differential evolution

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.

Standard differential evolution (DE) suffers from premature diversity loss due to fixed population size, while archive-based variants introduce significant implementation complexity. To address this, we propose Unbounded Differential Evolution (UDE): a paradigm that eliminates generational replacement and external archives entirely; instead, all generated individuals are retained in an unbounded population, and optimization is driven solely by selection operators—specifically, elitist preservation and diversity-aware sampling. UDE is the first DE framework that is fully replacement-free, archive-free, and devoid of dynamic population control, thereby establishing “pure selection” as a theoretically grounded and empirically effective pathway for black-box optimization. On the CEC benchmark suite, UDE demonstrates markedly improved convergence robustness and sustained diversity under limited evaluation budgets, consistently outperforming state-of-the-art archive-assisted DE variants.

Handcrafted design of differential evolution (DE) algorithms for black-box optimization suffers from strong reliance on expert knowledge and poor generalization across problems. Method: This paper proposes a reinforcement learning–based framework for automatic DE algorithm design, introducing a double deep Q-network (DDQN) as the meta-optimizer for the first time. The DDQN jointly learns initialization strategies, mutation/crossover operators, and hyperparameter configurations, supporting 40 distinct operator combinations and problem-feature-driven meta-learning. Contribution/Results: The framework enables fully automated, end-to-end customization of DE—breaking away from fixed variants and manual parameter tuning. Evaluated on standard black-box optimization benchmarks, it significantly outperforms state-of-the-art DE variants and advanced evolutionary algorithms, demonstrating superior effectiveness, adaptability, and cross-problem generalization capability.

Differential Evolution (DE) performance is highly sensitive to hyperparameter settings and mutation strategy selection, yet conventional tuning methods suffer from poor generalizability. To address this, we propose a self-referential optimization framework wherein DE dynamically evolves its own core parameters and mutation strategies at the meta-level, unifying the solver and configurator within a single adaptive mechanism. Our contributions include: (i) introducing the first self-evolving DE paradigm; (ii) designing a strategy-parameter co-adaptive dynamic adjustment mechanism; and (iii) integrating meta-level DE, GPU-accelerated parallelization, and evolutionary reinforcement learning. Empirical evaluation on the CEC2022 benchmark suite demonstrates statistically significant superiority over state-of-the-art DE variants. Furthermore, we validate strong generalizability and practical utility in real-world robotic control tasks, confirming robust cross-domain adaptability.

Non-convex, multimodal optimization on the Grassmann manifold (mathrm{Gr}(k,n)) poses significant challenges for conventional Riemannian first- and second-order methods, which often converge prematurely to poor local minima. Method: We propose the first differential evolution (DE)-based global optimization framework tailored to the Grassmann manifold. It employs QR decomposition for geometrically exact manifold projection, integrates adaptive control parameters, and introduces a manifold-aware mutation strategy—thereby balancing global exploration with intrinsic manifold structure preservation—while operating entirely without gradient information. Contribution/Results: Our approach overcomes the local convergence limitations inherent in standard Riemannian optimizers. Extensive experiments on subspace learning and low-rank matrix recovery demonstrate that it consistently outperforms state-of-the-art Riemannian optimization methods, achieving superior global convergence, robustness to initialization, and generalization across diverse problem instances.

To address the exploration-exploitation imbalance and inefficient utilization of historical evaluation data in evolutionary algorithms (EAs) for hyperparameter optimization (HPO), this paper proposes an enhanced genetic algorithm (GA) framework integrated with a lightweight linear surrogate model. The linear surrogate is seamlessly embedded into GA’s selection and mutation operators, enabling a population-driven hybrid search strategy and performance-feedback-driven adaptive model updating—without requiring gradient computation or expensive modeling overhead. This design dynamically balances global exploration and local exploitation. On standard HPO benchmarks, the method achieves an average performance improvement of 1.89% (range: −3.45% to +6.55%) over state-of-the-art approaches, with negligible increase in training cost. Its core contribution lies in the first structured integration of linear surrogates with genetic operations, achieving a favorable trade-off among efficiency, accuracy, and scalability.

This work proposes a development-biased restart differential evolution algorithm for single-objective numerical optimization under fixed-budget and bound-constrained settings. By integrating Success-History Based Adaptive Differential Evolution (SHADE), a hybrid branching mutation strategy, and lightweight local perturbations, the algorithm effectively balances exploration and exploitation within a limited number of function evaluations. Evaluated on 29 benchmark functions from the CEC 2025 suite using the U-score assessment framework, the proposed method demonstrates statistically significant superiority in both convergence speed and solution accuracy, offering a robust and efficient approach for computationally expensive optimization scenarios.

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 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 proposes GAReg, a unified genetic algorithm framework designed to address high-dimensional discrete regression optimization problems where traditional gradient-based methods fail due to non-differentiable, non-convex objective functions or the presence of numerous local optima. GAReg employs compact chromosome encoding, constraint-preserving crossover and mutation operators, a steady-state population update mechanism, and supports island-model parallelization. This approach effectively overcomes the computational bottlenecks of enumeration and dynamic programming in high-dimensional spaces. Experimental results demonstrate that GAReg efficiently explores the model space in scenarios where standard methods are inapplicable, yielding near-optimal solutions and significantly outperforming conventional approaches such as exhaustive search and integer programming.

This work addresses the persistent challenge in unconstrained single-objective numerical optimization of simultaneously achieving effective global exploration, efficient late-stage exploitation, and high evaluation efficiency. Building upon the RDEx framework, the authors propose a smooth, exploitation-biased branch rate update mechanism complemented by a budget-aware coordinate-pattern local search strategy. Through phased ablation studies and comprehensive U-score evaluation, they identify a conservative yet highly effective configuration for late-stage local search. The resulting algorithm substantially enhances both convergence speed and solution quality, improving the U-score from 33,602.0 to 37,448.0 (+11.45%). Furthermore, it outperforms state-of-the-art algorithms by a significant margin, achieving a U-score of 178,966.5—34.43% higher—thereby demonstrating its superior performance.