The Watermelon Algorithm for The Bilevel Integer Linear Programming Problem

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2017-01-01
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Wang, Lizhi
Xu, Pan
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Abstract

This paper presents an exact algorithm for the bilevel integer linear programming (BILP) problem. The proposed algorithm, which we call the watermelon algorithm, uses a multiway disjunction cut to remove bilevel infeasible solutions from the search space, which was motivated by how watermelon seeds can be carved out by a scoop. Serving as the scoop, a polyhedron is designed to enclose as many bilevel infeasible solutions as possible, and then the complement of this polyhedron is applied to the search space as a multiway disjunction cut in a branch-and-bound framework. We have proved that the watermelon algorithm is able to solve all BILP instances finitely and correctly, providing either a global optimal solution or a certificate of infeasibility or unboundedness. Computational experiment results on two sets of small- to medium-sized instances suggest that the watermelon algorithm could be significantly more efficient than previous branch-and-bound based BILP algorithms.

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This article is published as Wang, Lizhi, and Pan Xu. "The Watermelon Algorithm for The Bilevel Integer Linear Programming Problem." SIAM Journal on Optimization 27, no. 3 (2017): 1403-1430. doi: 10.1137/15M1051592. Posted with permission.

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