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An Overview of Techniques for Solving Multiobjective Mathematical Programs

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  • Gerald W. Evans

    (Speed Scientific School, University of Louisville, Louisville, Kentucky 40292)

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    Abstract

    Multiobjective mathematical programming has been one of the fastest growing areas of OR/MS during the last 15 years. This paper presents: (1) some reasons for the rapidly growing increase in interest in multiobjective mathematical programming, (2) a discussion of the advantages and disadvantages of the three general approaches (articulation of the decision maker's preference structure over the multiple objectives prior to, during, or after the optimization) towards multiobjective mathematical programming, (3) a nontechnical overview of many of the specific solution techniques for multiobjective mathematical programming, and (4) a discussion of important areas for further research. The overview concentrates on those techniques which require an articulation of the decision maker's preference structure either during or after the optimization, since these are the areas where most of the recent research has been conducted. It differs from previous overviews in that, in addition to the timing of the elicited preference information, the techniques are also classified according to the types of decision variables contained in the model (i.e., only continuous decision variables, or at least some discrete decision variables). In addition, the types of preference information (e.g., a ranking of outcomes) required of the various techniques are also discussed.

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    File URL: http://dx.doi.org/10.1287/mnsc.30.11.1268
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 30 (1984)
    Issue (Month): 11 (November)
    Pages: 1268-1282

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    Handle: RePEc:inm:ormnsc:v:30:y:1984:i:11:p:1268-1282

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    Keywords: programming: multiple criteria; multiple objectives; algorithms; utility/preference: multiattribute;

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    Cited by:
    1. Crowe, Kevin, 2008. "Modeling the effects of introducing timber sales into volume-based tenure agreements," Forest Policy and Economics, Elsevier, vol. 10(3), pages 174-182, January.
    2. Metev, Boyan S. & Yordanova-Markova, Irena T., 1997. "Multi-objective optimization over convex disjunctive feasible sets using reference points," European Journal of Operational Research, Elsevier, vol. 98(1), pages 124-137, April.
    3. Michael Brusco & Stephanie Stahl, 2001. "An interactive multiobjective programming approach to combinatorial data analysis," Psychometrika, Springer, vol. 66(1), pages 5-24, March.
    4. Metev, Boyan, 1995. "Use of reference points for solving MONLP problems," European Journal of Operational Research, Elsevier, vol. 80(1), pages 193-203, January.
    5. Escobar, María Teresa & Moreno-Jiménez, José María, 2002. "A linkage between the Analytic Hierarchy Process and the Compromise Programming Models," Omega, Elsevier, vol. 30(5), pages 359-365, October.
    6. Alves, Maria Joao & Climaco, Joao, 1999. "Using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems," European Journal of Operational Research, Elsevier, vol. 117(3), pages 565-577, September.
    7. Mustafa, A. & Goh, M., 1996. "Multi-criterion models for higher education administration," Omega, Elsevier, vol. 24(2), pages 167-178, April.
    8. Kalu, Timothy Ch. U., 1999. "Capital budgeting under uncertainty: An extended goal programming approach," International Journal of Production Economics, Elsevier, vol. 58(3), pages 235-251, January.
    9. Francisco J. André & Laura Riesgo, 2006. "A Duality Procedure to Elicit Nonlinear Multiattribute Utility Functions," Working Papers 06.02, Universidad Pablo de Olavide, Department of Economics.
    10. Liu, Fuh-Hwa Franklin & Huang, Chueng-Chiu & Yen, Yu-Lee, 2000. "Using DEA to obtain efficient solutions for multi-objective 0-1 linear programs," European Journal of Operational Research, Elsevier, vol. 126(1), pages 51-68, October.
    11. Agrell, Per J. & Stam, Antonie & Fischer, Gunther W., 2004. "Interactive multiobjective agro-ecological land use planning: The Bungoma region in Kenya," European Journal of Operational Research, Elsevier, vol. 158(1), pages 194-217, October.
    12. Mavrotas, G. & Diakoulaki, D., 1998. "A branch and bound algorithm for mixed zero-one multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 107(3), pages 530-541, June.
    13. Zhang, Weihua & Reimann, Marc, 2014. "A simple augmented ∊-constraint method for multi-objective mathematical integer programming problems," European Journal of Operational Research, Elsevier, vol. 234(1), pages 15-24.
    14. Enriquez-Andrade, Roberto Ramon & Vaca-Rodriguez, Juan Guillermo, 2004. "Evaluating ecological tradeoffs in fisheries management: a study case for the yellowfin tuna fishery in the Eastern Pacific Ocean," Ecological Economics, Elsevier, vol. 48(3), pages 303-315, March.
    15. Francisco J. André & M. Alejandro Cardenete, 2009. "Efficient Economic and Environmental Policies Combining Multicriteria Techniques and General Equilibrium Modelling," Working Papers 09.08, Universidad Pablo de Olavide, Department of Economics.
    16. Dung-Ying Lin & Chi Xie, 2011. "The Pareto-optimal Solution Set of the Equilibrium Network Design Problem with Multiple Commensurate Objectives," Networks and Spatial Economics, Springer, vol. 11(4), pages 727-751, December.
    17. Zhang, Cai Wen & Ong, Hoon Liong, 2004. "Solving the biobjective zero-one knapsack problem by an efficient LP-based heuristic," European Journal of Operational Research, Elsevier, vol. 159(3), pages 545-557, December.
    18. Aouni, Belaid & Kettani, Ossama, 2001. "Goal programming model: A glorious history and a promising future," European Journal of Operational Research, Elsevier, vol. 133(2), pages 225-231, January.
    19. Vetschera, Rudolf, 1992. "Estimating preference cones from discrete choices: Computational techniques and experiences," Discussion Papers, Series 1 259, University of Konstanz, Department of Economics.
    20. Gass, Saul I. & Roy, Pallabi Guha, 2003. "The compromise hypersphere for multiobjective linear programming," European Journal of Operational Research, Elsevier, vol. 144(3), pages 459-479, February.
    21. Benson, Harold P. & Sun, Erjiang, 2002. "A weight set decomposition algorithm for finding all efficient extreme points in the outcome set of a multiple objective linear program," European Journal of Operational Research, Elsevier, vol. 139(1), pages 26-41, May.
    22. Barker, Theresa J. & Zabinsky, Zelda B., 2011. "A multicriteria decision making model for reverse logistics using analytical hierarchy process," Omega, Elsevier, vol. 39(5), pages 558-573, October.
    23. Bennell, Julia A. & Soon Lee, Lai & Potts, Chris N., 2013. "A genetic algorithm for two-dimensional bin packing with due dates," International Journal of Production Economics, Elsevier, vol. 145(2), pages 547-560.
    24. Mehrez, Abraham, 1997. "The interface between OR/MS and decision theory," European Journal of Operational Research, Elsevier, vol. 99(1), pages 38-47, May.

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