A Memetic Algorithm for Solving Single Objective Bilevel Optimization Problems

In recent years, research in the field of bilevel optimization has gathered pace and it is increasingly being used to solve problems in engineering, logistics, economics, transportation etc. Rapid increase in the size and complexity of the problems emerging from these domains has prompted active interest in the design of efficient algorithms for bilevel optimization. While Memetic Algorithms (MAs) have been quite successful in solving single level optimization problems, there have been very few studies exploring their application in bilevel problems. MAs essentially attempt to combine advantages of global and local search strategies to locate optimum solutions with low computational cost (function evaluations). In this paper, we present a new nested approach for solving bilevel optimization problems. The presented approach uses memetic algorithm at the upper level, while a global or a local search method is used in the lower level during various phases of the search. The performance of the proposed approach is compared with two established approaches, NBLEA and BLEAQ, using SMD benchmark problem set. The numerical experiments demonstrate the benefits of the proposed approach both in terms of accuracy and computational cost, establishing its potential for solving bilevel optimization problems.