An efficient solution strategy for bilevel multiobjective optimization problems using multiobjective evolutionary algorithm

Abstract

An efficient solution strategy is proposed for bilevel multiobjective optimization problem (BLMOP) with multiple objectives at both levels when multiobjective optimization problem (MOP) at the lower level satisfies the convexity and differentiability for the lower-level decision variables. In the proposed strategy, the MOP at the lower level is first converted into a single-objective optimization formulation through adopting adaptive weighted sum scalarization, in which the lower-level weight vector is adjusted adaptively while the iteration progressing. The Karush-Kuhn-Tucker optimality conditions are used to the lower-level single-objective scalarization problem, thus the original BLMOP can be converted into a single-level MOP with complementarity constraints. Then an effective smoothing technique is suggested to cope with the complementarity constraints. In such a way, the BLMOP is finally formalized as a single-level constrained nonlinear MOP. A decomposition-based constrained multiobjective differential evolution is developed to solve this transformed MOP and some instances are tested to illustrate the feasibility and effectiveness of the solution methodology. The experimental results show that the proposed solution method possesses favorite convergence and diversity.