Deep reinforcement learning (DRL) has been widely used for dynamic algorithm configuration, particularly in evolutionary computation, which benefits from the adaptive update of parameters during the algorithmic execution. However, applying DRL to algorithm configuration for multi-objective combinatorial optimization (MOCO) problems remains relatively unexplored. This paper presents a novel graph neural network (GNN) based DRL to configure multi-objective evolutionary algorithms. We model the dynamic algorithm configuration as a Markov decision process, representing the convergence of solutions in the objective space by a graph, with their embeddings learned by a GNN to enhance the state representation. Experiments on diverse MOCO challenges indicate that our method outperforms traditional and DRL-based algorithm configuration methods in terms of efficacy and adaptability. It also exhibits advantageous generalizability across objective types and problem sizes, and applicability to different evolutionary computation methods.
Multi-objective reinforcement learning (MORL) addresses the challenge of simultaneously optimizing multiple, often conflicting, rewards, moving beyond the single-reward focus of conventional reinforcement learning (RL). This approach is essential for applications where agents must balance trade-offs between diverse goals, such as speed, energy efficiency, or stability, as a series of sequential decisions. This paper investigates the applicability and limitations of multi-objective evolutionary algorithms (MOEAs) in solving complex MORL problems. We assess whether these algorithms can effectively address the unique challenges posed by MORL and how MORL instances can serve as benchmarks to evaluate and improve MOEA performance. In particular, we propose a framework to characterize the features influencing MORL instance complexity, select representative MORL problems from the literature, and benchmark a suite of MOEAs alongside single-objective EAs using scalarized MORL formulations. Additionally, we evaluate the utility of existing multi-objective quality indicators in MORL scenarios, such as hypervolume conducting a comparison of the algorithms supported by statistical analysis. Our findings provide insights into the interplay between MORL problem characteristics and algorithmic effectiveness, highlighting opportunities for advancing both MORL research and the design of evolutionary algorithms.
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.
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.
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.
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.
NSGA-III is one of the most widely adopted algorithms for tackling many-objective optimization problems. However, its CPU-based design severely limits scalability and computational efficiency. To address the limitations, we propose {TensorNSGA-III}, a fully tensorized implementation of NSGA-III that leverages GPU parallelism for large-scale many-objective optimization. Unlike conventional GPU-accelerated evolutionary algorithms that rely on heuristic approximations to improve efficiency, TensorNSGA-III maintains the exact selection and variation mechanisms of NSGA-III while achieving significant acceleration. By reformulating the selection process with tensorized data structures and an optimized caching strategy, our approach effectively eliminates computational bottlenecks inherent in traditional CPU-based and na\"ive GPU implementations. Experimental results on widely used numerical benchmarks show that TensorNSGA-III achieves speedups of up to $3629\times$ over the CPU version of NSGA-III. Additionally, we validate its effectiveness in multiobjective robotic control tasks, where it discovers diverse and high-quality behavioral solutions. Furthermore, we investigate the critical role of large population sizes in many-objective optimization and demonstrate the scalability of TensorNSGA-III in such scenarios. The source code is available at https://github.com/EMI-Group/evomo
Brain-body co-optimization suffers from fragile co-adaptation where brains become over-specialized for particular bodies, hindering their ability to transfer well to others. Evolutionary algorithms tend to discard such low-performing solutions, eliminating promising morphologies. Previous work considered applying MAP-Elites, where niche descriptors are based on morphological features, to promote better search over morphology space. In this work, we show that this approach still suffers from fragile co-adaptation: where a core mechanism of MAP-Elites, creating stepping stones through solutions that migrate from one niche to another, is disrupted. We suggest that this disruption occurs because the body mutations that move an offspring to a new morphological niche break the robots' fragile brain-body co-adaptation and thus significantly decrease the performance of those potential solutions -- reducing their likelihood of outcompeting an existing elite in that new niche. We utilize a technique, we call Pollination, that periodically replaces the controllers of certain solutions with a distilled controller with better generalization across morphologies to reduce fragile brain-body co-adaptation and thus promote MAP-Elites migrations. Pollination increases the success of body mutations and the number of migrations, resulting in better quality-diversity metrics. We believe we develop important insights that could apply to other domains where MAP-Elites is used.
