An adaptive genetic algorithm for solving bilevel linear programming problem

Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem. Of all the algorithms, the genetic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming. In this paper, we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes may be infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references.