Learning in games is a fundamental problem in machine learning and artificial intelligence, with numerous applications~\citep{silver2016mastering,schrittwieser2020mastering}. This work investigates two-player zero-sum matrix games with an unknown payoff matrix and bandit feedback, where each player observes their actions and the corresponding noisy payoff. Prior studies have proposed algorithms for this setting~\citep{o2021matrix,maiti2023query,cai2024uncoupled}, with \citet{o2021matrix} demonstrating the effectiveness of deterministic optimism (e.g., \ucb) in achieving sublinear regret. However, the potential of randomised optimism in matrix games remains theoretically unexplored. We propose Competitive Co-evolutionary Bandit Learning (\coebl), a novel algorithm that integrates evolutionary algorithms (EAs) into the bandit framework to implement randomised optimism through EA variation operators. We prove that \coebl achieves sublinear regret, matching the performance of deterministic optimism-based methods. To the best of our knowledge, this is the first theoretical regret analysis of an evolutionary bandit learning algorithm in matrix games. Empirical evaluations on diverse matrix game benchmarks demonstrate that \coebl not only achieves sublinear regret but also consistently outperforms classical bandit algorithms, including \exptr~\citep{auer2002nonstochastic}, the variant \exptrni~\citep{cai2024uncoupled}, and \ucb~\citep{o2021matrix}. These results highlight the potential of evolutionary bandit learning, particularly the efficacy of randomised optimism via evolutionary algorithms in game-theoretic settings.
It is well known that evolutionary algorithms can benefit from dynamic choices of the key parameters that control their behavior, to adjust their search strategy to the different stages of the optimization process. A prominent example where dynamic parameter choices have shown a provable super-constant speed-up is the $(1+(\lambda,\lambda))$ Genetic Algorithm optimizing the OneMax function. While optimal parameter control policies result in linear expected running times, this is not possible with static parameter choices. This result has spurred a lot of interest in parameter control policies. However, many works, in particular theoretical running time analyses, focus on controlling one single parameter. Deriving policies for controlling multiple parameters remains very challenging. In this work we reconsider the problem of the $(1+(\lambda,\lambda))$ Genetic Algorithm optimizing OneMax. We decouple its four main parameters and investigate how well state-of-the-art deep reinforcement learning techniques can approximate good control policies. We show that although making deep reinforcement learning learn effectively is a challenging task, once it works, it is very powerful and is able to find policies that outperform all previously known control policies on the same benchmark. Based on the results found through reinforcement learning, we derive a simple control policy that consistently outperforms the default theory-recommended setting by $27\%$ and the irace-tuned policy, the strongest existing control policy on this benchmark, by $13\%$, for all tested problem sizes up to $40{,}000$.
Model merging allows combining the capabilities of existing models into a new one - post hoc, without additional training. This has made it increasingly popular thanks to its low cost and the availability of libraries that support merging on consumer GPUs. Recent work shows that pairing merging with evolutionary algorithms can boost performance, but no framework currently supports flexible experimentation with such strategies in language models. We introduce Mergenetic, an open-source library for evolutionary model merging. Mergenetic enables easy composition of merging methods and evolutionary algorithms while incorporating lightweight fitness estimators to reduce evaluation costs. We describe its design and demonstrate that Mergenetic produces competitive results across tasks and languages using modest hardware.
Graph-structured combinatorial problems in complex networks are prevalent in many domains, and are computationally demanding due to their complexity and non-linear nature. Traditional evolutionary algorithms (EAs), while robust, often face obstacles due to content-shallow encoding limitations and lack of structural awareness, necessitating hand-crafted modifications for effective application. In this work, we introduce an original framework, Visual Evolutionary Optimization (VEO), leveraging multimodal large language models (MLLMs) as the backbone evolutionary optimizer in this context. Specifically, we propose a context-aware encoding way, representing the solution of the network as an image. In this manner, we can utilize MLLMs' image processing capabilities to intuitively comprehend network configurations, thus enabling machines to solve these problems in a human-like way. We have developed MLLM-based operators tailored for various evolutionary optimization stages, including initialization, crossover, and mutation. Furthermore, we propose that graph sparsification can effectively enhance the applicability and scalability of VEO on large-scale networks, owing to the scale-free nature of real-world networks. We demonstrate the effectiveness of our method using a well-known task in complex networks, influence maximization, and validate it on eight different real-world networks of various structures. The results have confirmed VEO's reliability and enhanced effectiveness compared to traditional evolutionary optimization.
