Searching for Robustness Intervals in Evolutionary Robust Optimization

In many real-world optimization applications, a goal solution (i.e., scenario) is often provided by a user according to his/her experience. Due to the presence of a wide range of uncertainties, one may be interested in identifying the robustness interval of the solution, i.e., the range of the decision variables in which the solution remains robust. This paper investigates how to find the robustness intervals of the goal solution in evolutionary robust optimization and formulates this as a bilevel optimization problem. Then a novel algorithm framework is proposed to solve the bilevel problem: an efficient heuristic-based approach is developed to optimize the upper level task, while a global optimizer is utilized to tackle the lower level task. The proposed heuristic-based approach contains four key components: peak detection, peak allocation, calculation of next perturbation value, and robustness interval fine-tuning, aiming to enhance the efficiency of searching for the target intervals. Finally, three types of artificial test problems and a practical problem are provided to verify the effectiveness of the proposed algorithm framework. The results show that all the robustness intervals can be successfully found when the goal solution is given by means of the proposed algorithm framework.