Linear bilevel programming solution by genetic algorithm

Bilevel programming, a tool for modeling decentralized decisions, consists of the objective of the leader at its first level and that of the follower at the second level. Bilevel programming has been proved to be NP-hard problem. Numerous algorithms have been developed so far for solving bilevel programming problem. In this paper, an attempt has been made to develop an efficient approach based on genetic algorithm. The efficiency of the algorithm is ascertained by comparing the results with Gendreau et al. (J. Global Optimization 8 (1996) 217–233) method. Multilevel programming techniques are developed to solve decentralized planning problems with multiple decision makers in a hierarchical organization. The bilevel programming (BLP) problem is a special case of multilevel programming problems with a two level structure. This problem is an important case in nonconvex optimization, and a leader–follower game in which play is sequential and cooperation is not permitted. In this paper, we propose a method based on genetic algorithm approach for solving a BLP problem. For solving constrained optimization problem with genetic algorithm, the difficulty is that most of the chromosomes may be infeasible. In the existing methods in the literature, less attention has been provided for this difficulty. By providing some theorems, this matter has been tackled and hence makes the algorithm more efficient than other techniques.