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A Primal Heuristic for Nonsmooth Mixed Integer Nonlinear Optimization

  • Chapter
Facets of Combinatorial Optimization

Abstract

Complex real-world optimization tasks often lead to mixed-integer nonlinear problems (MINLPs). However, current MINLP algorithms are not always able to solve the resulting large-scale problems. One remedy is to develop problem specific primal heuristics that quickly deliver feasible solutions. This paper presents such a primal heuristic for a certain class of MINLP models. Our approach features a clear distinction between nonsmooth but continuous and genuinely discrete aspects of the model. The former are handled by suitable smoothing techniques; for the latter we employ reformulations using complementarity constraints. The resulting mathematical programs with equilibrium constraints (MPEC) are finally regularized to obtain MINLP-feasible solutions with general purpose NLP solvers.

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Acknowledgements

This work has been funded by the Federal Ministry of Economics and Technology owing to a decision of the German Bundestag. We would next like to thank our industry partner Open Grid Europe GmbH and the project partners in the ForNe consortium. The authors are also indebted to an anonymous referee whose comments and suggestions greatly improved the quality of the paper. Finally, the second author would like to express his gratitude for the challenging and stimulating scientific environment and the personal support that Martin Grötschel provided to him as a PostDoc in his research group at ZIB, and for the continued fruitful cooperation that he is now experiencing as a ZIB Fellow with his own research group at Leibniz Universität Hannover. We dedicate this paper to Martin Grötschel on the occasion of his 65th birthday.

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  1. Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    Martin Schmidt, Marc C. Steinbach & Bernhard M. Willert

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  1. Martin Schmidt
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Correspondence to Marc C. Steinbach .

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  1. Dept. of Computer Science, University of Cologne, Pohligstr. 1, Cologne, 50969, Germany

    Michael Jünger

  2. Dept. of Computer Science, University of Heidelberg, Im Neuenheimer Feld 326, Heidelberg, 69120, Germany

    Gerhard Reinelt

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Schmidt, M., Steinbach, M.C., Willert, B.M. (2013). A Primal Heuristic for Nonsmooth Mixed Integer Nonlinear Optimization. In: Jünger, M., Reinelt, G. (eds) Facets of Combinatorial Optimization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38189-8_13

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