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01-Applied Mathematics & Information Sciences
An International Journal


Volumes > Volume 5 > No. 5-2S


An Evolutionary Algorithm with Local Search for Convex Quadratic Bilevel Programming Problems

PP: 139S-146S
Hecheng Li, Yuping Wang,
We present an evolutionary algorithm based on a local search scheme for convex quadratic bilevel programming problems. At first, based on Karush-Kuhn-Tucher conditions, the follower’s problem is replaced by its linear complementarity systems, and the bases of the linear systems are encoded as individuals of populations. For each fixed individual l, we can obtain the follower’s optimal solution y(x). In addition, we replace the follower vector y in the leader’s problem by the solution function y(x), and then the leader’s problem is converted to a convex quadratic problem which only involves x. At last, we solve the problem using a classical local search technique and obtain an optimal objective value F, which is taken as the fitness of l. The distinct characteristic of the algorithm is that the bases of the follower’s complementarity systems are searched instead of the variable values, which makes the search space become finite. In order to illustrate the efficiency of the proposed algorithm, 10 test problems selected from literature are solved, and the results show that the proposed algorithm is efficient and robust.

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