SMPSO Revisited : A Theoretical Analysis of Exponentially-Averaged Momentum in Multi-Objective Problems

It has been well documented that the use of exponentially-averaged momentum (EM) in particle swarm optimization (PSO) is advantageous over the vanilla PSO algorithm. In the single-objective setting, it leads to faster convergence and avoidance of local minima. Naturally, one would expect that the same advantages of EM carry over to the multi-objective setting. Hence, we extend the state of the art Multi-objective optimization (MOO) solver, SMPSO, by incorporating EM in it. As a consequence, we develop the mathematical formalism of constriction fairness which is at the core of extended SMPSO algorithm. The proposed solver matches the performance of SMPSO across the ZDT, DTLZ and WFG problem suites and even outperforms it in certain instances.