Large Language Models (LLMs) have unveiled remarkable capabilities in understanding and generating both natural language and code, but LLM reasoning is prone to hallucination and struggle with complex, novel scenarios, often getting stuck on partial or incorrect solutions. However, the inherent ability of Evolutionary Algorithms (EAs) to explore extensive and complex search spaces makes them particularly effective in scenarios where traditional optimization methodologies may falter. However, EAs explore a vast search space when applied to complex problems. To address the computational bottleneck of evaluating large populations, particularly crucial for complex evolutionary tasks, we introduce a highly efficient evaluation framework. This implementation maintains compatibility with existing primitive definitions, ensuring the generation of valid individuals. Using LLMs, we propose an enhanced evolutionary search strategy that enables a more focused exploration of expansive solution spaces. LLMs facilitate the generation of superior candidate solutions, as evidenced by empirical results demonstrating their efficacy in producing improved outcomes.
Together with the NSGA-II and SMS-EMOA, the strength Pareto evolutionary algorithm 2 (SPEA2) is one of the most prominent dominance-based multi-objective evolutionary algorithms (MOEAs). Different from the NSGA-II, it does not employ the crowding distance (essentially the distance to neighboring solutions) to compare pairwise non-dominating solutions but a complex system of $\sigma$-distances that builds on the distances to all other solutions. In this work, we give a first mathematical proof showing that this more complex system of distances can be superior. More specifically, we prove that a simple steady-state SPEA2 can compute optimal approximations of the Pareto front of the OneMinMax benchmark in polynomial time. The best proven guarantee for a comparable variant of the NSGA-II only assures approximation ratios of roughly a factor of two, and both mathematical analyses and experiments indicate that optimal approximations are not found efficiently.
The chance constrained travelling thief problem (chance constrained TTP) has been introduced as a stochastic variation of the classical travelling thief problem (TTP) in an attempt to embody the effect of uncertainty in the problem definition. In this work, we characterise the chance constrained TTP using a limited number of weighted scenarios. Each scenario represents a similar TTP instance, differing slightly in the weight profile of the items and associated with a certain probability of occurrence. Collectively, the weighted scenarios represent a relaxed form of a stochastic TTP instance where the objective is to maximise the expected benefit while satisfying the knapsack constraint with a larger probability. We incorporate a set of evolutionary algorithms and heuristic procedures developed for the classical TTP, and formulate adaptations that apply to the weighted scenario-based representation of the problem. The analysis focuses on the performance of the algorithms on different settings and examines the impact of uncertainty on the quality of the solutions.
Black-box discrete optimization (BB-DO) problems arise in many real-world applications, such as neural architecture search and mathematical model estimation. A key challenge in BB-DO is epistasis among parameters where multiple variables must be modified simultaneously to effectively improve the objective function. Estimation of Distribution Algorithms (EDAs) provide a powerful framework for tackling BB-DO problems. In particular, an EDA leveraging a Variational Autoencoder (VAE) has demonstrated strong performance on relatively low-dimensional problems with epistasis while reducing computational cost. Meanwhile, evolutionary algorithms such as DSMGA-II and P3, which integrate bit-flip-based local search with linkage learning, have shown excellent performance on high-dimensional problems. In this study, we propose a new memetic algorithm that combines VAE-based sampling with local search. The proposed method inherits the strengths of both VAE-based EDAs and local search-based approaches: it effectively handles high-dimensional problems with epistasis among parameters without incurring excessive computational overhead. Experiments on NK landscapes -- a challenging benchmark for BB-DO involving epistasis among parameters -- demonstrate that our method outperforms state-of-the-art VAE-based EDA methods, as well as leading approaches such as P3 and DSMGA-II.
