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Procedures for Finding Nondominated Solutions for Multiple Objective Network Programming Problems

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  • Minghe Sun

    (College of Business, The University of Texas at San Antonio, San Antonio, Texas 78249)

Abstract

Procedures for finding nondominated solutions for multiple objective network programming problems are developed and tested. Nondominated solutions are obtained by solving augmented weighted Tchebycheff network programs. The procedures exploit the network structure of the problem in order to speed up the solution process. To use the network structure as much as possible, a weighted-sum network problem and/or a min-max network problem are solved in order to find a basic solution that is close to the optimal solution of the augmented weighted Tchebycheff network program. Starting from this basic solution, the special simplex method for network problems with side constraints is finally applied to solve the augmented weighted Tchebycheff network program. Computational results show that, for the test problems used in this study, up to 70% of computation time can be saved with the proposed procedures as compared with the sole application of the special simplex method for network problems with side constraints. These procedures can be incorporated into any interactive multiple-objective programming procedure which uses sample nondominated solutions to solve multiple-objective network programming problems.

Suggested Citation

  • Minghe Sun, 2003. "Procedures for Finding Nondominated Solutions for Multiple Objective Network Programming Problems," Transportation Science, INFORMS, vol. 37(2), pages 139-152, May.
    • Handle: RePEc:inm:ortrsc:v:37:y:2003:i:2:p:139-152
    DOI: 10.1287/trsc.37.2.139.15249
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    Cited by:

    1. Jyrki Wallenius & James S. Dyer & Peter C. Fishburn & Ralph E. Steuer & Stanley Zionts & Kalyanmoy Deb, 2008. "Multiple Criteria Decision Making, Multiattribute Utility Theory: Recent Accomplishments and What Lies Ahead," Management Science, INFORMS, vol. 54(7), pages 1336-1349, July.
    2. Minghe Sun, 2005. "Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 422-437, November.
    3. Mingue SUn, 2010. "A Branch-and-Bound Algorithm for Representative Integer Efficient Solutions in Multiple Objective Network Programming Problems," Working Papers 0007, College of Business, University of Texas at San Antonio.
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    5. Hamacher, Horst W. & Pedersen, Christian Roed & Ruzika, Stefan, 2007. "Multiple objective minimum cost flow problems: A review," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1404-1422, February.

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