Solving optimistic bi level programs by iteratively approximating lower level optimal value function

Abstract

Bilevel optimization is a nested optimization problem that contains one optimization task as a constraint to another optimization task. Owing to enormous applications that are bilevel in nature, these problems have received attention from mathematical programming as well as evolutionary optimization community. However, most of the available solution methods can either be applied to highly restrictive class of problems, or are highly computationally expensive that they do not scale for large scale bilevel problems. The difficulties in bilevel programming arise primarily from the nested structure of the problem. In this paper, we propose a metamodeling based solution strategy that attempts to iteratively approximate the optimal lower level value function. To the best knowledge of the authors, this kind of a strategy has not been used to solve bilevel optimization problems, particularly in the context of evolutionary computation. The proposed method has been evaluated on a number of test problems from the literature.