE) has been proposed, according to which mutations are neither random nor Lamarckian, but are influenced by information accumulating internally in the genome over generations. Based on the estimation-of-distribution algorithms framework, we present a simulation model that demonstrates nonrandom, non-Lamarckian mutation concretely while capturing indirectly several aspects of IBE: selection, recombination, and nonrandom, non-Lamarckian mutation interact in a complementary fashion; evolution is driven by the interaction of parsimony and fit; and random bits do not directly encode improvement but enable generalization by the manner in which they connect with the rest of the evolutionary process. Connections are drawn to Darwin's observations that changed conditions increase the rate of production of heritable variation; to the causes of bell-shaped distributions of traits and how these distributions respond to selection; and to computational learning theory, where analogizing evolution to learning in accord with IBE casts individuals as examples and places the learned hypothesis at the population level. The model highlights the importance of incorporating internal integration of information through heritable change in both evolutionary theory and evolutionary computation.

Streaming Data-Driven Optimization (SDDO) problems arise in many applications where data arrive continuously and the optimization environment evolves over time. Concept drift produces non-stationary landscapes, making optimization methods challenging due to outdated models. Existing approaches often rely on simple surrogate combinations or directly injecting solutions, which may cause negative transfer under sudden environmental changes. We propose GeM-EA, a Generative and Meta-learning Enhanced Evolutionary Algorithm for SDDO that unifies meta-learned surrogate adaptation with generative replay for effective evolutionary search. Upon detecting concept drift, a bi-level meta-learning strategy rapidly initializes the surrogate using environment-relevant priors, while a linear residual component captures global trends. A multi-island evolutionary strategy further leverages historical knowledge via generative replay to accelerate optimization. Experimental results on benchmark SDDO problems demonstrate that GeM-EA achieves faster adaptation and improved robustness compared with state-of-the-art methods.

In optimization problems, some variable subsets may have a joint non-linear or non-monotonical influence on the function value. Therefore, knowledge of variable dependencies may be crucial for effective optimization, and many state-of-the-art optimizers leverage it to improve performance. However, some real-world problem instances may be the subject of noise of various origins. In such a case, variable dependencies relevant to optimization may be hard or impossible to tell using dependency checks sufficient for problems without noise, making highly effective operators, e.g., Partition Crossover (PX), useless. Therefore, we use Statistical Linkage Learning (SLL) to decompose problems with noise and propose a new SLL-dedicated mask construction algorithm. We prove that if the quality of the SLL-based decomposition is sufficiently high, the proposed clustering algorithm yields masks equivalent to PX masks for the noise-free instances. The experiments show that the optimizer using the proposed mechanisms remains equally effective despite the noise level and outperforms state-of-the-art optimizers for the problems with high noise.

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".

As high-performance computing and AI workloads become increasingly dependent on GPUs, maintaining high performance across rapidly evolving hardware generations has become a major challenge. Developers often spend months tuning scientific applications to fully exploit new architectures, navigating a complex optimization space that spans algorithm design, source implementation, compiler flags and pass sequences, and kernel launch parameters. Existing approaches can effectively search parts of this space in isolation, such as launch configurations or compiler settings, but optimizing across the full space still requires substantial human expertise and iterative manual effort. In this paper, we present Record-Remix-Replay (R^3), a hierarchical optimization framework that combines LLM-driven evolutionary search, Bayesian optimization, and record-replay compilation techniques to efficiently explore GPU kernel optimizations from source-level implementation choices down to compiler pass ordering and runtime configuration. By making candidate evaluation fast and scalable, our approach enables practical end-to-end search over optimization dimensions that are typically treated separately. We show that Record-Remix-Replay can optimize full scientific applications better than traditional approaches over kernel parameters and compiler flags, while also being nearly an order of magnitude faster than modern evolutionary search approaches.

LLM-driven program evolution can discover high-quality programs, but high API cost and run-to-run variance hinder reliable progress. We propose TurboEvolve, a multi-island evolutionary framework that improves sample efficiency and stability under matched API-cost budgets. Inspired by multiple-offspring strategies in evolutionary algorithms, TurboEvolve introduces Verbalized Sampling, which elicits K diverse candidates in one LLM call while using self-assigned probabilities only as generation signals, together with an online scheduler that adapts K to expand exploration under stagnation and reduce redundant generation during steady progress. To exploit existing solution pools, TurboEvolve further introduces island-aware initialization, which clusters seed programs into mode-specific subpopulations and applies controlled cross-cluster mixing with elitist preservation to balance diversity, sharing, and refinement. We also curate a reusable cross-task solution-pool dataset to support warm-start initialization studies and matched-resource comparisons. Across mathematical discovery and GPU-kernel optimization tasks, TurboEvolve achieves stronger cost-quality trade-offs and more stable performance than controlled baselines, while reaching competitive reported scores.

