Adaptive elite learning particle swarm optimization algorithm with complementary sub-strategies for multimodal problems

Diverse and elite groups can provide the optimal solution to a complex problem thanks to their exceptional learning abilities, humble attitude towards learning, and excellent information exchange. Inspired by this, an adaptive elite learning particle swarm optimization algorithm (AELPSO) is proposed based on the elite learning method and the idea of multiple sub-swarms collaboration. AELPSO employs four sub-swarms with complementary strategies (CODA, denotes Cross-, Ortho-, Dynamic-, All-strategies). Cross- and All-strategies offer rich population diversity, improving the global search ability of the algorithm, especially in the exploration stage; Dynamic-strategy improves the local search ability, retaining fast convergence speed in the exploitation stage; Ortho-strategy is relatively universal but has high time complexity. These strategies are specifically adjusted and hybridized for multimodal problems via the elite learning (AEL) method to balance exploration and exploitation. In the AEL, better particles are selected to execute more strategies to escape local optima quickly; the number of particles executing all strategies is adaptively increased to prevent premature convergence from the exploratory to the exploitative state; finally, a subset of poorly performing particles is replaced through fixed elimination and competition methods to mitigate the decline in population diversity. Promising particles in AELPSO explore the search space in multiple ways and are more likely to find better solutions when faced with multimodal problems. Experimental results demonstrate that AELPSO outperforms its counterparts in accuracy, robustness, and convergence speed for almost all problems across 37 benchmark functions and two real-world applications.