A Chaotic Search-Enhanced Genetic Algorithm for Bilevel Programming Problems

Abstract

In this chapter, we propose chaotic search-enhanced genetic algorithm for solving bilevel programming problem (BLPP). The proposed algorithm is a combination between enhanced genetic algorithm based on new selection technique named effective selection technique (EST) and chaos searching technique. Firstly, the upper level problem is solved using enhanced genetic algorithm based on EST. EST enables the upper level decision maker to choose an appropriate solution in anticipation of the lower level’s decision. Then, lower level problem is solved using genetic algorithm for the upper level solution. Secondly, local search based on chaos theory is applied for the upper level problem around the enhanced genetic algorithm solution. Finally, lower level problem is solved again using genetic algorithm for the chaos search solution. The incorporating between enhanced genetic algorithm supported by EST and chaos theory increases the search efficiency and helps in faster convergence of the algorithm. The performance of the algorithm has been evaluated on different sets of test problems linear and nonlinear problems, constrained and unconstrained problems and low-dimensional and high-dimensional problems. Also, comparison between the proposed algorithm results and other state-of-the-art algorithms is introduced to show the effectiveness and efficiency of our algorithm.