Branching and bounds tighteningtechniques for non-convex MINLP

Many industrial problems can be naturally formulated using mixed integer non-linear programming (MINLP) models and can be solved by spatial Branch&Bound (sBB) techniques. We study the impact of two important parts of sBB methods: bounds tightening (BT) and branching strategies. We extend a branc...

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Bibliographic Details
Published inOptimization methods & software Vol. 24; no. 4-5; pp. 597 - 634
Main Authors Belotti, Pietro, Lee, Jon, Liberti, Leo, Margot, François, Wächter, Andreas
Format Journal Article
LanguageEnglish
Published Taylor & Francis 01.10.2009
Subjects
bounds tightening
branching rules
Couenne
mixed-integer non-linear programming
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Summary:Many industrial problems can be naturally formulated using mixed integer non-linear programming (MINLP) models and can be solved by spatial Branch&Bound (sBB) techniques. We study the impact of two important parts of sBB methods: bounds tightening (BT) and branching strategies. We extend a branching technique originally developed for MILP, reliability branching, to the MINLP case. Motivated by the demand for open-source solvers for real-world MINLP problems, we have developed an sBB software package named couenne (Convex Over- and Under-ENvelopes for Non-linear Estimation) and used it for extensive tests on several combinations of BT and branching techniques on a set of publicly available and real-world MINLP instances. We also compare the performance of couenne with a state-of-the-art MINLP solver.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556780903087124