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A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems

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Abstract

The bilevel programming problem is strongly NP-hard and non-convex, which implies that the problem is very challenging for most canonical optimization approaches using single-point search techniques to find global optima. In the present paper, a class of nonlinear bilevel programming problems are considered where the follower is a linear fractional program. Based on a novel coding scheme, a genetic algorithm with global convergence was developed. First, potential bases of the follower’s problem were taken as individuals, and a genetic algorithm was used to explore these bases. In addition, in order to evaluate each individual, a fitness function was presented by making use of the optimality conditions of linear fractional programs. Also, the fitness evaluation, as a sub-procedure of optimization, can partly improve the leader’s objective. Finally, some computational examples were solved and the results show that the proposed algorithm is efficient and robust.

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Acknowledgments

The research work was supported by the National Natural Science Foundation of China under Grant Nos. 61463045 and 61065009, the Natural Science Foundation of Qinghai Provincial under Grant No. 2013-z-937Q, and the National Social Science Fund of China under Grant No. 13BXW037.

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  1. Department of Mathematics, Qinghai Normal University, Xining, 810008, China

    Hecheng Li

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  1. Hecheng Li
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Correspondence to Hecheng Li.

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Li, H. A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems. Ann Oper Res 235, 543–558 (2015). https://doi.org/10.1007/s10479-015-1878-5

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