A Learning-Based Cooperative Coevolution Framework for Heterogeneous Large-Scale Global Optimization

Cooperative Coevolution (CC) and Non-Decomposition Algorithms (NDAs) are two primary approaches for large-scale global optimization (LSGO). Although both have achieved success, they exhibit markedly different performance across problem types and each faces approach-specific limitations, leaving the question of "when to use CC" unresolved. We address this gap with WCC, a novel learning-based framework that dynamically decides when to deploy CC in LSGO. WCC employs a streamlined design for efficient adaptive learning. We formulate the decision as a Markov decision process, designing a targeted feature set, a robust reward, and a tailored network architecture to provide the agent with rich information about the problem state and optimization progress. Our auto-regressive policy enables WCC to perform fine-grained, dynamic switching between CC and NDAs while conditionally allocating the computational budget without expert specifications. WCC shows strong competitiveness and superior generalization across problems, optimization horizons, and baseline optimizers. It realizes a "train-once and reuse" paradigm under a low budget, significantly curbing LSGO cost. Additionally, in-depth analyses yield insights not captured by existing theory, offering practical guidance on when and how to effectively deploy CC.

Many real-world optimization problems consist of multiple tightly coupled subproblems whose solutions must be coordinated to achieve high overall performance. However, existing large language model driven automated heuristic design approaches are limited to single-problem settings. In this paper, we propose CoupleEvo. CoupleEvo proposes three evolutionary coordination strategies to evolve heuristics for coupled optimization problems: the sequential strategy evolves heuristics for one subproblem after the other; the iterative strategy alternates the evolution of heuristics for different subproblems over successive generations; and the integrated strategy evolves heuristics for all problems simultaneously. The approach is evaluated on two representative coupled optimization problems. Experimental results show that decomposition-based strategies (sequential and iterative) provide more stable convergence and higher solution quality, while the integrated evolution strategy suffers from increased search complexity and variability. These findings highlight the importance of coordinating evolutionary search across interdependent subproblems and demonstrate the potential of LLM-driven heuristic design for complex coupled optimization problems. The code is available: https://github.com/tb-git-kit-research/CoupleEvo.

Distributed blackbox consensus optimization is a fundamental problem in multi-agent systems, where agents must improve a global objective using only local objective queries and limited neighbor communication. Existing methods largely rely on handcrafted update rules and static cooperation patterns, which often struggle to balance local adaptation, global coordination, and communication efficiency in heterogeneous nonconvex environments. In this paper, we take an initial step toward trajectory-driven self-design for distributed black-box consensus optimization. We first redesign the agent-level swarm dynamics with an adaptive internal mechanism tailored to decentralized consensus settings, improving the balance between exploration, convergence, and local escape. Built on top of this adaptive execution layer, we propose Learning to Act and Cooperate (LACMAS), a trajectorydriven framework in which large language models provide sparse highlevel guidance for shaping both agentinternal action behaviors and agentexternal cooperation patterns from historical optimization trajectories. We further introduce a phased cognitive scheduling strategy to activate different forms of adaptation in a resource-aware manner. Experiments on standard distributed black-box benchmarks and real-world distributed tasks show that LAC-MAS consistently improves solution quality, convergence efficiency, and communication efficiency over strong baselines, suggesting a practical route from handcrafted distributed coordination toward self-designing multi-agent optimization systems.