Generative Adversarial Networks (GANs) are very useful methods to address semi-supervised learning (SSL) datasets, thanks to their ability to generate samples similar to real data. This approach, called SSL-GAN has attracted many researchers in the last decade. Evolutionary algorithms have been used to guide the evolution and training of SSL-GANs with great success. In particular, several co-evolutionary approaches have been applied where the two networks of a GAN (the generator and the discriminator) are evolved in separate populations. The co-evolutionary approaches published to date assume some spatial structure of the populations, based on the ideas of cellular evolutionary algorithms. They also create one single individual per generation and follow a generational replacement strategy in the evolution. In this paper, we re-consider those algorithmic design decisions and propose a new co-evolutionary approach, called Co-evolutionary Elitist SSL-GAN (CE-SSLGAN), with panmictic population, elitist replacement, and more than one individual in the offspring. We evaluate the performance of our proposed method using three standard benchmark datasets. The results show that creating more than one offspring per population and using elitism improves the results in comparison with a classical SSL-GAN.
Evolutionary algorithms often struggle to find well converged (e.g small inverted generational distance on test problems) solutions to multi-objective optimization problems on a limited budget of function evaluations (here, a few hundred). The family of surrogate-assisted evolutionary algorithms (SAEAs) offers a potential solution to this shortcoming through the use of data driven models which augment evaluations of the objective functions. A surrogate model which has shown promise in single-objective optimization is to predict the "comparison relationship" between pairs of solutions (i.e. who's objective function is smaller). In this paper, we investigate the performance of this model on multi-objective optimization problems. First, we propose a new algorithm "CRSEA" which uses the comparison-relationship model. Numerical experiments are then performed with the DTLZ and WFG test suites plus a real-world problem from the field of accelerator physics. We find that CRSEA finds better converged solutions than the tested SAEAs on many of the medium-scale, biobjective problems chosen from the WFG suite suggesting the comparison-relationship surrogate as a promising tool for improving the efficiency of multi-objective optimization algorithms.
Neural Architecture Search (NAS) has gained widespread attention for its transformative potential in deep learning model design. However, the vast and complex search space of NAS leads to significant computational and time costs. Neural Architecture Generation (NAG) addresses this by reframing NAS as a generation problem, enabling the precise generation of optimal architectures for specific tasks. Despite its promise, mainstream methods like diffusion models face limitations in global search capabilities and are still hindered by high computational and time demands. To overcome these challenges, we propose Evolutionary Diffusion-based Neural Architecture Generation (EDNAG), a novel approach that achieves efficient and training-free architecture generation. EDNAG leverages evolutionary algorithms to simulate the denoising process in diffusion models, using fitness to guide the transition from random Gaussian distributions to optimal architecture distributions. This approach combines the strengths of evolutionary strategies and diffusion models, enabling rapid and effective architecture generation. Extensive experiments demonstrate that EDNAG achieves state-of-the-art (SOTA) performance in architecture optimization, with an improvement in accuracy of up to 10.45%. Furthermore, it eliminates the need for time-consuming training and boosts inference speed by an average of 50 times, showcasing its exceptional efficiency and effectiveness.
Symbolic regression is a technique that can automatically derive analytic models from data. Traditionally, symbolic regression has been implemented primarily through genetic programming that evolves populations of candidate solutions sampled by genetic operators, crossover and mutation. More recently, neural networks have been employed to learn the entire analytical model, i.e., its structure and coefficients, using regularized gradient-based optimization. Although this approach tunes the model's coefficients better, it is prone to premature convergence to suboptimal model structures. Here, we propose a neuro-evolutionary symbolic regression method that combines the strengths of evolutionary-based search for optimal neural network (NN) topologies with gradient-based tuning of the network's parameters. Due to the inherent high computational demand of evolutionary algorithms, it is not feasible to learn the parameters of every candidate NN topology to full convergence. Thus, our method employs a memory-based strategy and population perturbations to enhance exploitation and reduce the risk of being trapped in suboptimal NNs. In this way, each NN topology can be trained using only a short sequence of backpropagation iterations. The proposed method was experimentally evaluated on three real-world test problems and has been shown to outperform other NN-based approaches regarding the quality of the models obtained.
