Feasibility pump 2.0. Finding a feasible solution of a given mixed-integer programming (MIP) model is a very important đť’©đť’«-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. Wolsey, Laurence A.: Integer programming (2021)
  2. Androutsopoulos, Konstantinos N.; Manousakis, Eleftherios G.; Madas, Michael A.: Modeling and solving a bi-objective airport slot scheduling problem (2020)
  3. Bernal, David E.; Vigerske, Stefan; Trespalacios, Francisco; Grossmann, Ignacio E.: Improving the performance of DICOPT in convex MINLP problems using a feasibility pump (2020)
  4. GrĂĽbel, Julia; Kleinert, Thomas; Krebs, Vanessa; Orlinskaya, Galina; Schewe, Lars; Schmidt, Martin; ThĂĽrauf, Johannes: On electricity market equilibria with storage: modeling, uniqueness, and a distributed ADMM (2020)
  5. Neumann, Christoph; Stein, Oliver; Sudermann-Merx, Nathan: Granularity in nonlinear mixed-integer optimization (2020)
  6. Takapoui, Reza; Moehle, Nicholas; Boyd, Stephen; Bemporad, Alberto: A simple effective heuristic for embedded mixed-integer quadratic programming (2020)
  7. Berthold, Timo; Lodi, Andrea; Salvagnin, Domenico: Ten years of feasibility pump, and counting (2019)
  8. Carvalho, Iago A.: On the statistical evaluation of algorithmic’s computational experimentation with infeasible solutions (2019)
  9. Gamrath, Gerald; Berthold, Timo; Heinz, Stefan; Winkler, Michael: Structure-driven fix-and-propagate heuristics for mixed integer programming (2019)
  10. Göttlich, S.; Potschka, A.; Teuber, C.: A partial outer convexification approach to control transmission lines (2019)
  11. Miertoiu, Florin Ilarion; Dumitrescu, Bogdan: Feasibility pump algorithm for sparse representation under Laplacian noise (2019)
  12. Neumann, Christoph; Stein, Oliver; Sudermann-Merx, Nathan: A feasible rounding approach for mixed-integer optimization problems (2019)
  13. Pal, Aritra; Charkhgard, Hadi: FPBH: a feasibility pump based heuristic for multi-objective mixed integer linear programming (2019)
  14. Pal, Aritra; Charkhgard, Hadi: A feasibility pump and local search based heuristic for bi-objective pure integer linear programming (2019)
  15. Sadykov, Ruslan; Vanderbeck, François; Pessoa, Artur; Tahiri, Issam; Uchoa, Eduardo: Primal heuristics for branch and price: the assets of diving methods (2019)
  16. Schewe, Lars; Schmidt, Martin: Computing feasible points for binary MINLPs with MPECs (2019)
  17. Wei, Mingyuan; Qi, Mingyao; Wu, Tao; Zhang, Canrong: Distance and matching-induced search algorithm for the multi-level lot-sizing problem with substitutable bill of materials (2019)
  18. Yu, Bin; Mitchell, John E.; Pang, Jong-Shi: Solving linear programs with complementarity constraints using branch-and-cut (2019)
  19. Berthold, Timo: A computational study of primal heuristics inside an MI(NL)P solver (2018)
  20. Berthold, Timo; Perregaard, Michael; Mészáros, Csaba: Four good reasons to use an interior point solver within a MIP solver (2018)

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