Abstract
An interactive procedure for multiple-objective analysis of linear and non-linear programs is presented. At the decision phase of the procedure, a sample of points, composed of the current point and a number of alternative proposals, is presented to the decision maker (DM). The sample is constructed to ensure a relatively easy evaluation of the sample by the DM. To this end an outranking relation is used as a local preference model in a neighbourhood of the current point. The outranking relation is used to define a sub-region of the non-dominated set the sample presented to the DM comes from. The DM has two possibilities, or degrees of freedom, to move from one sub-region to another which better fits his/her preferences. The first possibility consists in specifying a new reference point which is then projected onto the non-dominated set in order to find a better non-dominated point. The second possibility consists in shifting the current point to a selected point from the sub-region. In both cases, a new sub-region is defined around the updated current point. This technique can be compared to projecting a focused beam of light from a spotlight at the reference point onto the non-dominated set; the highlighted sub-region changes when either the reference point or the point of interest in the non-dominated set are changed.
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References
Benayoun R., de Montgolfier J., Tergny J. and Larichev 0., Linear programming with multiple objective functions: step method (STEM). Operational Research Quarterly, 24: 65–77, 1971
Jacquet-Lagré ze E., Meziani R. and Slowiñski R, MOLP with an interactive assessment of a piecewise-linear utility function. Eur. J. Oper. Res., 31: 350–357, 1987
Jaszkiewicz A. and Slowiñski R, Cone Contraction Method with Visual Interaction for Multiple-Objective Non-Linear Programmes. Journal of Multi-Criteria Decision Analysis, 1: 29–46, 1992
Korhonen P ., VIG - a visual interactive support system for multiple criteria decision making. Belg. J. Ops Res. Statist. Comput. Sci., 27: 3–15, 1987
Korhonen P. and Wallenius J., A Pareto race. Naval Research Logistics, 35: 615–623, 1988
Korhonen P., Wallenius J. and Zionts S., A Computer Graphics-Based Decision Support System for Multiple Objective Linear Programming. Eur. J. Oper. Res., 60: 280–286, 1992
Lee S.M. and Shim J.P., Interactive goal programming on the microcomputer to establish priorities for small business. Journal of the Operational Research Society, 37: 571 - 577, 1986.
Lotfi V., Stewart T.J. and Zionts S., An aspiration-level interactive model for multiple critirea decision making. Comput. Oper. Res., in press
Luce D., Semiorders and a theory of utility discrimination. Econometrica, 24: 178 – 191, 1956.
Narula S.C., Kirilov L. and Vassilev V., Reference direction approach for solving multiple objective nonlinear programming problems. Proceedings of the Tenth International Conference on Multiple Criteria Decision Making, Taipei, 2: 355 - 362, 1992.
Poincaré H ., La valeur de la Science, Paris. Flammarion, 1935
Rosen J.B., The gradient projection method for nonlinear programming. Part I: Linear constraints. SIAM J. Appl. Math., 8, 1960.
Roy B., ELECTRE III - un algorithme de classement fondé sur une représentation floue des préférences en présence de critb res multiples. Cahiers du CERO, 20. 3–24, 1978
Roy B., Méthodologie Multicrite re d’Aide à la Décision, Paris: Economica, 1985.
Roy B., The outranking approach and the foundations of ELECTRE methods. In: Bana e Costa C.A. (ed.) Readings in Multiple Criteria Decision Aid, Berlin: Springer-Verlag, 155–183, 1990
Vincke P ., Basic concepts of preference modelling. In: Bana e Costa C.A. (ed.) Readings in Multiple Criteria Decision Aid, Berlin: Springer-Verlag, 101–118, 1990
Wierzbicki A.P., The use of reference objective in Multiobjective Optimization. In: Fandel G. and Gal T. (eds.) Multiple Criteria Decision Making, Theory and Application, Berlin. Springer-Verlag, 468 - 486, 1980.
Wierzbicki A.P., On the completeness and constructiveness of parametric characterizations to vector optimization problems. OR Spectrum, 8: 73–87, 1986
Zionts S. and Wallenius J., An interactive programming method for solving the multiple criteria problem. Management Science, 22: 652–663, 1976.
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© 1994 Springer-Verlag New York, Inc.
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Jaszkiewicz, A., Słowińsk, R. (1994). The Light Beam Search Over a Non-dominated Surface of a Multiple-objective Programming Problem. 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_10
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DOI: https://doi.org/10.1007/978-1-4612-2666-6_10
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