Solving dynamic optimization problems using parent–child multi-swarm clustered memory (PCSCM) algorithm

The Particle Swarm Optimization (PSO) algorithm faces several inherent challenges when applied to dynamic and large-scale optimization problems. These challenges encompass the issues of outdated particle memory, inadequate scalability in high-dimensional search spaces, the incapability to detect environmental changes, a continual trade-off between exploration and exploitation, and the potential loss of population diversity within the problem space. To address these challenges, we propose a novel hybrid PSO algorithm, denoted as Parent–Child Multi-Swarm Clustered Memory (PCSCM). PCSCM is explicitly designed to leverage an enhanced memory system, capable of mitigating the issue of outdated particle memory after convergence, and efficiently adapting to changing environmental conditions. This innovative memory system retains and retrieves promising solutions from the past when environmental alterations occur. Additionally, PCSCM introduces clustering mechanisms for particles within each swarm, aimed at augmenting diversity within the problem space. This clustering strategy substantially bolsters the algorithm’s performance in tracking evolving optimal solutions and positively contributes to its scalability. Crucially, the clustering approach is implemented not only for the main population but also for stored solutions in memory, which collectively strike a balance between exploration and exploitation. In the proposed method, particle swarms are divided into parent and child swarms, with parent swarms dedicated to preserving diversity; while, child swarms focus on identifying local solutions. These clustering and memory strategies are consistently applied within each sub-swarm to effectively address the challenges posed by high-dimensional search spaces. In addition to addressing challenges related to dynamic optimization, our proposed Parent–Child Multi-Swarm Clustered Memory (PCSCM) algorithm introduces an innovative mechanism for detecting environmental changes. This novel approach enhances the algorithm’s adaptability by efficiently identifying moments when the optimization environment undergoes significant shifts. The detection of such changes is a crucial aspect of the PCSCM algorithm, contributing to its robust performance in dynamic scenarios. The effectiveness and robustness of the PCSCM algorithm are substantiated through extensive simulation experiments. These experiments provide insights into PCSCM’s behavior in dynamic environments and showcase its ability to scale proficiently in high-dimensional settings. Particularly noteworthy are the results obtained when benchmarked against the Moving Peaks Benchmark and Generalized Moving Peaks Benchmark. These results not only underscore the algorithm’s efficiency but also demonstrate its superiority when compared to several existing state-of-the-art optimization methods, including Multi-Swarm PSO, AmQSO, CPSO, Cellular PSO, FMSO, mQSO10 (5 + 5q), and DPSABC.