Interactive methods for multiobjective robust optimization

Abstract

Practical optimization problems usually have multiple objectives, and they also involve uncertainty from different sources. Various robustness concepts have been proposed to handle multiple objectives and the involved uncertainty simultaneously. However, the practical applicability of the proposed concepts in decision making has not been widely studied in the literature. Developing solution methods to support a decision maker to find a most preferred robust solution is an even more rarely studied topic. Thus, we focus on two goals in this thesis including 1) analyzing the practical applicability of different robustness concepts in decision making and 2) developing interactive methods for supporting decision makers to find most preferred robust solutions under different types of uncertainty. We first consider decision uncertainty (i.e., the optimized solutions cannot be guaranteed with exact implementations). We propose a robustness measure to quantify the effects of uncertainty in the objective function values of solutions. We incorporate the robustness measure to an interactive method, where the solutions are presented to the decision maker with enhanced visualization. We then consider parameter uncertainty (i.e., the parameters in the objective functions involve uncertainty). We first utilize the concept of set-based minmax robustness and develop a two-stage interactive method to support the decision maker to find a most preferred set-based minmax robust Pareto optimal solution. Since set-based minmax robust Pareto optimal solutions are difficult to compute, we propose an evolutionary multiobjective optimization method to approximate a set of them. We then analyze different robustness concepts and verify that lightly robust Pareto optimal solutions are good trade-offs between robustness and objective function values. For supporting a decision maker to find a most preferred lightly robust Pareto optimal solution, we propose an interactive method. The results of this thesis extend the applicability of robustness concepts in decision making to practical problems. In addition, the proposed methods bring decision support in multiobjective robust optimization into practice.