Decomposition and merging cooperative particle swarm optimization with random grouping for large-scale optimization problems

Particle swarm optimization (PSO) is a metaheuristic commonly used for optimization problems. However, PSO does not scale well to large-scale optimization problems (LSOPs). A divide-and-conquer approach to PSO has shown to be effective when scaling up to LSOPs. Two cooperative PSO (CPSO) approaches, decomposition CPSO (DCPSO) and merging CPSO (MCPSO), were previously introduced, but are limited when it comes to exploring variable dependencies. An improvement to DCPSO and MCPSO incorporating a random grouping of decision variables at a fixed rate, referred to as RG-DCPSO and RG-MCPSO, was introduced recently in order to better explore variable dependencies. This work introduces two additional approaches to incorporating the random grouping of decision variables, denoted by \(\hbox {RG-DCPSO}_{\hbox {cv}}\), \(\hbox {RG-DCPSO}_{\hbox {sp}}\), \(\hbox {RG-MCPSO}_{\hbox {cv}}\), and \(\hbox {RG-MCPSO}_{\hbox {sp}}\). The various random grouping approaches were compared to five other decomposition-based PSO approaches found in the literature to determine their relative performance. The \(\hbox {RG-DCPSO}_{\hbox {cv}}\) approach introduced in this paper has competitive performance in the CEC’2010 large-scale global optimization benchmark set on environments with up to 1000 decision variables. Furthermore, \(\hbox {RG-DCPSO}_{\hbox {cv}}\) had the best performance out of all tested approaches on the CEC’2013 large-scale global optimization benchmark set.