We test whether artificial intelligence architectural evolution obeys the same statistical laws as biological evolution. Compiling 935 ablation experiments from 161 publications, we show that the distribution of fitness effects (DFE) of architectural modifications follows a heavy-tailed Student's t-distribution with proportions (68% deleterious, 19% neutral, 13% beneficial for major ablations, n=568) that place AI between compact viral genomes and simple eukaryotes. The DFE shape matches D. melanogaster (normalized KS=0.07) and S. cerevisiae (KS=0.09); the elevated beneficial fraction (13% vs. 1-6% in biology) quantifies the advantage of directed over blind search while preserving the distributional form. Architectural origination follows logistic dynamics (R^2=0.994) with punctuated equilibria and adaptive radiation into domain niches. Fourteen architectural traits were independently invented 3-5 times, paralleling biological convergences. These results demonstrate that the statistical structure of evolution is substrate-independent, determined by fitness landscape topology rather than the mechanism of selection.

Text-to-image diffusion models exhibit strong generative performance but remain highly sensitive to prompt formulation, often requiring extensive manual trial and error to obtain satisfactory results. This motivates the development of automated, model-agnostic prompt optimization methods that can systematically explore the conditioning space beyond conventional text rewriting. This work investigates the use of a Genetic Algorithm (GA) for prompt optimization by directly evolving the token vectors employed by CLIP-based diffusion models. The GA optimizes a fitness function that combines aesthetic quality, measured by the LAION Aesthetic Predictor V2, with prompt-image alignment, assessed via CLIPScore. Experiments on 36 prompts from the Parti Prompts (P2) dataset show that the proposed approach outperforms the baseline methods, including Promptist and random search, achieving up to a 23.93% improvement in fitness. Overall, the method is adaptable to image generation models with tokenized text encoders and provides a modular framework for future extensions, the limitations and prospects of which are discussed.

While artificial intelligence has mastered structured games like chess and Go, vision-language agents still struggle in visually-driven 3D games without access to game states. Existing game environments typically evaluate a fixed agent configuration, rather than an agent's ability to improve its configuration across consecutive episodes of the same task---a paradigm known as test-time learning (TTL). Furthermore, current TTL methods typically optimize single modalities---such as text prompts or actions---in isolation, ignoring the synergy between perception, reasoning, and control. To bridge these gaps, we first introduce PokeGym, a long-horizon benchmark built upon the 3D open-world game Pokémon Legends: Z-A, where agents act from visual observations without access to game states, designed to evaluate an agent's ability to learn and adapt across consecutive episodes of the task. To tackle this challenging environment, we propose Graph-Guided Evolutionary Multimodal Agent Configuration (G-EvoMAC), a graph-guided framework that jointly optimizes visual perception, strategy, and action set synergistically. Extensive experiments show that G-EvoMAC achieves a 60.18% average success rate on PokeGym, outperforming the strongest baseline by over 11 percentage points, validating the power of cross-modal co-evolution.

We consider the classic Multi-Armed Bandit setting to understand the exploration/exploitation tradeoffs made by different search heuristics. Since many search heuristics work by comparing different options (in evolutionary algorithms called "individuals"; in the Bandit literature called "arms"), we work with the "Dueling Bandits" setting. In each iteration, a comparison between different arms can be made; in the binary stochastic setting, each arm has a fixed winning probability against any other arm. A Condorcet winner is any arm that beats every other arm with a probability strictly higher than $1/2$. We show that evolutionary algorithms are rather bad at identifying the Condorcet winner: Even if the Condorcet winner beats every other arm with a probability $1-p$, the (1+1) EA, in its stationary distribution, chooses the Condorcet winner only with constant probability if $p=Ω(1/n)$. By contrast, we show that a simple EDA (based on the Max-Min Ant System with iteration-best update) will choose the Condorcet winner in its maintained distribution with probability $1-Θ(p)$. As a remedy for the (1+1) EA, we show how repeated duels can significantly boost the probability of the Condorcet winner in the stationary distribution.

