Structure-Based Primal Heuristics for Mixed Integer Programming

  • Gerald Gamrath
  • Timo Berthold
  • Stefan Heinz
  • Michael Winkler
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 13)


Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They help to reach optimality faster and provide good feasible solutions early in the solving process. In this paper, we present two new primal heuristics which take into account global structures available within MIP solvers to construct feasible solutions at the beginning of the solving process. These heuristics follow a large neighborhood search (LNS) approach and use global structures to define a neighborhood that is with high probability significantly easier to process while (hopefully) still containing good feasible solutions. The definition of the neighborhood is done by iteratively fixing variables and propagating these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. The neighborhood is solved as a sub-MIP and solutions are transferred back to the original problem. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about every third instance and therewith help to improve the average solving time.


Large neighborhood search Mixed-integer programming  Primal heuristics Domain propagation 



The work for this article has been conducted within the Research Campus Modal funded by the German Federal Ministry of Education and Research (fund number 05M14ZAM). The authors would like to thank the anonymous reviewer for helpful comments on the paper.


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Copyright information

© Springer Japan 2016

Authors and Affiliations

  • Gerald Gamrath
    • 1
  • Timo Berthold
    • 2
  • Stefan Heinz
    • 2
  • Michael Winkler
    • 3
  1. 1.Zuse Institute BerlinBerlinGermany
  2. 2.Fair Isaac Europe Ltdc/o ZIBBerlinGermany
  3. 3.Gurobi GmbHc/o ZIBBerlinGermany

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