Particle Swarm Optimization for Large-Scale Mixed-Variable Optimization Problems

Mixed-variable optimization problems (MVOPs), involving both continuous and discrete decision variables, are frequently encountered in practical engineering design. The presence of mixed decision variables increases the complexity of the search space, making these problems difficult to solve. Furthermore, recent societal trends have led to an increase in the scale of design targets and the sophistication of design requirements, resulting in a higher number of design and behavioral variables. Consequently, MVOPs are expected to become more complex and large-scale. Particle Swarm Optimization (PSO), developed by Kennedy et al., is widely recognized for its simplicity and high convergence performance. Although originally designed for continuous variables, PSO has been successfully applied to mixed-variable problems, demonstrating its effectiveness. However, most existing PSO approaches for MVOPs focus primarily on handling mixed variables, with applicability limited to problems involving a relatively small number of design variables. This paper presents a novel PSO-based approach to address large-scale MVOPs. The proposed method utilizes three types of dimensionality reduction: one for continuous variables, one for discrete variables, and one for mixed variables, effectively mitigating the complexity of large-scale mixed-variable problems. The capabilities and characteristics of the proposed approach are illustrated through test problems and an engineering design case study.