A Highly Efficient Approach for Bi-Level Programming Problems Based on Dominance Determination

Abstract

Bi-level programming, where one objective is nested within the other, is widely used in engineering design, e.g., structural optimization and electronic system design. One major issue of current solvers for these bi-level problems is their low computational efficiency, especially for complex nonlinear problems. The existing methods usually applied time-consuming nested computational structure, which requires an amount of function evaluations (FEs) since a lower-level (LL) optimization needs to be constructed for each upper-level (UL) solution. To solve this issue, a new method based on bi-level grey wolf optimizer (BLGWO) is proposed in this paper. The basic idea is to drop the conventional nested computational structure and instead use a simultaneous computational structure. The simultaneous structure is built on top of a dominance determination process for the grey wolf optimizer, so that the upper-level and lower-level problems can be optimized simultaneously, which greatly improves the efficiency of solving the bi-level problems. The effectiveness of this new method has been validated with ten benchmark functions and two engineering design examples, as well as comparisons with three important existing methods in the bi-level programming domain.