A branch-and-cut algorithm for Mixed-Integer Bilinear Programming

•We consider the Mixed-Integer Bilinear Programming problem.•We design an exact branch-and-cut algorithm, based on a new branching rule.•A new family of intersection cuts derived from bilinear disjunctions is proposed.•We analyze the algorithm’s performance on a large instance set from the literatur...

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Bibliographic Details
Published in:European journal of operational research Vol. 282; no. 2; pp. 506 - 514
Main Authors: Fischetti, Matteo, Monaci, Michele
Format: Journal Article
Language:English
Published: Elsevier B.V 16.04.2020
Subjects:
Bilinear programming
Branch-and-cut algorithms
Combinatorial optimization
Intersection cuts
Mixed-integer quadratic programming
Branch-and-cut algorithms
Intersection cuts
Bilinear programming
Combinatorial optimization
Mixed-integer quadratic programming
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•We consider the Mixed-Integer Bilinear Programming problem.•We design an exact branch-and-cut algorithm, based on a new branching rule.•A new family of intersection cuts derived from bilinear disjunctions is proposed.•We analyze the algorithm’s performance on a large instance set from the literature. In this paper, we consider the Mixed-Integer Bilinear Programming problem, a widely-used reformulation of the classical mixed-integer quadratic programming problem. For this problem we describe a branch-and-cut algorithm for its exact solution, based on a new family of intersection cuts derived from bilinear-specific disjunctions. We also introduce a new branching rule that is specifically designed for bilinear problems. We computationally analyze the behavior of the proposed algorithm on a large set of mixed-integer quadratic instances from the MINLPlib problem library. Our results show that our method, even without intersection cuts, is competitive with a state-of-the-art mixed-integer nonlinear solver. As to intersection cuts, their extensive use at each branching node tends to slow down the solver for most problems in our test bed, but they are extremely effective for some specific instances.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2019.09.043