Solving a type of biobjective bilevel programming problem using NSGA-II

Authors:
Minqiang Li;Dan Lin;Shouyang Wang
Affiliations:
School of Management, Tianjin University, Tianjin 300072, PR China;Department of Mathematics, Tianjin University, Tianjin 300072, PR China;Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, PR China
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

This paper considers a type of biobjective bilevel programming problem, which is derived from a single objective bilevel programming problem via lifting the objective function at the lower level up to the upper level. The efficient solutions to such a model can be considered as candidates for the after optimization bargaining between the decision-makers at both levels who retain the original bilevel decision-making structure. We use a popular multiobjective evolutionary algorithm, NSGA-II, to solve this type of problem. The algorithm is tested on some small-dimensional benchmark problems from the literature. Computational results show that the NSGA-II algorithm is capable of solving the problems efficiently and effectively. Hence, it provides a promising visualization tool to help the decision-makers find the best trade-off in bargaining.