Designing high-performing metaheuristics for NP-hard combinatorial optimization problems, such as the Vehicle Routing Problem (VRP), remains a significant challenge, often requiring extensive domain expertise and manual tuning. Recent advances have demonstrated the potential of large language models (LLMs) to automate this process through evolutionary search. However, existing methods are largely reactive, relying on immediate performance feedback to guide what are essentially black-box code mutations. Our work departs from this paradigm by introducing Metacognitive Evolutionary Programming (MEP), a framework that elevates the LLM to a strategic discovery agent. Instead of merely reacting to performance scores, MEP compels the LLM to engage in a structured Reason-Act-Reflect cycle, forcing it to explicitly diagnose failures, formulate design hypotheses, and implement solutions grounded in pre-supplied domain knowledge. By applying MEP to evolve core components of the state-of-the-art Hybrid Genetic Search (HGS) algorithm, we discover novel heuristics that significantly outperform the original baseline. By steering the LLM to reason strategically about the exploration-exploitation trade-off, our approach discovers more effective and efficient heuristics applicable across a wide spectrum of VRP variants. Our results show that MEP discovers heuristics that yield significant performance gains over the original HGS baseline, improving solution quality by up to 2.70% and reducing runtime by over 45% on challenging VRP variants.

We show that verifier-free evolution is bottlenecked by both diversity and efficiency: without external correction, repeated evolution accelerates collapse toward narrow modes, while the uniform use of a high-cost model wastes compute and quickly becomes economically impractical. We introduce Squeeze Evolve, a unified multi-model orchestration framework for verifier-free evolutionary inference. Our approach is guided by a simple principle: allocate model capability where it has the highest marginal utility. Stronger models are reserved for high-impact stages, while cheaper models handle the other stages at much lower costs. This principle addresses diversity and cost-efficiency jointly while remaining lightweight. Squeeze Evolve naturally supports open-source, closed-source, and mixed-model deployments. Across AIME 2025, HMMT 2025, LiveCodeBench V6, GPQA-Diamond, ARC-AGI-V2, and multimodal vision benchmarks, such as MMMU-Pro and BabyVision, Squeeze Evolve consistently improves the cost-capability frontier over single-model evolution and achieves new state-of-the-art results on several tasks. Empirically, Squeeze Evolve reduces API cost by up to $\sim$3$\times$ and increases fixed-budget serving throughput by up to $\sim$10$\times$. Moreover, on discovery tasks, Squeeze Evolve is the first verifier-free evolutionary method to match, and in some cases exceed, the performance of verifier-based evolutionary methods.

While most theoretical run time analyses of discrete randomized search heuristics provide bounds on the expected number of evaluations to find the global optimum, we consider the anytime performance of evolutionary and estimation-of-distribution algorithms. For this purpose, we analyze the fixed-target run time of various algorithms using BinVal as fitness function and bound the run time to optimize the most significant $k \in o(n)$ bits of a bit string with length $n$. We analyze the run times such that they hold not only for a fixed $k$, but simultaneously for all $k \in o(n)$. For the standard (1+1) EA with fixed mutation rate $1/n$, we show that the fixed-target run time for all $k \in o(n)$ is in $Θ(n \log k)$. Using an EDA instead, we get an expected number of evaluations of $Θ(k \log n)$ for the sig-cGA. Replacing in the standard (1+1) EA the fixed mutation rate with a self-adjusting rate, we show that the fixed-target run time for $k \in o(n)$ and a constant $\varepsilon >0$ arbitrarily close to zero is in $\mathcal{O}\left(k^{1+\varepsilon}\right)$ for this algorithm. In particular, this run time is independent of $n$, holds simultaneously for all $k \in o(n)$, and is close to the run time of $Θ(k \log k)$ for the (1+1) EA with the best fixed mutation rate if $k$ is known.

Traffic signal control TSC requires strategies that are both effective and interpretable for deployment, yet reinforcement learning produces opaque neural policies while program synthesis depends on restrictive domain-specific languages. We present SIGNALCLAW, a framework that uses large language models LLMs as evolutionary skill generators to synthesize and refine interpretable control skills for adaptive TSC. Each skill includes rationale, selection guidance, and executable code, making policies human-inspectable and self-documenting. At each generation, evolution signals from simulation metrics such as queue percentiles, delay trends, and stagnation are translated into natural language feedback to guide improvement. SignalClaw also introduces event-driven compositional evolution: an event detector identifies emergency vehicles, transit priority, incidents, and congestion via TraCI, and a priority dispatcher selects specialized skills. Each skill is evolved independently, and a priority chain enables runtime composition without retraining. We evaluate SignalClaw on routine and event-injected SUMO scenarios against four baselines. On routine scenarios, it achieves average delay of 7.8 to 9.2 seconds, within 3 to 10 percent of the best method, with low variance across random seeds. Under event scenarios, it yields the lowest emergency delay 11.2 to 18.5 seconds versus 42.3 to 72.3 for MaxPressure and 78.5 to 95.3 for DQN, and the lowest transit person delay 9.8 to 11.5 seconds versus 38.7 to 45.2 for MaxPressure. In mixed events, the dispatcher composes skills effectively while maintaining stable overall delay. The evolved skills progress from simple linear rules to conditional strategies with multi-feature interactions, while remaining fully interpretable and directly modifiable by traffic engineers.

