Finding integer efficient solutions for multiple objective network programming problems

  • Sun M
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Abstract

For many practical multiple objective network programming ({MONP}) problems, only integer solutions are meaningful and acceptable. Representative efficient solutions are usually generated by solving augmented weighted Tchebycheff network programs ({AWTNPs}), sub-problems derived from {MONP} problems. However, efficient solutions generated this way are usually not integer valued. In this study, two algorithms are developed to construct integer efficient solutions starting from fractional efficient solutions. One algorithm finds a single integer efficient solution in the neighborhood of the fractional efficient solution. The other enumerates all integer efficient solutions in the same neighborhood. Theory supporting the proposed algorithms is developed. Two detailed examples are presented to demonstrate the algorithms. Computational results are reported. The best integer efficient solution is very close, if not equal, to the integer optimal solution. The {CPU} time taken to find integer efficient solutions is negligible, when compared with that taken to solve {AWTNPs}. © 2010 Wiley Periodicals, Inc. {NETWORKS}, Vol. 57(4), 362-375 2011

Author-supplied keywords

  • integer programming
  • multiple criteria decision making
  • multiple objective programming
  • network flow algorithms

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Authors

  • Minghe Sun

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