Policy optimization seeks the best solution to a control problem according to an objective or fitness function, serving as a fundamental field of engineering and research with applications in robotics. Traditional optimization methods like reinforcement learning and evolutionary algorithms struggle with deceptive fitness landscapes, where following immediate improvements leads to suboptimal solutions. Quality-diversity (QD) algorithms offer a promising approach by maintaining diverse intermediate solutions as stepping stones for escaping local optima. However, QD algorithms require domain expertise to define hand-crafted features, limiting their applicability where characterizing solution diversity remains unclear. In this paper, we show that unsupervised QD algorithms - specifically the AURORA framework, which learns features from sensory data - efficiently solve deceptive optimization problems without domain expertise. By enhancing AURORA with contrastive learning and periodic extinction events, we propose AURORA-XCon, which outperforms all traditional optimization baselines and matches, in some cases even improving by up to 34%, the best QD baseline with domain-specific hand-crafted features. This work establishes a novel application of unsupervised QD algorithms, shifting their focus from discovering novel solutions toward traditional optimization and expanding their potential to domains where defining feature spaces poses challenges.
In recent years, there has been a growing interest in data-driven evolutionary algorithms (DDEAs) employing surrogate models to approximate the objective functions with limited data. However, current DDEAs are primarily designed for lower-dimensional problems and their performance drops significantly when applied to large-scale optimization problems (LSOPs). To address the challenge, this paper proposes an offline DDEA named DSKT-DDEA. DSKT-DDEA leverages multiple islands that utilize different data to establish diverse surrogate models, fostering diverse subpopulations and mitigating the risk of premature convergence. In the intra-island optimization phase, a semi-supervised learning method is devised to fine-tune the surrogates. It not only facilitates data argumentation, but also incorporates the distribution information gathered during the search process to align the surrogates with the evolving local landscapes. Then, in the inter-island knowledge transfer phase, the algorithm incorporates an adaptive strategy that periodically transfers individual information and evaluates the transfer effectiveness in the new environment, facilitating global optimization efficacy. Experimental results demonstrate that our algorithm is competitive with state-of-the-art DDEAs on problems with up to 1000 dimensions, while also exhibiting decent parallelism and scalability. Our DSKT-DDEA is open-source and accessible at: https://github.com/LabGong/DSKT-DDEA.
Evolutionary Algorithms (EAs) employ random or simplistic selection methods, limiting their exploration of solution spaces and convergence to optimal solutions. The randomness in performing crossover or mutations may limit the model's ability to evolve efficiently. This paper introduces Preference-Aligned Individual Reciprocity (PAIR), a novel selection approach leveraging Large Language Models to emulate human-like mate selection, thereby introducing intelligence to the pairing process in EAs. PAIR prompts an LLM to evaluate individuals within a population based on genetic diversity, fitness level, and crossover compatibility, guiding more informed pairing decisions. We evaluated PAIR against a baseline method called LLM-driven EA (LMEA), published recently. Results indicate that PAIR significantly outperforms LMEA across various TSP instances, achieving lower optimality gaps and improved convergence. This performance is especially noticeable when combined with the flash thinking model, demonstrating increased population diversity to escape local optima. In general, PAIR provides a new strategy in the area of in-context learning for LLM-driven selection in EAs via sophisticated preference modelling, paving the way for improved solutions and further studies into LLM-guided optimization.
Data increasingly abounds, but distilling their underlying relationships down to something interpretable remains challenging. One approach is genetic programming, which `symbolically regresses' a data set down into an equation. However, symbolic regression (SR) faces the issue of requiring training from scratch for each new dataset. To generalize across all datasets, deep learning techniques have been applied to SR. These networks, however, are only able to be trained using a symbolic objective: NN-generated and target equations are symbolically compared. But this does not consider the predictive power of these equations, which could be measured by a behavioral objective that compares the generated equation's predictions to actual data. Here we introduce a method that combines gradient descent and evolutionary computation to yield neural networks that minimize the symbolic and behavioral errors of the equations they generate from data. As a result, these evolved networks are shown to generate more symbolically and behaviorally accurate equations than those generated by networks trained by state-of-the-art gradient based neural symbolic regression methods. We hope this method suggests that evolutionary algorithms, combined with gradient descent, can improve SR results by yielding equations with more accurate form and function.
