Convergence Rates Of Sms-Emoa On Continuous Bi-Objective Problem Classes

Convergence rate analyses of evolutionary multi-objective optimization algorithms in continuous search space are yet rare. First results have been obtained for simple algorithms. Here, we provide concrete results of convergence rates for a state-of-the-art algorithm, namely the S-metric selection evolutionary multi-objective optimization algorithm (SMS-EMOA). We show that the SMS-EMOA produces the same sequence of populations as certain single-objective evolutionary algorithms on arbitrary problem classes. Thereby we are able to transfer known convergence properties for classes of convex functions. We especially consider the SMS-EMOA with populations of parents and offspring greater than one and different concepts for the choice of the reference point used for the internal calculation of the dominated hypervolume within the selection operator.