A hybrid heuristic approach with adaptive scalarization for linear semivectorial bilevel programming and its application

This article focuses on a heuristic solution strategy with adaptive scalarization for linear semivectorial bilevel programming (LSVBLP) as well as its practical application. An adaptive scalarization approach is adopted to the lower level multiobjective optimization problem to make it become a single objective linear programming (LP). The linear bilevel formulation can be reformulated as single-level programming with complementary constraints using the duality theory of LP, such that it is now equivalent to a single-level mixed-integer LP. To solve this resulting mixed-integer LP, a specific variable grouping strategy is proposed to reduce the computational complexity, in which all variables are divided into two groups: one group includes mixed-integer variables, and the other group only contains real-valued variables. In each iteration, the mixed-integer variables in the first group only need to be obtained by the improved mixed-coding differential evolution, while the pure real-valued variables in the second group are obtained by an LP solver. Experimental results on some numerical instances indicate that the proposed hybrid heuristic algorithm is comparable to or better than other algorithms in the literature. To demonstrate its practicability, a customer-oriented production-distribution planning problem is modeled as an LSVBLP, and then the model is solved effectively.