Incremental particle swarm optimization for large-scale dynamic optimization with changing variable interactions

Abstract

Cooperative coevolutionary algorithms have been developed for large-scale dynamic optimization problems via divide-and-conquer mechanisms. Interacting decision variables are divided into the same subproblem for optimization. Their performance greatly depends on problem decomposition and response abilities to environmental changes. However, existing algorithms usually adopt offline decomposition and hence are insufficient to adapt to changes in the underlying interaction structure of decision variables. Quick online decomposition then becomes a crucial issue, along with solution reconstruction for new subproblems. This paper proposes incremental particle swarm optimization to address the two issues. In the proposed method, the incremental differential grouping obtains accurate groupings by iteratively performing edge contractions on the interaction graph of historical groups. A recombination-based sampling strategy is developed to generate high-quality solutions from historical solutions for new subproblems. In order to coordinate with the multimodal property of the problem, swarms are restarted after convergence to search for multiple high-quality solutions. Experimental results on problem instances up to 1000-D show the superiority of the proposed method to state-of-the-art algorithms in terms of solution optimality. The incremental differential grouping can obtain accurate groupings using less function evaluations.