A multitasking surrogate-assisted differential evolution method for solving bi-level optimization problems

Abstract

Bi-level programming (BLP) is a hierarchical decision-making problem in which part of the constraints is determined by solving other optimization problems. Classic op-timization techniques cannot be applied directly, while standard metaheuristics often demand high computational costs. The transfer optimization paradigm uses the experience acquired when solving one optimization problem to speed up a distinct but related task. In particular, the multitasking technique ad-dresses two or more optimization tasks simultaneously to explore similarities and improve convergence. BLPs can benefit from multitasking as many (potentially similar) lower-level problems must be solved. Recently, several studies used surrogate methods to save expensive upper-level function evaluations in BLPs. This work proposes an algorithm based on Differential Evolution supported by transfer optimization and surrogate models to solve BLPs more efficiently. Experiments show a reduction of up to 86% regarding the number of function evaluations of the upper-level problem while achieving similar or superior accuracy when compared to state-of-the-art solvers.