GA/PD: a genetic algorithm based on problem decomposition for solving interval linear bilevel programming problems

Abstract

For dealing with uncertain optimization problems, interval programming is a common model that can provide a risk range for decision makers between the best and the worst optimal solutions. Among all interval programming problems, the interval bilevel programming problem has always known as one of the hardest problems to solve. In this work, an efficient solution method is developed for general interval linear bilevel programs in which all coefficients and right-hand vectors are given by intervals. Firstly, a decomposition scheme is adopted to transform the original problem into two simplified subproblems in which only the follower's problem involves interval coefficients. Secondly, a genetic algorithm, one of the more effective evolutionary algorithms, is designed to search these intervals, and linear program optimality conditions are utilized to evaluate each individual in populations. Finally, by comparing the fitness values according to pre-determined rules, the best and the worst optimal solutions to the interval linear bilevel programming problem can be achieved. Simulation results show that the proposed algorithm is efficient and can obtain larger intervals of the optimal values on some computational examples than those in the literature.