Surrogate-Assisted Evolutionary Multitasking for Expensive Minimax Optimization in Multiple Scenarios

Abstract

Minimax optimization is a widely-used formulation for robust design in multiple operating or environmental scenarios, where the worst-case performance among multiple scenarios is the optimization objective requiring a large number of quality assessments. Consequently, minimax optimization using evolutionary algorithms becomes prohibitive when each quality assessment involves computationally expensive numerical simulations or costly physical experiments. This work employs evolutionary multitasking optimization and surrogate techniques to address the challenges of the high-dimensional search space and high computation cost of minimax optimization. To this end, finding the worst-case scenario for different candidate solutions is considered as the optimization of multiple problems that can be solved simultaneously using the evolutionary multitasking optimization approach. In order to further speed up the proposed algorithm, a surrogate model in the joint space of the decision and scenario spaces is built to replace part of the expensive function evaluations. A generation-based model management strategy using a statistical hypothesis test is designed to manage the surrogate model. Experimental results on both benchmark problems and an airfoil design application indicate that the proposed algorithm can find satisfactory solutions with a very limited computational budget.