The Impact of Variation Operators on the Performance of SMS-EMOA on the Bi-objective BBOB-2016 Test Suite

Abstract : The S-metric-Selection Evolutionary Multi-objective Optimization Algorithm (SMS-EMOA) is one of the best-known indicator-based multi-objective optimization algorithms. It employs the S-metric or hypervolume indicator in its (steady-state) selection by deleting in each iteration the solution that has the smallest contribution to the hypervolume indicator. In the SMS-EMOA, the conceptual idea is this hypervolume-based selection. Hence the algorithm can, for example, be combined with several variation operators. Here, we benchmark two versions of SMS-EMOA which employ differential evolution (DE) and simulated binary crossover (SBX) with polynomial mutation (PM) respectively on the newly introduced bi-objective bbob-biobj test suite of the Comparing Continuous Optimizers (COCO) platform. The results un-surprisingly reveal that the choice of the variation operator is crucial for performance with a clear advantage of the DE variant on almost all functions.