Population state-driven surrogate-assisted differential evolution for expensive constrained optimization problems with mixed-integer variables

Abstract Many surrogate-assisted evolutionary algorithms (SAEAs) have been shown excellent search performance in solving expensive constrained optimization problems (ECOPs) with continuous variables, but few of them focus on ECOPs with mixed-integer variables (ECOPs-MI). Hence, a population state-driven surrogate-assisted differential evolution algorithm (PSSADE) is proposed for solving ECOPs-MI, in which the adaptive population update mechanism (APUM) and the collaborative framework of global and local surrogate-assisted search (CFGLS) are combined effectively. In CFGLS, a probability-driven mixed-integer mutation (PMIU) is incorporated into the classical global DE/rand/2 and local DE/best/2 for improving the diversity and potentials of candidate solutions, respectively, and the collaborative framework further integrates both the superiority of global and local mutation for the purpose of achieving a good balance between exploration and exploitation. Moreover, the current population is adaptively reselected based on the efficient non-dominated sorting technique in APUM when the population distribution is too dense. Empirical studies on 10 benchmark problems and 2 numerical engineering cases demonstrate that the PSSADE shows a more competitive performance than the existing state-of-the-art algorithms. More importantly, PSSADE provides excellent performance in the design of infrared stealth material film.