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.

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  1. Berthold, Timo: A computational study of primal heuristics inside an MI(NL)P solver (2018)
  2. Buchheim, Christoph; Kuhlmann, Renke; Meyer, Christian: Combinatorial optimal control of semilinear elliptic PDEs (2018)
  3. Cozad, Alison; Sahinidis, Nikolaos V.: A global MINLP approach to symbolic regression (2018)
  4. Delfino, A.; de Oliveira, W.: Outer-approximation algorithms for nonsmooth convex MINLP problems (2018)
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  6. Kronqvist, Jan; Lundell, Andreas; Westerlund, Tapio: Reformulations for utilizing separability when solving convex MINLP problems (2018)
  7. Lee, Jon; Skipper, Daphne; Speakman, Emily: Algorithmic and modeling insights via volumetric comparison of polyhedral relaxations (2018)
  8. Liu, Kanglin; Zhang, Zhi-Hai: Capacitated disassembly scheduling under stochastic yield and demand (2018)
  9. Ljubić, Ivana; Moreno, Eduardo: Outer approximation and submodular cuts for maximum capture facility location problems with random utilities (2018)
  10. Lu, Jie; Gupte, Akshay; Huang, Yongxi: A mean-risk mixed integer nonlinear program for transportation network protection (2018)
  11. Belotti, Pietro; Berthold, Timo: Three ideas for a feasibility pump for nonconvex MINLP (2017)
  12. Camm, Jeffrey D.; Magazine, Michael J.; Kuppusamy, Saravanan; Martin, Kipp: The demand weighted vehicle routing problem (2017)
  13. Canca, David; De-Los-Santos, Alicia; Laporte, Gilbert; Mesa, Juan A.: An adaptive neighborhood search metaheuristic for the integrated railway rapid transit network design and line planning problem (2017)
  14. 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)
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  16. Lee, Jon; Skipper, Daphne: Virtuous smoothing for global optimization (2017)
  17. Mencarelli, Luca; Sahraoui, Youcef; Liberti, Leo: A multiplicative weights update algorithm for MINLP (2017)
  18. Pecci, Filippo; Abraham, Edo; Stoianov, Ivan: Penalty and relaxation methods for the optimal placement and operation of control valves in water supply networks (2017)
  19. 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)
  20. Belotti, Pietro; Bonami, Pierre; Fischetti, Matteo; Lodi, Andrea; Monaci, Michele; Nogales-Gómez, Amaya; Salvagnin, Domenico: On handling indicator constraints in mixed integer programming (2016)

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