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An Evolutionary Algorithm Based on a New Decomposition Scheme for Nonlinear Bilevel Programming Problems

DOI: 10.4236/ijcns.2010.31013, PP. 87-93

Keywords: Nonlinear Bilevel Programming, Decomposition Scheme, Evolutionary Algorithm, Optimal Solutions

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Abstract:

In this paper, we focus on a class of nonlinear bilevel programming problems where the follower’s objective is a function of the linear expression of all variables, and the follower’s constraint functions are convex with respect to the follower’s variables. First, based on the features of the follower’s problem, we give a new decomposition scheme by which the follower’s optimal solution can be obtained easily. Then, to solve efficiently this class of problems by using evolutionary algorithm, novel evolutionary operators are designed by considering the best individuals and the diversity of individuals in the populations. Finally, based on these techniques, a new evolutionary algorithm is proposed. The numerical results on 20 test problems illustrate that the proposed algorithm is efficient and stable.

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