Couenne

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.


References in zbMATH (referenced in 60 articles )

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  1. Buchheim, C.; De Santis, M.; Palagi, L.; Piacentini, M.: An exact algorithm for nonconvex quadratic integer minimization using ellipsoidal relaxations (2013)
  2. Buchheim, Christoph; Wiegele, Angelika: Semidefinite relaxations for non-convex quadratic mixed-integer programming (2013)
  3. Cassioli, A.; Consolini, L.; Locatelli, M.; Longo, A.: Optimization and homotopy methods for the Gibbs free energy of simple magmatic mixtures (2013)
  4. Gentilini, Iacopo; Margot, François; Shimada, Kenji: The travelling salesman problem with neighbourhoods: MINLP solution (2013)
  5. Gleixner, Ambros M.; Weltge, Stefan: Learning and propagating Lagrangian variable bounds for mixed-integer nonlinear programming (2013)
  6. Gupte, Akshay; Ahmed, Shabbir; Cheon, Myun Seok; Dey, Santanu: Solving mixed integer bilinear problems using MILP formulations (2013)
  7. Janes, Pete P.; Rendell, Alistair P.: Deterministic global optimization in ab-initio quantum chemistry (2013)
  8. Kirches, Christian; Leyffer, Sven: TACO: a toolkit for AMPL control optimization (2013)
  9. Misener, Ruth; Floudas, Christodoulos A.: GLOMIQO: global mixed-integer quadratic optimizer (2013)
  10. Ruiz, Manuel; Briant, Olivier; Clochard, Jean-Maurice; Penz, Bernard: Large-scale standard pooling problems with constrained pools and fixed demands (2013)
  11. Azad, Md. Abul Kalam; Fernandes, Edite M. G. P.: A modified differential evolution based solution technique for economic dispatch problems (2012)
  12. Chen, Jieqiu; Burer, Samuel: Globally solving nonconvex quadratic programming problems via completely positive programming (2012)
  13. Exler, Oliver; Lehmann, Thomas; Schittkowski, Klaus: A comparative study of SQP-type algorithms for nonlinear and nonconvex mixed-integer optimization (2012)
  14. Nannicini, Giacomo; Belotti, Pietro: Rounding-based heuristics for nonconvex MINLPS (2012)
  15. 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)
  16. Kirches, Christian: Fast numerical methods for mixed-integer nonlinear model-predictive control (2011)
  17. Liberti, Leo; Mladenović, Nenad; Nannicini, Giacomo: A recipe for finding good solutions to MINLPs (2011)
  18. Nannicini, Giacomo; Belotti, Pietro; Lee, Jon; Linderoth, Jeff; Margot, François; Wächter, Andreas: A probing algorithm for MINLP with failure prediction by SVM (2011)
  19. Sager, Sebastian; Barth, Carola M.; Diedam, Holger; Engelhart, Michael; Funke, Joachim: Optimization as an analysis tool for human complex problem solving (2011)
  20. Belotti, Pietro; Lee, Jon; Liberti, Leo; Margot, François; Wächter, Andreas: Branching and bounds tightening techniques for non-connvex MINLP (2009)