evolutionary algorithms

Evolutionary computation and bio-inspired optimization suffer from insufficient benchmarking, severe overfitting, weak theoretical foundations, and ineffective “biological metaphor-driven” innovation. This paper systematically diagnoses the methodological crisis in the field and proposes a rigorous, problem-solving–oriented research paradigm. Methodologically, it introduces a structured guideline covering algorithm design, experimental evaluation, and novel proposal generation; establishes a reproducible framework integrating metaheuristic assessment, experimental design modeling, and automated algorithm synthesis; and emphasizes theoretical grounding, empirical validation, and practical applicability. The core contribution is a paradigm shift—from metaphor-centric heuristics toward theoretically sound, empirically robust, and problem-driven science—thereby establishing new standards for verifiable, reproducible, and performance-oriented research in evolutionary computation.

Multi-objective optimization requires simultaneously ensuring solution quality and inter-solution diversity; however, existing methods struggle to achieve optimal fitness under minimum distance constraints—and sometimes perform worse than random sampling. Method: We propose a cascaded CMA-ES framework that runs multiple CMA-ES instances in parallel, dynamically inherits forbidden regions to enforce spatial separation among solutions, and incorporates distance-aware trajectory optimization—enabling cooperative exploration of high-fitness, strictly separated solution batches without compromising single-solution optimality. Contribution/Results: This is the first CMA-ES-based co-optimization architecture to explicitly model and satisfy hard minimum distance constraints. On standard benchmarks, our method significantly outperforms random sampling, multimodal optimization algorithms, and vanilla CMA-ES in both solution quality and pairwise separation.

Existing research on Meta-Black-Box Optimization (MetaBBO) lacks systematic taxonomies and reproducible implementation guidance. Method: We propose the first unified MetaBBO paradigm, establishing a four-category task taxonomy—algorithm selection, configuration, operation, and generation—and integrate multi-paradigm methodologies including reinforcement learning, supervised learning, neural evolution, and large language model context learning to distill core design principles for enhancing generalization and learning efficiency. Contribution/Results: We conduct empirical evaluations of mainstream MetaBBO methods across performance, computational efficiency, and cross-task generalization. Furthermore, we release a structured practical guide and an actively maintained open-source repository (Awesome-MetaBBO), bridging the critical gap between theoretical unification and engineering deployment.

This study systematically evaluates the robustness and structural invariance of hybrid population-based metaheuristics under objective-space transformations—including translation, scaling, rotation, and composite deformations. We propose a lightweight, plug-and-play generic hybrid framework that seamlessly integrates 19 state-of-the-art algorithms and conduct comprehensive multi-dimensional comparative experiments on the CEC-2017 benchmark suite. Leveraging Wilcoxon and Friedman nonparametric tests, Bayesian dominance analysis, and convergence trajectory profiling, we find that DE-based hybrids (e.g., hIMODE, hSHADE) significantly outperform PSO- and bio-inspired methods in stability and invariance—particularly in high-dimensional, non-separable, and rotation/composite-deformation scenarios, where they maintain high accuracy and strong robustness. This work is the first to empirically uncover the intrinsic structural advantages of DE-family algorithms under geometric distortions, providing both theoretical foundations and practical design principles for optimization algorithms targeting complex, dynamically transforming environments.

Manual design of metaheuristic algorithms is time-consuming, inefficient, and structurally inflexible; existing automated approaches are constrained by fixed algorithmic templates and linear representations. Method: This paper proposes the first general-purpose automated design framework applicable to the entire family of metaheuristics. It introduces (1) a unified algorithmic prototype covering all metaheuristic variants; (2) a directed acyclic graph (DAG)-based representation enabling structural evolution; and (3) a compact yet expressive graph embedding and differentiable architecture encoding scheme. Integrating graph representation learning with evolutionary search, the framework enables end-to-end generation of diverse, nonlinear algorithmic structures. Results: Extensive evaluation on numerical optimization benchmarks and real-world tasks demonstrates that the automatically generated algorithms achieve superior efficiency, generalizability, and novelty compared to both human-designed and state-of-the-art automated methods.

This study addresses the limitation that existing improvement mechanisms for evolution strategies are typically investigated in isolation, with their interaction effects remaining underexplored. To this end, this work proposes a modular framework for Covariance Matrix Adaptation Evolution Strategy (CMA-ES). For the first time, core mechanisms such as sampling and adaptation are decoupled into interchangeable modules. By integrating automated algorithm configuration techniques, the framework enables systematic exploration of the algorithm design space and quantitative analysis of combinatorial effects. Experimental results validate the effectiveness and reproducibility of the proposed framework in terms of computational overhead, optimization performance, and customized benchmarking. Ultimately, this research establishes a novel paradigm for the modular design and automated tuning of evolutionary algorithms.

This work addresses the challenges in black-box optimization posed by heteroscedastic noise—namely, uncertain fitness evaluations, inaccurate solution ranking, and excessive computational cost—by introducing a confidence-driven dynamic sampling mechanism. The proposed approach integrates adaptive budget allocation and explicit averaging strategies within both CMA-ES and genetic algorithm frameworks. It further presents the first systematically constructed benchmark suite for heteroscedastic noise, thereby overcoming the conventional reliance on homoscedasticity and function smoothness assumptions. Experimental results demonstrate that the method consistently outperforms state-of-the-art algorithms under both homoscedastic and heteroscedastic noise conditions, achieving superior robustness and computational efficiency.

This study addresses the lack of theoretical foundation for parameter selection in the bat algorithm, which has traditionally relied on empirical tuning. For the first time, it integrates dynamical systems theory with population variance evolution analysis to construct a theoretical framework characterizing the influence of key parameters. Within this framework, analytically derived effective ranges for critical parameters are established. Numerical experiments confirm that the theoretical predictions align closely with the observed convergence behavior in practice. The work further uncovers the intrinsic mechanisms governing the trade-off between exploration and exploitation and the algorithm’s convergence properties, thereby providing the first systematic theoretical guidance for parameter configuration in the bat algorithm.

This work addresses the inefficiency of traditional genetic algorithms in solving optimization problems due to their reliance on random mutation and recombination, which lack goal-directedness. The authors formulate the problem through the lens of query complexity and propose objective-guided mutation and recombination operators informed by the optimization target. Leveraging reinforcement learning and formal language theory, they analyze the theoretical properties of these operators. For the first time, the study mathematically characterizes the mechanism of goal-directed genetic operators and demonstrates the necessity of population diversity for certain classes of optimization problems. A general model of genetic algorithms is established, enabling the design of a tight algorithm for a specific problem class, and proving that the synergy among generation, mutation, and recombination is essential for efficient optimization.

This study addresses the challenge of optimizing mixed-variable problems involving continuous, ordinal, and categorical variables simultaneously—a scenario where existing swarm intelligence algorithms often struggle. To this end, the authors propose a Firefly Algorithm for Mixed Variables (FAmv), which introduces a novel unified mixed-distance model to naturally and cohesively handle heterogeneous variable types. By redefining the attraction mechanism based on this distance model, FAmv achieves a more accurate representation of the search space while maintaining an effective balance between exploration and exploitation. Comprehensive experiments demonstrate that FAmv either outperforms or is competitive with state-of-the-art algorithms on the CEC2013 mixed-variable benchmark suite and several real-world engineering design problems, thereby confirming its efficacy and practical applicability.