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

Hecheng Li ()

Annals of Operations Research, 2015, vol. 235, issue 1, 543-558

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. Copyright Springer Science+Business Media New York 2015

Keywords: Bilevel programming; Genetic algorithm; Optimal solutions; Bases (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10479-015-1878-5

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