Learning to Decompose and Optimize for Large-Scale Overlapping Problems

Large-scale overlapping problems (LSOPs) pose significant challenges in optimization due to the intricate interactions among the subcomponents. Traditional decomposition-based cooperative co-evolution (CC) algorithms generally rely on predefined rules or randomized grouping strategies, making it difficult to achieve reasonable and effective decomposition tailored to the specific characteristics of LSOPs. To address this, we propose a novel reinforcement learning (RL)-based framework, called RLDO, which utilizes a policy network to learn decomposition knowledge for efficient optimization. During each learning iteration, the policy network processes the features of the LSOP instance and generates the subcomponent interaction probability matrix. By sampling from this matrix, RLDO produces multiple decomposition results, which are subsequently integrated into the CC framework for optimization. The fitness values derived from the optimization process are normalized to serve as reward signals. Using the proximal policy optimization (PPO) algorithm, RLDO updates the policy network based on this feedback, enabling the network to learn more effective decomposition strategies. Finally, the well-trained policy network is capable of effectively decomposing and optimizing LSOPs with various complex topologies. Experimental results demonstrate that the proposed RLDO framework, with its interactive learning of decomposition mechanisms guided by optimization feedback, achieves significantly superior optimization performance compared to state-of-the-art LSOP algorithms.