Bonmin

An algorithmic framework for convex mixed integer nonlinear programs. This paper is motivated by the fact that mixed integer nonlinear programming is an important and difficult area for which there is a need for developing new methods and software for solving large-scale problems. Moreover, both fundamental building blocks, namely mixed integer linear programming and nonlinear programming, have seen considerable and steady progress in recent years. Wishing to exploit expertise in these areas as well as on previous work in mixed integer nonlinear programming, this work represents the first step in an ongoing and ambitious project within an open-source environment. COIN-OR is our chosen environment for the development of the optimization software. A class of hybrid algorithms, of which branch-and-bound and polyhedral outer approximation are the two extreme cases, are proposed and implemented. Computational results that demonstrate the effectiveness of this framework are reported. Both the library of mixed integer nonlinear problems that exhibit convex continuous relaxations, on which the experiments are carried out, and a version of the software used are publicly available.


References in zbMATH (referenced in 134 articles )

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  1. Berthold, Timo: A computational study of primal heuristics inside an MI(NL)P solver (2018)
  2. Delfino, A.; de Oliveira, W.: Outer-approximation algorithms for nonsmooth convex MINLP problems (2018)
  3. Holzapfel, Andreas; Kuhn, Heinrich; Sternbeck, Michael G.: Product allocation to different types of distribution center in retail logistics networks (2018)
  4. Liu, Kanglin; Zhang, Zhi-Hai: Capacitated disassembly scheduling under stochastic yield and demand (2018)
  5. Ljubić, Ivana; Moreno, Eduardo: Outer approximation and submodular cuts for maximum capture facility location problems with random utilities (2018)
  6. Lu, Jie; Gupte, Akshay; Huang, Yongxi: A mean-risk mixed integer nonlinear program for transportation network protection (2018)
  7. Belotti, Pietro; Berthold, Timo: Three ideas for a feasibility pump for nonconvex MINLP (2017)
  8. Fernández, F. J.; Alvarez-Vázquez, L. J.; Martínez, A.; Vázquez-Méndez, M. E.: A 3D optimal control problem related to the urban heat islands (2017)
  9. Gemine, Quentin; Ernst, Damien; Cornélusse, Bertrand: Active network management for electrical distribution systems: problem formulation, benchmark, and approximate solution (2017)
  10. Lee, Jon; Skipper, Daphne: Virtuous smoothing for global optimization (2017)
  11. Mencarelli, Luca; Sahraoui, Youcef; Liberti, Leo: A multiplicative weights update algorithm for MINLP (2017)
  12. Pecci, Filippo; Abraham, Edo; Stoianov, Ivan: Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks (2017)
  13. Scioletti, Michael S.; Newman, Alexandra M.; Goodman, Johanna K.; Zolan, Alexander J.; Leyffer, Sven: Optimal design and dispatch of a system of diesel generators, photovoltaics and batteries for remote locations (2017)
  14. Belotti, Pietro; Bonami, Pierre; Fischetti, Matteo; Lodi, Andrea; Monaci, Michele; Nogales-Gómez, Amaya; Salvagnin, Domenico: On handling indicator constraints in mixed integer programming (2016)
  15. Borraz-Sánchez, Conrado; Bent, Russell; Backhaus, Scott; Hijazi, Hassan; Van Hentenryck, Pascal: Convex relaxations for gas expansion planning (2016)
  16. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  17. Buchheim, Christoph; De Santis, Marianna; Lucidi, Stefano; Rinaldi, Francesco; Trieu, Long: A feasible active set method with reoptimization for convex quadratic mixed-integer programming (2016)
  18. de Oliveira, Welington: Regularized optimization methods for convex MINLP problems (2016)
  19. Fampa, Marcia; Lee, Jon; Maculan, Nelson: An overview of exact algorithms for the Euclidean Steiner tree problem in $n$-space (2016)
  20. Fampa, Marcia; Lee, Jon; Melo, Wendel: A specialized branch-and-bound algorithm for the Euclidean Steiner tree problem in $n$-space (2016)

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