关键词: 区间系数, 二次双层规划, 遗传算法, 最优性条件, 最优解

Abstract: For a class of quadratic bilevel programming problems with interval objective coefficients in the leader’s and lower’s levels, a genetic algorithm with two fitness functions is presented. Firstly, the coefficient interval of the lower’s level objective is taken as the search space of the genetic algorithm. After doing so, for each individual, the lower’s level of the resulting problem doesn’t involve interval coefficients; In addition, the optimality conditions of quadratic programming are used to further transform the resulting problem into two exact quadratic programs. Furthermore, these two quadratic programs are solved by the base-enumerating method and its optimal values are taken as two fitness values. Finally, the best and the worst optimal solutions can be obtained by comparing two fitness values of all individuals. The simulation results show that the proposed algorithm is feasible and efficient.

Key words: interval coefficients, quadratic bilevel programming, genetic algorithm, optimality condition, optimal solutions