The energy transition is driving rapid growth in renewable energy generation, creating the need to balance energy supply and demand with energy price awareness. One such approach for manufacturers to balance their energy demand with available energy is energyaware production planning. Through energy-aware production planning, manufacturers can align their energy demand with dynamic grid conditions, supporting renewable energy integration while benefiting from lower prices and reduced emissions. Energy-aware production planning can be modeled as a multi-criteria scheduling problem, where the objectives extend beyond traditional metrics like makespan or required workers to also include minimizing energy costs and emissions. Due to market dynamics and the NP-hard multi-objective nature of the problem, evolutionary algorithms are widely used for energy-aware scheduling. However, existing research focuses on the design and analysis of single algorithms, with limited comparisons between different approaches. In this study, we adapt NSGA-III, HypE, and $\theta$-DEA as memetic metaheuristics for energy-aware scheduling to minimize makespan, energy costs, emissions, and the number of workers, within a real-time energy market context. These adapted metaheuristics present different approaches for environmental selection. In a comparative analysis, we explore differences in solution efficiency and quality across various scenarios which are based on benchmark instances from the literature and real-world energy market data. Additionally, we estimate upper bounds on the distance between objective values obtained with our memetic metaheuristics and reference sets obtained via an exact solver.
Compliant mechanisms achieve motion through elastic deformation. In this work, we address the synthesis of a compliant cross-hinge mechanism capable of large angular strokes while approximating the behavior of an ideal revolute joint. To capture the competing demands of kinematic fidelity, rotational stiffness, and resistance to parasitic motion, we formulate a multi-objective optimization problem based on kinetostatic performance measures. A hybrid design strategy is employed: an efficient beam-based structural model enables extensive exploration of a high-dimensional design space using evolutionary algorithms, followed by fine-tuning with high-fidelity three-dimensional finite element analysis. The resulting Pareto-optimal designs reveal diverse geometric configurations and performance trade-offs.
Different from single-objective evolutionary algorithms, where non-elitism is an established concept, multi-objective evolutionary algorithms almost always select the next population in a greedy fashion. In the only notable exception, Bian, Zhou, Li, and Qian (IJCAI 2023) proposed a stochastic selection mechanism for the SMS-EMOA and proved that it can speed up computing the Pareto front of the bi-objective jump benchmark with problem size $n$ and gap parameter $k$ by a factor of $\max\{1,2^{k/4}/n\}$. While this constitutes the first proven speed-up from non-elitist selection, suggesting a very interesting research direction, it has to be noted that a true speed-up only occurs for $k \ge 4\log_2(n)$, where the runtime is super-polynomial, and that the advantage reduces for larger numbers of objectives as shown in a later work. In this work, we propose a different non-elitist selection mechanism based on aging, which exempts individuals younger than a certain age from a possible removal. This remedies the two shortcomings of stochastic selection: We prove a speed-up by a factor of $\max\{1,\Theta(k)^{k-1}\}$, regardless of the number of objectives. In particular, a positive speed-up can already be observed for constant $k$, the only setting for which polynomial runtimes can be witnessed. Overall, this result supports the use of non-elitist selection schemes, but suggests that aging-based mechanisms can be considerably more powerful than stochastic selection mechanisms.
This paper focuses on the problem of evolving Boolean functions of odd sizes with high nonlinearity, a property of cryptographic relevance. Despite its simple formulation, this problem turns out to be remarkably difficult. We perform a systematic evaluation by considering three solution encodings and four problem instances, analyzing how well different types of evolutionary algorithms behave in finding a maximally nonlinear Boolean function. Our results show that genetic programming generally outperforms other evolutionary algorithms, although it falls short of the best-known results achieved by ad-hoc heuristics. Interestingly, by adding local search and restricting the space to rotation symmetric Boolean functions, we show that a genetic algorithm with the bitstring encoding manages to evolve a $9$-variable Boolean function with nonlinearity 241.
High-level synthesis (HLS) design space exploration (DSE) is an optimization process in electronic design automation (EDA) that systematically explores high-level design configurations to achieve Pareto-optimal hardware implementations balancing performance, area, and power (PPA). To optimize this process, HLS prediction tasks often employ message-passing neural networks (MPNNs), leveraging complex architectures to achieve high accuracy. These predictors serve as evaluators in the DSE process, effectively bypassing the time-consuming estimations traditionally required by HLS tools. However, existing models often prioritize structural complexity and minimization of training loss, overlooking task-specific characteristics. Additionally, while evolutionary algorithms are widely used in DSE, they typically require extensive domain-specific knowledge to design effective crossover and mutation operators. To address these limitations, we propose CoGNNs-LLMEA, a framework that integrates a graph neural network with task-adaptive message passing and a large language model-enhanced evolutionary algorithm. As a predictive model, CoGNNs directly leverages intermediate representations generated from source code after compiler front-end processing, enabling prediction of quality of results (QoR) without invoking HLS tools. Due to its strong adaptability to tasks, CoGNNs can be tuned to predict post-HLS and post-implementation outcomes, effectively bridging the gap between high-level abstractions and physical implementation characteristics. CoGNNs achieves state-of-the-art prediction accuracy in post-HLS QoR prediction, reducing mean prediction errors by 2.8$\times$ for latency and 3.4$\times$ for resource utilization compared to baseline models.