To fully leverage the capabilities of diffusion models, we are often interested in optimizing downstream reward functions during inference. While numerous algorithms for reward-guided generation have been recently proposed due to their significance, current approaches predominantly focus on single-shot generation, transitioning from fully noised to denoised states. We propose a novel framework for inference-time reward optimization with diffusion models inspired by evolutionary algorithms. Our approach employs an iterative refinement process consisting of two steps in each iteration: noising and reward-guided denoising. This sequential refinement allows for the gradual correction of errors introduced during reward optimization. Besides, we provide a theoretical guarantee for our framework. Finally, we demonstrate its superior empirical performance in protein and cell-type-specific regulatory DNA design. The code is available at \href{https://github.com/masa-ue/ProDifEvo-Refinement}{https://github.com/masa-ue/ProDifEvo-Refinement}.
Quality-Diversity is a family of evolutionary algorithms that generate diverse, high-performing solutions through local competition principles inspired by natural evolution. While research has focused on improving specific aspects of Quality-Diversity algorithms, surprisingly little attention has been paid to investigating alternative formulations of local competition itself -- the core mechanism distinguishing Quality-Diversity from traditional evolutionary algorithms. Most approaches implement local competition through explicit collection mechanisms like fixed grids or unstructured archives, imposing artificial constraints that require predefined bounds or hard-to-tune parameters. We show that Quality-Diversity methods can be reformulated as Genetic Algorithms where local competition occurs through fitness transformations rather than explicit collection mechanisms. Building on this insight, we introduce Dominated Novelty Search, a Quality-Diversity algorithm that implements local competition through dynamic fitness transformations, eliminating the need for predefined bounds or parameters. Our experiments show that Dominated Novelty Search significantly outperforms existing approaches across standard Quality-Diversity benchmarks, while maintaining its advantage in challenging scenarios like high-dimensional and unsupervised spaces.
The search for symbolic regression models with genetic programming (GP) has a tendency of revisiting expressions in their original or equivalent forms. Repeatedly evaluating equivalent expressions is inefficient, as it does not immediately lead to better solutions. However, evolutionary algorithms require diversity and should allow the accumulation of inactive building blocks that can play an important role at a later point. The equality graph is a data structure capable of compactly storing expressions and their equivalent forms allowing an efficient verification of whether an expression has been visited in any of their stored equivalent forms. We exploit the e-graph to adapt the subtree operators to reduce the chances of revisiting expressions. Our adaptation, called eggp, stores every visited expression in the e-graph, allowing us to filter out from the available selection of subtrees all the combinations that would create already visited expressions. Results show that, for small expressions, this approach improves the performance of a simple GP algorithm to compete with PySR and Operon without increasing computational cost. As a highlight, eggp was capable of reliably delivering short and at the same time accurate models for a selected set of benchmarks from SRBench and a set of real-world datasets.
Evolutionary Reinforcement Learning (EvoRL) has emerged as a promising approach to overcoming the limitations of traditional reinforcement learning (RL) by integrating the Evolutionary Computation (EC) paradigm with RL. However, the population-based nature of EC significantly increases computational costs, thereby restricting the exploration of algorithmic design choices and scalability in large-scale settings. To address this challenge, we introduce $\texttt{$\textbf{EvoRL}$}$, the first end-to-end EvoRL framework optimized for GPU acceleration. The framework executes the entire training pipeline on accelerators, including environment simulations and EC processes, leveraging hierarchical parallelism through vectorization and compilation techniques to achieve superior speed and scalability. This design enables the efficient training of large populations on a single machine. In addition to its performance-oriented design, $\texttt{$\textbf{EvoRL}$}$ offers a comprehensive platform for EvoRL research, encompassing implementations of traditional RL algorithms (e.g., A2C, PPO, DDPG, TD3, SAC), Evolutionary Algorithms (e.g., CMA-ES, OpenES, ARS), and hybrid EvoRL paradigms such as Evolutionary-guided RL (e.g., ERL, CEM-RL) and Population-Based AutoRL (e.g., PBT). The framework's modular architecture and user-friendly interface allow researchers to seamlessly integrate new components, customize algorithms, and conduct fair benchmarking and ablation studies. The project is open-source and available at: https://github.com/EMI-Group/evorl.
