memetic optimization

Designing effective hybrid metaheuristics for single-objective continuous optimization remains challenging due to heavy reliance on expert knowledge and the vast combinatorial space of algorithm components. Method: This paper proposes METAFOR, a modular hybrid metaheuristic framework that supports configurable and extensible automatic composition of PSO, DE, CMA-ES, and local search, integrated with irace for end-to-end algorithm auto-generation. It introduces a hierarchical training set construction and leave-one-class-out cross-validation strategy to systematically analyze component interactions. Contribution/Results: METAFOR reveals optimal hybridization patterns and component contribution trends across problem classes. Evaluated on diverse benchmark suites, the 17 automatically generated hybrid algorithms significantly outperform tuned individual algorithms. This work provides the first empirical characterization of the effectiveness boundaries and applicability conditions of hybrid strategies—establishing foundational insights for principled hybrid metaheuristic design.

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.

NP-hard combinatorial optimization problems (COPs) pose challenges for existing heuristics—handcrafted methods lack adaptability, while neural approaches cannot perform adaptive refinement of constructed solutions during inference. Method: We propose Moco, a learnable meta-optimizer that employs graph neural networks to dynamically model search states and end-to-end learn solution construction policies, supporting computational-budget-aware adaptive decision-making. Contribution/Results: Moco introduces the first problem-agnostic meta-optimization paradigm—requiring neither problem-specific local search nor decomposition—and enables cross-budget generalization and online policy adaptation. On the Maximum Independent Set problem, it significantly outperforms state-of-the-art methods. For the Traveling Salesman Problem, it achieves superior overall performance, notably surpassing comparable learnable solvers—even those augmented with additional local search procedures.

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 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 work proposes a metabolic multi-agent optimization framework grounded in endogenous resource cycling, addressing the limited intrinsic adaptability of traditional metaheuristic algorithms that rely on external scheduling mechanisms. The framework employs a shared metabolic controller to dynamically regulate agent lifecycles, role transitions, and resource allocation, thereby establishing a lightweight, self-consistent closed-loop resource system. It unifies energy budgeting, normalized reward signals, and continuous role adaptation, enabling effective handling of both continuous and discrete optimization problems. Empirical evaluations on benchmark functions—including Sphere and Rastrigin—as well as synthetic and TSPLIB traveling salesman problem instances demonstrate the method’s cross-domain stability and computational efficiency, highlighting its compact architecture and general-purpose adaptive capabilities.

This study investigates the scalability of multi-objective evolutionary algorithms (MOEAs) on combinatorial optimization problems as problem dimensionality increases from 50 to 5,000. Through a comparative analysis of SEMO, NSGA-II, SMS-EMOA, and MOEA/D, the authors observe that SEMO exhibits significantly slower convergence in high-dimensional settings due to its lack of crossover operators. By innovatively incorporating crossover into SEMO, they achieve a substantial improvement in convergence efficiency, albeit with a slight reduction in the uniformity of the Pareto front. The findings underscore the critical role of crossover mechanisms in enabling effective search in large-scale multi-objective combinatorial optimization and provide empirical evidence to guide the design of scalable MOEAs.

This work proposes a constrained hybrid metaheuristic (cHM) framework to address the limitations of existing metaheuristic algorithms, which often struggle with general continuous optimization problems exhibiting complex characteristics such as non-convexity, non-separability, and varying smoothness. The cHM framework employs a modular architecture and a two-phase adaptive mechanism to dynamically coordinate multiple metaheuristic strategies and candidate solutions under black-box optimization settings, enabling efficient optimization of heterogeneous and unknown objective functions. By adaptively adjusting its search behavior according to the optimization stage, the method significantly enhances convergence speed and robustness. Experimental results demonstrate that cHM matches or outperforms state-of-the-art algorithms across 28 benchmark functions and exhibits strong generality and practical utility in real-world feature selection tasks.

This work addresses the limitation of existing large language model (LLM)-driven heuristic design approaches, which typically focus on optimizing individual components in isolation and struggle to coordinate interdependent heuristics within practical optimization frameworks. To overcome this, the authors propose MuEvo, a novel framework that jointly optimizes multiple heuristics through dynamic component management with reversible lifecycles and a relation-guided co-evolution mechanism, guided by ensemble-level feedback. MuEvo integrates short-budget probing, multi-ensemble evaluation, cross-component information sharing, and adaptive budget allocation, leveraging an LLM to orchestrate the evolution of component populations, thereby effectively capturing interdependencies and preserving components with latent long-term potential. Experimental results demonstrate that MuEvo significantly outperforms both manually designed frameworks and current LLM-based automated heuristic design methods across four combinatorial optimization problems, showing broad applicability to controller-driven heuristic pools and functionally differentiated algorithmic components.