Abstract
In this paper we develop an interactive approach for solving the continuous solution space multiobjective decision making problem. We assume that the decision maker’s preferences can be approximately represented by an Lq distance function from an ideal point. In each iteration the decision maker compares a pair of alternatives. Based on the decision maker’s responses a distance function is estimated. We try to converge to a good solution by improving the estimate of the distance function in each iteration. We also discuss some variations of the approach.
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References
Benayoun, R., J. de Montgolfier, J. Tergny, and O. Larichev, “Linear Programming with Multiple Objective Functions: Step Method (STEM),” Mathematical Programming, 1 (1971), 366–375
Cohon, J. L. Multiobjective Programming and Planning, Academic Press, New York,1978.
Dell, R. F. and M. H. Karwan “An Interactive MCDM Weight Space Reduction Method Utilizing a Tchebycheff Utility Function, ” Naval Research Logistics, 37 (1990), 263 - 277.
Dyer, J. S. and R. K. Sarin, “Measurable Multiattribute Value Functions,” Operations Research, 27 (1979a), 810–822
Dyer, J. S. and R. K. Sarin,“ Group Preference Aggregation Rules Based on Strength of Preference,” Management Science, 25 (1979b), 822 - 832.
Geoffrion, A., J. Dyer, and A. Feinberg, “An Interactive Approach for Multi- criterion Optimization with an Application to the Operations of an Academic Department,” Management Science, 19 (1972), 357 - 368.
Koksalan, M.M., M.H. Karwan, and S. Zionts, “An Improved Method for Solving Multiple Criteria Problems Involving Discrete Alternatives,” IEEE Transactions on SMC, 14 (1984), 24 - 34.
Korhonen, P. and J. Laakso, “A Visual Interactive Method for Solving the Multiple Criteria Problem,” European ]. Operational Research, 24 (1986), 277 - 287.
Korhonen, P. and J. Wallenius, “A Pareto Race,” Naval Research Logistics, 35 (1988), 615 - 623.
Malakooti, B. “ Assessment Through Strength of Preference,” Large Scale Systems, 8 (1985), 169 - 182.
Steuer, R.E . Multiple Criteria Optimization: Theory, Computation, and Application, Wiley, New York, 1986
Steuer, R.E. and E.U. Choo, “An Interactive Weighted Tchebycheff Procedure for Multiple Objective Programming,” Mathematical Programming, 26(1983), 326- 344
Shin, W. S. and A. Ravindran, “ Interactive Multiple Objective Optimization: Survey I - Continuous Case,” Computers and Operations Research, 18, (1991), 97- 114
Wierzbicki, A ., “ On the Completeness and Constructiveness of Parametric Characterizations to Vector Optimization Problems,” OR Spektrum, 8(1986), 73- 87
Zionts, S. and J. Wallenius, “An Interactive Programming Method for Solving the Multiple Criteria Problem,” Management Science, 22 (1976), 652 - 663.
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© 1994 Springer-Verlag New York, Inc.
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Köksalan, M.M., Moskowitz, H. (1994). Solving the Multiobjective Decision Making Problem Using a Distance Function. In: Tzeng, G.H., Wang, H.F., Wen, U.P., Yu, P.L. (eds) Multiple Criteria Decision Making. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2666-6_11
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DOI: https://doi.org/10.1007/978-1-4612-2666-6_11
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7626-5
Online ISBN: 978-1-4612-2666-6
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