Feasibility pump 2.0. Finding a feasible solution of a given mixed-integer programming (MIP) model is a very important 𝒩𝒫-complete problem that can be extremely hard in practice. Feasibility Pump (FP) is a heuristic scheme for finding a feasible solution to general MIPs that can be viewed as a clever way to round a sequence of fractional solutions of the LP relaxation, until a feasible one is eventually found. In this paper we study the effect of replacing the original rounding function (which is fast and simple, but somehow blind) with more clever rounding heuristics. In particular, we investigate the use of a diving-like procedure based on rounding and constraint propagation-a basic tool in Constraint Programming. Extensive computational results on binary and general integer MIPs from the literature show that the new approach produces a substantial improvement of the FP success rate, without slowing-down the method and with a significantly better quality of the feasible solutions found.

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  1. Belotti, Pietro; Berthold, Timo: Three ideas for a feasibility pump for nonconvex MINLP (2017)
  2. Dupin, Nicolas: Tighter MIP formulations for the discretised unit commitment problem with MIN-stop ramping constraints (2017)
  3. Eronen, Ville-Pekka; Kronqvist, Jan; Westerlund, Tapio; Mäkelä, Marko M.; Karmitsa, Napsu: Method for solving generalized convex nonsmooth mixed-integer nonlinear programming problems (2017)
  4. Geißler, Björn; Morsi, Antonio; Schewe, Lars; Schmidt, Martin: Penalty alternating direction methods for mixed-integer optimization: a new view on feasibility pumps (2017)
  5. Hanafi, Saïd; Todosijević, Raca: Mathematical programming based heuristics for the 0--1 MIP: a survey (2017)
  6. Li, M.; Liu, Q.: Inexact feasibility pump for mixed integer nonlinear programming (2017)
  7. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  8. Fischetti, Matteo; Lodi, Andrea; Monaci, Michele; Salvagnin, Domenico; Tramontani, Andrea: Improving branch-and-cut performance by random sampling (2016)
  9. Sharma, Shaurya; Knudsen, Brage Rugstad; Grimstad, Bjarne: Towards an objective feasibility pump for convex minlps (2016)
  10. Soylu, Banu; Yıldız, Gazi Bilal: An exact algorithm for biobjective mixed integer linear programming problems (2016)
  11. Baena, Daniel; Castro, Jordi; González, José A.: Fix-and-relax approaches for controlled tabular adjustment (2015)
  12. Berthold, Timo; Hendel, Gregor: Shift-and-propagate (2015)
  13. Huang, Kuo-Ling; Mehrotra, Sanjay: An empirical evaluation of a walk-relax-round heuristic for mixed integer convex programs (2015)
  14. Humpola, Jesco; Fügenschuh, Armin; Lehmann, Thomas: A primal heuristic for optimizing the topology of gas networks based on dual information (2015)
  15. Kirst, Peter; Stein, Oliver; Steuermann, Paul: Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints (2015)
  16. Obuchowska, Wiesława T.: Irreducible infeasible sets in convex mixed-integer programs (2015)
  17. Agra, Agostinho; Christiansen, Marielle; Delgado, Alexandrino; Simonetti, Luidi: Hybrid heuristics for a short sea inventory routing problem (2014)
  18. Berthold, Timo: RENS. The optimal rounding (2014)
  19. Berthold, Timo; Gleixner, Ambros M.: Undercover: a primal MINLP heuristic exploring a largest sub-MIP (2014)
  20. Boland, Natashia; Eberhard, Andrew; Engineer, Faramroze; Fischetti, Matteo; Savelsbergh, Martin; Tsoukalas, Angelos: Boosting the feasibility pump (2014)

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