A novel approach for solving bi-level mono-objective and multi-objective programming problems using evolutionary algorithms

Bi-level programming problems (BLP) constitute an important class of non-convex optimization problems, which makes it challenging to find a global optimal solution. In this article, we propose an efficient technique to solve this category of problems. We reformulated the initial problem as a single-level optimization problem using the optimal value function of the lower-level problem. To solve the latter, we employed a technique based on -dense curves to approximate the value function of the lower-level problem. Two evolutionary algorithms were then used to solve the reformulated problem. Furthermore, we extended our method to address multi-objective bi-level programming problems with a single objective at the upper level and multiple objectives at the lower level, known as a semi-vectorial bi-level programming problem. Several numerical experiments on nonlinear BLP show the outstanding efficiency of our approach.