Convergence analysis of evolutionary algorithms solving the Flexible Job Shop Problem

Although several multi-objective evolutionary algorithms (MOEA) have been proposed, proof of their convergence remains poorly evaluated, even when taking into account the many studies based on MOEA convergence that have appeared in the literature over the years. Then, as the number of MOEA proposals increases, the study of the convergence of these algorithms becomes increasingly important. Particle Swarm Optimization (PSO) is an example of an algorithm very much discussed in relation to convergence, in particular, its premature convergence. This work presents a comparative study of the asymptotic convergence of three algorithms, two of these are based on PSO and the third is an Estimation Distribution Algorithm (EDA). The parameters for standard PSO were defined taking into account theoretical aspects that lead to convergence. The Online Convergence Detection algorithm and the Hypervolume indicator were used to analyse the asymptotic convergence of the three algorithms applied to the Flexible Job Shop Problem. The results reinforce the premature convergence of the standard PSO, or convergence to local minima, which is a consequence of the absence of diversity. A hybrid PSO that uses genetic operators obtained better results along with the EDA.