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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  1. Belotti, Pietro; Berthold, Timo: Three ideas for a feasibility pump for nonconvex MINLP (2017)
  2. Gleixner, Ambros M.; Berthold, Timo; Müller, Benjamin; Weltge, Stefan: Three enhancements for optimization-based bound tightening (2017)
  3. Hart, William E.; Laird, Carl D.; Watson, Jean-Paul; Woodruff, David L.; Hackebeil, Gabriel A.; Nicholson, Bethany L.; Siirola, John D.: Pyomo -- optimization modeling in Python (2017)
  4. Khan, Kamil A.; Watson, Harry A.J.; Barton, Paul I.: Differentiable McCormick relaxations (2017)
  5. Araya, Ignacio; Reyes, Victor: Interval branch-and-bound algorithms for optimization and constraint satisfaction: a survey and prospects (2016)
  6. Dalkiran, Evrim; Sherali, Hanif D.: RLT-POS: reformulation-linearization technique-based optimization software for solving polynomial programming problems (2016)
  7. Gassmann, Horand; Ma, Jun; Martin, Kipp: Communication protocols for options and results in a distributed optimization environment (2016)
  8. Lejeune, Miguel A.; Margot, François: Solving chance-constrained optimization problems with stochastic quadratic inequalities (2016)
  9. Vismara, Philippe; Coletta, Remi; Trombettoni, Gilles: Constrained global optimization for wine blending (2016)
  10. Bao, Xiaowei; Khajavirad, Aida; Sahinidis, Nikolaos V.; Tawarmalani, Mohit: Global optimization of nonconvex problems with multilinear intermediates (2015)
  11. Gago-Vargas, J.; Hartillo, I.; Puerto, J.; Ucha, J.M.: An improved test set approach to nonlinear integer problems with applications to engineering design (2015)
  12. Humpola, Jesco; Fügenschuh, Armin; Lehmann, Thomas: A primal heuristic for optimizing the topology of gas networks based on dual information (2015)
  13. Sadeghi, Javad: A multi-item integrated inventory model with different replenishment frequencies of retailers in a two-echelon supply chain management: a tuned-parameters hybrid meta-heuristic (2015)
  14. Araya, Ignacio; Trombettoni, Gilles; Neveu, Bertrand; Chabert, Gilles: Upper bounding in inner regions for global optimization under inequality constraints (2014)
  15. Carrizosa, Emilio; Guerrero, Vanesa: $rs$-sparse principal component analysis: a mixed integer nonlinear programming approach with VNS (2014)
  16. Kogan, Alexander; Lejeune, Miguel A.: Threshold Boolean form for joint probabilistic constraints with random technology matrix (2014)
  17. Le Thi, Hoai An; Tran, Duc Quynh: Optimizing a multi-stage production/inventory system by DC programming based approaches (2014)
  18. Patil, Bhagyesh V.; Nataraj, P.S.V.: An improved Bernstein global optimization algorithm for MINLP problems with application in process industry (2014)
  19. Pruitt, Kristopher A.; Leyffer, Sven; Newman, Alexandra M.; Braun, Robert J.: A mixed-integer nonlinear program for the optimal design and dispatch of distributed generation systems (2014)
  20. Zorn, Keith; Sahinidis, Nikolaos V.: Global optimization of general non-convex problems with intermediate bilinear substructures (2014)

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