Branching and bounds tighteningtechniques for non-convex MINLP

Authors:
Pietro Belotti;Jon Lee;Leo Liberti;Francois Margot;Andreas Wachter
Affiliations:
Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA;IBM T.J. Watson Research Center, Yorktown Heights, NY, USA;LIX, Ecole Polytechnique, Palaiseau, France;Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA;IBM T.J. Watson Research Center, Yorktown Heights, NY, USA
Venue:
Optimization Methods & Software - GLOBAL OPTIMIZATION
Year:
2009

Citing 26
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Abstract

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.