Vision systems in nature show remarkable diversity, from simple light-sensitive patches to complex camera eyes with lenses. While natural selection has produced these eyes through countless mutations over millions of years, they represent just one set of realized evolutionary paths. Testing hypotheses about how environmental pressures shaped eye evolution remains challenging since we cannot experimentally isolate individual factors. Computational evolution offers a way to systematically explore alternative trajectories. Here we show how environmental demands drive three fundamental aspects of visual evolution through an artificial evolution framework that co-evolves both physical eye structure and neural processing in embodied agents. First, we demonstrate computational evidence that task specific selection drives bifurcation in eye evolution - orientation tasks like navigation in a maze leads to distributed compound-type eyes while an object discrimination task leads to the emergence of high-acuity camera-type eyes. Second, we reveal how optical innovations like lenses naturally emerge to resolve fundamental tradeoffs between light collection and spatial precision. Third, we uncover systematic scaling laws between visual acuity and neural processing, showing how task complexity drives coordinated evolution of sensory and computational capabilities. Our work introduces a novel paradigm that illuminates evolutionary principles shaping vision by creating targeted single-player games where embodied agents must simultaneously evolve visual systems and learn complex behaviors. Through our unified genetic encoding framework, these embodied agents serve as next-generation hypothesis testing machines while providing a foundation for designing manufacturable bio-inspired vision systems. Website: http://eyes.mit.edu/
This study compares three evolutionary algorithms for the problem of fog service placement: weighted sum genetic algorithm (WSGA), non-dominated sorting genetic algorithm II (NSGA-II), and multiobjective evolutionary algorithm based on decomposition (MOEA/D). A model for the problem domain (fog architecture and fog applications) and for the optimization (objective functions and solutions) is presented. Our main concerns are related to optimize the network latency, the service spread and the use of the resources. The algorithms are evaluated with a random Barabasi-Albert network topology with 100 devices and with two experiment sizes of 100 and 200 application services. The results showed that NSGA-II obtained the highest optimizations of the objectives and the highest diversity of the solution space. On the contrary, MOEA/D was better to reduce the execution times. The WSGA algorithm did not show any benefit with regard to the other two algorithms.
Glioblastoma, a highly aggressive brain tumor, poses major challenges due to its poor prognosis and high morbidity rates. Partial differential equation-based models offer promising potential to enhance therapeutic outcomes by simulating patient-specific tumor behavior for improved radiotherapy planning. However, model calibration remains a bottleneck due to the high computational demands of optimization methods like Monte Carlo sampling and evolutionary algorithms. To address this, we recently introduced an approach leveraging a neural forward solver with gradient-based optimization to significantly reduce calibration time. This approach requires a highly accurate and fully differentiable forward model. We investigate multiple architectures, including (i) an enhanced TumorSurrogate, (ii) a modified nnU-Net, and (iii) a 3D Vision Transformer (ViT). The optimized TumorSurrogate achieved the best overall results, excelling in both tumor outline matching and voxel-level prediction of tumor cell concentration. It halved the MSE relative to the baseline model and achieved the highest Dice score across all tumor cell concentration thresholds. Our study demonstrates significant enhancement in forward solver performance and outlines important future research directions.
Solving NP-hard problems traditionally relies on heuristics, yet manually designing effective heuristics for complex problems remains a significant challenge. While recent advancements like FunSearch have shown that large language models (LLMs) can be integrated into evolutionary algorithms (EAs) for heuristic design, their potential is hindered by limitations in balancing exploitation and exploration. We introduce Quality-Uncertainty Balanced Evolution (QUBE), a novel approach that enhances LLM+EA methods by redefining the priority criterion within the FunSearch framework. QUBE employs the Quality-Uncertainty Trade-off Criterion (QUTC), based on our proposed Uncertainty-Inclusive Quality metric, to evaluate and guide the evolutionary process. Through extensive experiments on challenging NP-complete problems, QUBE demonstrates significant performance improvements over FunSearch and baseline methods. Our code are available at https://github.com/zzjchen/QUBE_code.