A comparison on the search of particle swarm optimization and differential evolution on multi-objective optimization

Particle swarm optimization (PSO) and differential evolution (DE) are meta-heuristics which have been found to be successful in a wide variety of optimization tasks. The high speed of convergence and the relative simplicity of PSO make it a highly viable candidate to be used in multi-objective optimization problems (MOPs). Therefore, several PSO approaches capable to handle MOPs (MOPSOs) have appeared in the past. There are some problems, however, where PSO-based algorithms have shown a premature convergence. On the other hand, multi- objective DEs (MODE) have shown lower speed of convergence than MOPSOs but they have been successfully used in problems where MOPSO have mistakenly converged. In this work, we have developed experiments to observe the convergence behavior, the online convergence, and the diversity of solutions of both meta-heuristics in order to have a better understanding about how particles and solutions move in the search space. To this end, MOPSO and MODE algorithms under (to our best effort) similar conditions were used. Moreover, the ZDT test suite was used on all experiments since it allows to observe Pareto fronts in two-dimensional scatter plots (more details on this are presented on the experiments section). Based on the observations found, modifications to two PSO-based algorithms from the state of the art were proposed resulting in a rise on their performance. It is concluded that MOPSO presents a poor distributed scheme that leads to a more aggressive search. This aggressiveness showed to be detrimental for the selected problems. On the other hand, MODE seemed to generate better distributed points on both decision and objective space allowing it to produce better results.