Multi-objective Robust Optimization and Decision-Making Using Evolutionary Algorithms

Evolutionary multi-objective optimization (EMO) algorithms are predominantly used for solving multi- and many-objective optimization problems to arrive at the respective Pareto front. From a practical point of view, it is desirable for a decision-maker (DM) to consider objective vectors that are less sensitive to the small perturbation in design variables and problem parameters. Such insensitive, yet closer to Pareto-optimal solutions, lie on the so-called robust front. In real-world applications, such as engineering design and process optimization problems, perturbations in variables come from manufacturing tolerances, uncertainties in material properties, variations in operating conditions, etc. The existing EMO literature on robustness studies emphasized on finding the entire robust front, but hardly considered robustness in both optimization and decision-making tasks. In this paper, we propose and evaluate different algorithmic implementations of three aspects - multi-objective optimization, robustness consideration, and multi-criterion decision-making - together. Based on experimental results on two to eight-objective problems, we discuss the outcomes and advantages of different integration approaches of these three aspects and present the most effective combined approach. The results are interesting and should pave the way to develop more efficient multi-objective robust optimization and decision-making (MORODM) procedures for handling practical problems with uncertainties.