Balancing convergence and diversity preservation in dual search space for large scale particle swarm optimization

Balancing convergence and diversity is a crucial challenge for particle swarm optimization in addressing large-scale optimization problems. A main reason is that it is difficult to simultaneously effectively manage diversity with specific parameters in both objective space and decision space. To address this issue, this paper introduces a novel velocity update structure that integrates diversity preservation in both objective space and decision space alongside convergence. Aligned with the proposed update structure, a new diversity enhancement mechanism is proposed. This mechanism comprises an entropy-based diversity preservation strategy and an adaptive difference-mutation-based diversity preservation strategy, designed to preserve diversity in objective space and decision space, respectively. By utilizing a dynamic convergence learning strategy, a novel large-scale swarm optimizer capable of explicitly and simultaneously balancing convergence and diversity in both spaces is developed. This paper theoretically proves the stability and analyzes the search behavior of the proposed algorithm. Comprehensive experiments are then conducted using two large-scale benchmark test suites, a real-case application model and several state-of-the-art algorithms. The results demonstrate the competitiveness of the proposed algorithm in large-scale optimization and the effectiveness of the proposed strategies in balancing convergence and diversity.