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Three ideas for a feasibility pump for nonconvex MINLP

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Abstract

We describe an implementation of the Feasibility Pump heuristic for nonconvex MINLPs. Our implementation takes advantage of three novel techniques, which we discuss here: a hierarchy of procedures for obtaining an integer solution, a generalized definition of the distance function that takes into account the nonlinear character of the problem, and the insertion of linearization cuts for nonconvex constraints at every iteration. We implemented this new variant of the Feasibility Pump as part of the global optimization solver Couenne. We present experimental results that compare the impact of the three discussed features on the ability of the Feasibility Pump to find feasible solutions and on the solution quality.

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Acknowledgments

The major part of this research was conducted while Timo Berthold was at Zuse Institute Berlin and Pietro Belotti was at Clemson University. We would like to thank our former affiliations for all the support they gave us, including, but not limited to, this project.

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Authors and Affiliations

  1. Fair Isaac Europe Ltd, International Square, Starley Way, Birmingham, B37 7GN, UK

    Pietro Belotti

  2. Fair Isaac Germany GmbH, Takustr.7, 14195, Berlin, Germany

    Timo Berthold

Authors
  1. Pietro Belotti
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  2. Timo Berthold
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Correspondence to Timo Berthold.

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Belotti, P., Berthold, T. Three ideas for a feasibility pump for nonconvex MINLP. Optim Lett 11, 3–15 (2017). https://doi.org/10.1007/s11590-016-1046-0

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