algorithmic operator design

Evolutionary algorithms (EAs) for flexible job-shop scheduling often stagnate in local optima, while conventional dynamic operators rely on predefined rules and locally tuned parameters, lacking global self-adaptation. To address these limitations, this paper proposes an LLM-based evolutionary-aware and operator meta-evolution framework. It leverages large language models to model population evolutionary dynamics, enabling knowledge-transfer-based initialization of operator structures, evolutionary-phase identification, and prompt-driven adaptive operator reconstruction—thereby facilitating co-evolution of populations and operators. Experiments across multiple benchmark instances demonstrate that the proposed method significantly accelerates convergence, improves solution quality and robustness, and outperforms state-of-the-art evolutionary programming and traditional EAs. Notably, it represents the first approach to deeply integrate LLMs into a closed-loop, operator-level adaptive optimization framework.

Parameter control in evolutionary algorithms lacks theoretical foundations for dynamically selecting optimal configurations based on real-time algorithmic state. Method: Focusing on the RLS$_k$ algorithm optimizing LeadingOnes, we incorporate runtime state features—such as OneMax value—into a reinforcement learning–inspired dynamic mutation strength selection mechanism. Contribution/Results: We introduce four novel benchmark problems, providing the first systematic demonstration that state information—particularly edge-case states—significantly accelerates parameter control. We theoretically prove that incorporating additional state information reduces the expected optimization time. Empirical results confirm that high-dimensional state representations enable effective learning of high-performance control policies and exhibit strong generalization across problem instances.

This work addresses the long-standing lack of theoretical foundations in online algorithm selection (OAS), particularly the absence of non-artificial problem instances demonstrating asymptotic speedups and principled switching strategies. The study introduces OneMax—a natural benchmark problem—and designs a practical switching strategy between the $(1+\lambda)$ EA and the $(1+(\lambda,\lambda))$ GA. By integrating fixed-start and fixed-target analytical perspectives, it reveals complementary strengths of the two algorithms across different optimization phases. Through rigorous probabilistic analysis and runtime complexity theory, the proposed strategy achieves an expected optimization time of $O(n \log \log n)$, significantly improving upon the best-known bound of $\Theta\left(n \sqrt{ \frac{ \log n \log \log \log n}{ \log \log n}}\right)$ for either algorithm used in isolation. This constitutes the first non-artificial theoretical evidence of asymptotic acceleration in OAS.

This work proposes E2OC, a novel framework for multi-objective evolutionary algorithms that addresses the challenge of modeling dynamic couplings among multiple neighborhood search operators—a task traditionally reliant on expert-designed heuristics and inadequately handled by existing large language model (LLM)-based approaches. E2OC formulates multi-operator optimization as a Markov decision process, explicitly capturing inter-operator dependencies for the first time. By integrating a co-evolutionary mechanism with an operator rotation strategy, it jointly optimizes both high-level design policies and executable code. Leveraging Monte Carlo tree search for progressive exploration and LLM-driven heuristic generation, E2OC consistently outperforms state-of-the-art methods across varying numbers of objectives and problem scales, demonstrating superior generalization and sustained optimization capability.

This work proposes an adaptive metaheuristic optimization framework that maximizes fitness gains under a fixed energy budget by leveraging operator-level energy efficiency. Introducing the Expected Improvement per Joule (EI/J) metric, the framework dynamically schedules lightweight and heavyweight operators to balance exploration and exploitation while optimizing energy utilization. For the first time, energy efficiency is explicitly integrated into the operator selection mechanism within a steady-state evolutionary algorithm that combines genetic operators, particle swarm optimization, and iterative local search. Evaluated on three combinatorial optimization problems—knapsack instances, NK landscapes, and error-correcting code design—the approach significantly reduces energy consumption compared to baseline methods while maintaining comparable solution quality. Empirical results further show that EI/J values converge early, leading to stable and reliable operator selection, thereby demonstrating the strategy’s generalizability across diverse problem domains.

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 two-level deep reinforcement learning framework for large-scale Traveling Salesman Problems (TSP), wherein a recurrent Proximal Policy Optimization (PPO) agent dynamically controls both numerical and structural parameters of a genetic algorithm, enabling their decoupled analysis. The study provides the first empirical evidence that dynamic adjustment of structural parameters is crucial for avoiding premature convergence and escaping local optima, whereas numerical parameters serve only a fine-tuning role. Evaluated on large-scale TSP instances such as rl5915, the proposed method significantly outperforms static baselines, reducing the optimality gap by approximately 45%. These results offer a novel direction for automated algorithm design through adaptive parameter control in evolutionary computation.

This study addresses the challenge of efficiently generating and managing Pareto-optimal solution sets (SOS) in heterogeneous multi-task environments. It proposes an evolutionary multi-task optimization framework to construct compact, task-specific SOS repositories for real-world applications such as engineering design, inventory management, and hyperparameter optimization. The work introduces a novel similarity metric between Pareto sets and, for the first time, systematically validates the cross-domain applicability of SOS. Through visualization and objective space analysis, it reveals dynamic patterns in solution set performance across diverse task contexts. Experimental results demonstrate that the proposed approach effectively captures inter-task differences in solution sets and significantly enhances decision-making support across varying scenarios.

This work addresses the challenge of generalization and rapid adaptation in multi-task optimal control, where the goal is to map task descriptions directly to optimal feedback policies. The authors propose a permutation-invariant neural operator architecture that learns this mapping end-to-end via behavioral cloning. Built upon a branch-trunk network design, the approach supports flexible adaptation strategies ranging from lightweight parameter updates to full-network fine-tuning, and incorporates meta-learning-based initialization to enable efficient few-shot adaptation. Evaluated across diverse parametric optimal control and locomotion benchmarks, the model demonstrates strong generalization to unseen tasks, out-of-distribution scenarios, and varying observation conditions, significantly outperforming existing meta-learning baselines in few-shot adaptation performance.

This work proposes an adaptive evolutionary framework that addresses the limitations of existing AI-driven evolutionary methods, which typically rely on static search strategies and struggle to accommodate task heterogeneity or dynamically changing search spaces. The proposed approach uniquely enables the co-evolution of candidate solutions and search strategies by integrating large language models with a meta-evolutionary mechanism. This integration allows the system to dynamically select and mutate historical solutions while continuously updating its search policy, thereby autonomously balancing exploration and exploitation. Extensive experiments across nearly 200 real-world optimization tasks demonstrate that the method significantly outperforms state-of-the-art AI-based evolutionary algorithms such as AlphaEvolve and OpenEvolve, confirming its generality and effectiveness.