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A new class of functions for measuring solution integrality in the Feasibility Pump approach

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  • Marianna De Santis

    ()
    (Dipartimento di Informatica e Sistemistica "Antonio Ruberti" Sapienza, Universita' di Roma)

  • Stefano Lucidi

    ()
    (Dipartimento di Informatica e Sistemistica "Antonio Ruberti" Sapienza, Universita' di Roma)

  • Francesco Rinaldi

    ()
    (Dipartimento di Informatica e Sistemistica "Antonio Ruberti" Sapienza, Universita' di Roma)

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    Abstract

    Mixed-Integer optimization is a powerful tool for modeling many optimization problems arising from real-world applications. Finding a rst feasible solution represents the rst step for several MIP solvers. The Feasibility pump is a heuristic for nding feasible solutions to mixed integer linear problems which is eective even when dealing with hard MIP instances. In this work, we start by interpreting the Feasibility Pump as a Frank-Wolfe method applied to a nonsmooth concave merit function. Then, we dene a general class of functions that can be included in the Feasibility Pump scheme for measuring solution integrality and we identify some merit functions belonging to this class. We further extend our approach by dynamically combining two dierent merit functions. Finally, we dene a new version of the Feasibility Pump algorithm, which includes the original version of the Feasibility Pump as a special case, and we present computational results on binary MILP problems showing the eectiveness of our approach.

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    File URL: http://www.dis.uniroma1.it/~bibdis/RePEc/aeg/wpaper/2011-08.pdf
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    Bibliographic Info

    Paper provided by Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza" in its series DIS Technical Reports with number 2011-08.

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    Date of creation: 2011
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    Handle: RePEc:aeg:wpaper:2011-8

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    Keywords: Mixed integer programming; Concave penalty functions; Frank-Wolfe algorithm; Feasibility Problem;

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    1. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2010. "Feasibility Pump-Like Heuristics for Mixed Integer Problems," DIS Technical Reports 2010-15, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    2. Robert M. Saltzman & Frederick S. Hillier, 1992. "A Heuristic Ceiling Point Algorithm for General Integer Linear Programming," Management Science, INFORMS, vol. 38(2), pages 263-283, February.
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