Multiobjective differential evolution algorithm based on decomposition for a type of multiobjective bilevel programming problems

This paper considers the multiobjective bilevel programming problem (MOBLPP) with multiple objective functions at the upper level and a single objective function at the lower level. By adopting the Karush-Kuhn-Tucker (KKT) optimality conditions to the lower level optimization, the original multiobjective bilevel problem can be transformed into a multiobjective single-level optimization problem involving the complementarity constraints. In order to handle the complementarity constraints, an existing smoothing technique for mathematical programs with equilibrium constraints is applied. Thus, a multiobjective single-level nonlinear programming problem is formalized. For solving this multiobjective single-level optimization problem, the scalarization approaches based on weighted sum approach and Tchebycheff approach are used respectively, and a constrained multiobjective differential evolution algorithm based on decomposition is presented. Some illustrative numerical examples including linear and nonlinear versions of MOBLPPs with multiple objectives at the upper level are tested to show the effectiveness of the proposed approach. Besides, NSGA-II is utilized to solve this multiobjective single-level optimization model. The comparative results among weighted sum approach, Tchebycheff approach, and NSGA-II are provided.