Campus Units

Industrial and Manufacturing Systems Engineering

Document Type

Article

Publication Version

Published Version

Publication Date

2017

Journal or Book Title

SIAM Journal on Optimization

Volume

27

Issue

3

First Page

1403

Last Page

1430

DOI

10.1137/15M1051592

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.

Comments

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.

Copyright Owner

Society for Industrial and Applied Mathematics

Language

en

File Format

application/pdf

Share

COinS