Branching and bounds tightening techniques for non-connvex 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 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.

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  2. Belotti, Pietro: Bound reduction using pairs of linear inequalities (2013)
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  6. Gentilini, Iacopo; Margot, François; Shimada, Kenji: The travelling salesman problem with neighbourhoods: MINLP solution (2013)
  7. Gleixner, Ambros M.; Weltge, Stefan: Learning and propagating Lagrangian variable bounds for mixed-integer nonlinear programming (2013)
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  14. Chen, Jieqiu; Burer, Samuel: Globally solving nonconvex quadratic programming problems via completely positive programming (2012)
  16. Nannicini, Giacomo; Belotti, Pietro: Rounding-based heuristics for nonconvex MINLPS (2012)
  17. Achterberg, Tobias (ed.); Beck, J. Christopher (ed.): Integration of AI and OR techniques in constraint programming for combinatorial optimization problems. 8th international conference, CPAIOR 2011, Berlin, Germany, May 23--27, 2011. Proceedings (2011)
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  20. Nannicini, Giacomo; Belotti, Pietro; Lee, Jon; Linderoth, Jeff; Margot, François; Wächter, Andreas: A probing algorithm for MINLP with failure prediction by SVM (2011)