Large Language Models (LLMs) exhibit remarkable capabilities but are susceptible to adversarial prompts that exploit vulnerabilities to produce unsafe or biased outputs. Existing red-teaming methods often face scalability challenges, resource-intensive requirements, or limited diversity in attack strategies. We propose RainbowPlus, a novel red-teaming framework rooted in evolutionary computation, enhancing adversarial prompt generation through an adaptive quality-diversity (QD) search that extends classical evolutionary algorithms like MAP-Elites with innovations tailored for language models. By employing a multi-element archive to store diverse high-quality prompts and a comprehensive fitness function to evaluate multiple prompts concurrently, RainbowPlus overcomes the constraints of single-prompt archives and pairwise comparisons in prior QD methods like Rainbow Teaming. Experiments comparing RainbowPlus to QD methods across six benchmark datasets and four open-source LLMs demonstrate superior attack success rate (ASR) and diversity (Diverse-Score $\approx 0.84$), generating up to 100 times more unique prompts (e.g., 10,418 vs. 100 for Ministral-8B-Instruct-2410). Against nine state-of-the-art methods on the HarmBench dataset with twelve LLMs (ten open-source, two closed-source), RainbowPlus achieves an average ASR of 81.1%, surpassing AutoDAN-Turbo by 3.9%, and is 9 times faster (1.45 vs. 13.50 hours). Our open-source implementation fosters further advancements in LLM safety, offering a scalable tool for vulnerability assessment. Code and resources are publicly available at https://github.com/knoveleng/rainbowplus, supporting reproducibility and future research in LLM red-teaming.
Several mating restriction techniques have been implemented in Evolutionary Algorithms to promote diversity. From similarity-based selection to niche preservation, the general goal is to avoid premature convergence by not having fitness pressure as the single evolutionary force. In a way, such methods can resemble the mechanisms involved in Sexual Selection, although generally assuming a simplified approach. Recently, a selection method called mating Preferences as Ideal Mating Partners (PIMP) has been applied to GP, providing promising results both in performance and diversity maintenance. The method mimics Mate Choice through the unbounded evolution of personal preferences rather than having a single set of rules to shape parent selection. As such, PIMP allows ideal mate representations to evolve freely, thus potentially taking advantage of Sexual Selection as a dynamic secondary force to fitness pressure. However, it is still unclear how mating preferences affect the overall population and how dependent they are on set-up choices. In this work, we tracked the evolution of individual preferences through different mutation types, searching for patterns and evidence of self-reinforcement. Results suggest that mating preferences do not stand on their own, relying on subtree mutation to avoid convergence to single-node trees. Nevertheless, they consistently promote smaller and more balanced solutions depth-wise than a standard tournament selection, reducing the impact of bloat. Furthermore, when coupled with subtree mutation it also results in more solution diversity with statistically significant results.
Multi-modal optimization involves identifying multiple global and local optima of a function, offering valuable insights into diverse optimal solutions within the search space. Evolutionary algorithms (EAs) excel at finding multiple solutions in a single run, providing a distinct advantage over classical optimization techniques that often require multiple restarts without guarantee of obtaining diverse solutions. Among these EAs, differential evolution (DE) stands out as a powerful and versatile optimizer for continuous parameter spaces. DE has shown significant success in multi-modal optimization by utilizing its population-based search to promote the formation of multiple stable subpopulations, each targeting different optima. Recent advancements in DE for multi-modal optimization have focused on niching methods, parameter adaptation, hybridization with other algorithms including machine learning, and applications across various domains. Given these developments, it is an opportune moment to present a critical review of the latest literature and identify key future research directions. This paper offers a comprehensive overview of recent DE advancements in multimodal optimization, including methods for handling multiple optima, hybridization with EAs, and machine learning, and highlights a range of real-world applications. Additionally, the paper outlines a set of compelling open problems and future research issues from multiple perspectives