A Simple Indicator Based Evolutionary Algorithm for Set-Based Minmax Robustness

Abstract

For multiobjective optimization problems with uncertain parameters in the objective functions, different variants of minmax robustness concepts have been defined in the literature. The idea of minmax robustness is to optimize in the worst case such that the solutions have the best objective function values even when the worst case happens. However, the computation of the minmax robust Pareto optimal solutions remains challenging. This paper proposes a simple indicator based evolutionary algorithm for robustness (SIBEA-R) to address this challenge by computing a set of non-dominated set-based minmax robust solutions. In SIBEA-R, we consider the set of objective function values in the worst case of each solution. We propose a set-based non-dominated sorting to compare the objective function values using the definition of lower set less order for set-based dominance. We illustrate the usage of SIBEA-R with two example problems. In addition, utilization of the computed set of solutions with SIBEA-R for decision making is also demonstrated. The SIBEA-R method shows significant promise for finding non-dominated set-based minmax robust solutions.