A scalability study of multi-objective particle swarm optimizers

Particle swarm optimization (PSO) is a well-known optimization technique originally proposed for solving single-objective, continuous optimization problems. However, PSO has been extended in various ways to handle multi-objective optimization problems (MOPs). The scalability of multi-objective PSO algorithms as the number of sub-objectives increases has not been well examined; most observations are for two to four objectives. It has been observed that the performance of multiobjective optimizers for a low number of sub-objectives can not be generalized to problems with higher numbers of sub-objectives. With this in mind, this paper presents a scalability study of three well-known multi-objective PSOs, namely vector evaluated PSO (VEPSO), optimized multi-objective PSO (oMOPSO), and speed-constrained multi-objective PSO (SMPSO) with up to eight sub-objectives. The study indicates that as the number of sub-objectives increases, SMPSO scaled the best, oMOPSO scaled the worst, while VEPSO's performance was dependent on the knowledge transfer strategy (KTS) employed, with parent centric recombination (PCX) based approaches scaling consistently better.