Multi-guide particle swarm optimization for multi-objective optimization: empirical and stability analysis

This article presents a new particle swarm optimization (PSO)-based multi-objective optimization algorithm, named multi-guide particle swarm optimization (MGPSO). The MGPSO is a multi-swarm approach, where each subswarm optimizes one of the objectives. An archive guide is added to the velocity update equation to facilitate convergence to a Pareto front of non-dominated solutions. An extensive empirical and stability analysis of the MGPSO is conducted. The empirical analysis focuses on the exploration behavior of the MGPSO and compares the performance of the MGPSO with that of state-of-the-art multi-objective PSO and evolutionary algorithms. The results show that the MGPSO is highly competitive on a number of benchmark functions. The paper provides a theoretical stability analysis which focuses on the sufficient and necessary conditions for order-1 and order-2 stability of the MGPSO. The paper extends existing work on MGPSO stability analysis by deriving new stability criteria for differing values of the acceleration coefficients used in the velocity update equation.