Solving Mixed Integer Bilinear Problems Using MILP Formulations

In this paper, we examine a mixed integer linear programming reformulation for mixed integer bilinear problems where each bilinearterm involves the product of a nonnegative integer variable and a nonnegative continuous variable. This reformulation is obtained by first replacing a general integer var...

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Bibliographic Details
Published in:SIAM journal on optimization Vol. 23; no. 2; pp. 721 - 744
Main Authors: Gupte, Akshay, Ahmed, Shabbir, Cheon, Myun Seok, Dey, Santanu
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Subjects:
Algorithms
Hulls
Hulls (structures)
Inequalities
Integer programming
Integers
Linear programming
Mathematical analysis
Mathematical models
Mixed integer
Optimization
Variables
ISSN:1052-6234, 1095-7189
Online Access:Get full text
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Summary:In this paper, we examine a mixed integer linear programming reformulation for mixed integer bilinear problems where each bilinearterm involves the product of a nonnegative integer variable and a nonnegative continuous variable. This reformulation is obtained by first replacing a general integer variable with its binary expansion and then using McCormick envelopes to linearize the resulting product of continuous and binary variables. We present the convex hull of the underlying mixed integer linear set. The effectiveness of this reformulation and associated facet-defining inequalities are computationally evaluated on five classes of instances. [PUBLICATION ABSTRACT]
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ISSN:1052-6234
1095-7189
DOI:10.1137/110836183