Many randomized optimization algorithms are rank-invariant, relying solely on the relative ordering of solutions rather than absolute fitness values. We introduce a stronger notion of rank landscape invariance: two problems are equivalent if their ranking, but also their neighborhood structure and symmetries (translation and rotation), induce identical landscapes. This motivates the study of rank landscapes rather than individual functions. While prior work analyzed the rankings of injective function classes in isolation, we provide an exhaustive inventory of the invariant landscape classes for pseudo-Boolean functions of dimensions 1, 2, and 3, including non-injective cases. Our analysis reveals 12,007 classes in total, a significant reduction compared to rank-invariance alone. We find that non-injective functions yield far more invariant landscape classes than injective ones. In addition, complex combinations of topological landscape properties and algorithm behaviors emerge, particularly regarding deceptiveness, neutrality, and the performance of hill-climbing strategies. The inventory serves as a resource for pedagogical purposes and benchmark design, offering a foundation for constructing larger problems with controlled hardness and advancing our understanding of landscape difficulty and algorithm performance.

Existing evolutionary algorithms for Constrained Multi-objective Optimization Problems (CMOPs) typically treat all constraints uniformly, overlooking their distinct geometric relationships with the true Constrained Pareto Front (CPF). In reality, constraints play different roles: some directly shape the final CPF, some create infeasible obstacles, while others are irrelevant. To exploit this insight, we propose a novel algorithm named RCCMO, which sequentially performs unconstrained exploration, single-constraint exploitation, and full-constraint refinement. The core innovation of RCCMO lies in a constraint prioritization method derived from these geometric insights, seamlessly coupled with a unique dual-directional search mechanism. Specifically, RCCMO first prioritizes constraints that constitute the final CPF, approaching them from the evolutionary direction (optimizing objectives) to locate the CPF directly shaped by single-constraint boundaries. Subsequently, for constraints that merely hinder the population's progress, RCCMO searches from the anti-evolutionary direction (targeting the infeasible boundaries where hindering constraints intersect with the CPF) to effectively discover how these constraints obstruct and form the final CPF. Meanwhile, irrelevant constraints are intentionally bypassed. Furthermore, a series of specialized mechanisms are proposed to accelerate the algorithm's execution, reduce heuristic misjudgments, and dynamically adjust search directions in real time. Extensive experiments on 5 benchmark test suites and 29 real-world CMOPs demonstrate that RCCMO significantly outperforms seven state-of-the-art algorithms.

Causal inference is central to scientific discovery, yet choosing appropriate methods remains challenging because of the complexity of both statistical methodology and real-world data. Inspired by the success of artificial intelligence in accelerating scientific discovery, we introduce InferenceEvolve, an evolutionary framework that uses large language models to discover and iteratively refine causal methods. Across widely used benchmarks, InferenceEvolve yields estimators that consistently outperform established baselines: against 58 human submissions in a recent community competition, our best evolved estimator lay on the Pareto frontier across two evaluation metrics. We also developed robust proxy objectives for settings without semi-synthetic outcomes, with competitive results. Analysis of the evolutionary trajectories shows that agents progressively discover sophisticated strategies tailored to unrevealed data-generating mechanisms. These findings suggest that language-model-guided evolution can optimize structured scientific programs such as causal inference, even when outcomes are only partially observed.

Parent selection methods are widely used in evolutionary computation to accelerate the optimization process, yet their theoretical benefits are still poorly understood. In this paper, we address this gap by proposing a parent selection strategy for the $(μ+1)$ genetic algorithm (GA) that prioritizes the selection of maximally distant parents for crossover. We show that, with an appropriately chosen population size, the resulting algorithm solves the Jump$_k$ problem in $O(k4^kn\log(n))$ expected time. This bound is significantly smaller than the best known bound of $O(nμ\log(μ)+n\log(n)+n^{k-1})$ for any $(μ+1)$~GA using no explicit diversity-preserving mechanism and a constant crossover probability. To establish this result, we introduce a novel diversity metric that captures both the maximum distance between pairs of individuals in the population and the number of pairs achieving this distance. The main novelty of our analysis is that it relies on crossover as a mechanism for creating and maintaining diversity throughout the run, rather than using crossover only in the final step to combine already diversified individuals. The insights provided by our analysis contribute to a deeper theoretical understanding of the role of crossover in the population dynamics of genetic algorithms.