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A heuristic algorithm for mixed-integer programming problems

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Approaches to Integer Programming

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 2))

Abstract

A heuristic algorithm for solving mixed-integer programming problems is proposed. The basic idea is to search good feasible solutions located near the LP optimal solution. It consists of four phases: Phase 0, computation of LP optimal solution; Phase 1, computation of the central trajectory T of the feasible region; Phase 2, search for (integer) feasible solutions along T; Phase 3, improvements of feasible solutions. The computational results are encouraging. For example, randomly generated problems with 50 constraints and 400 variables consumed 2∼3 minutes on a FACOM 230/60. The quality of the obtained solutions seem to be quite high. In fact, for many problems with known optimal solutions, our algorithm was successful in obtaining exact optimal solutions.

This paper is a slightly shortened version of the working paper [8], which is available from the authors. A FORTRAN list of the entire code is also available upon request.

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Author information

Authors and Affiliations

  1. Kyoto University, Kyoto, Japan

    Toshihide Ibaraki & Hisashi Mine

  2. Sumitomo Electric Industry, LTD., Osaka, Japan

    Tateaki Ohashi

Authors
  1. Toshihide Ibaraki
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  2. Tateaki Ohashi
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  3. Hisashi Mine
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M. L. Balinski

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© 1974 The Mathematical Programming Society

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Ibaraki, T., Ohashi, T., Mine, H. (1974). A heuristic algorithm for mixed-integer programming problems. In: Balinski, M.L. (eds) Approaches to Integer Programming. Mathematical Programming Studies, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120691

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  • DOI: https://doi.org/10.1007/BFb0120691

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00739-2

  • Online ISBN: 978-3-642-00740-8

  • eBook Packages: Springer Book Archive

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