Random-weight based genetic algorithm for multiobjective bilevel mixed linear integer programming

Abstract

In this paper, we address a class of multiobjective bilevel mixed linear integer programming in which the upper level is a multiobjective linear optimization problem, and the lower level is a single-objective linear programming. For this kind of problem, the leader's decision are represented by zero-one variables, and the follower's decision are represented by continuous variables. Using KKT condition, the lower level is transformed into a series of constraints for the upper level. Based on coding, crossover, mutation, fitness assignment method and select strategy, an improved random-weight genetic algorithm for multiobjective bilevel mixed linear integer programming is proposed. By designing benchmark problems and suitable transformation, the proposed algorithm is compared by an existed branch-bound algorithm.