Abstract
During the last few years, multiobjective optimization has received growing attention: the number of publications related to this subject between 1974 and 1979 exceeds 120. There are many approaches, techniques and tools related to multiobjective decision making and optimization; however, not all approaches are equally developed, and the resulting tools are often applied because of certain traditions rather than their suitability for solving a given problem. Therefore, this paper is devoted to a comparative evaluation of various approaches and tools. This evaluation is based, however, first on a classification of problems of multiobjective decision making and optimization. Thereafter, the available approaches, methods, techniques and tools are shortly presented and evaluated in terms of suitability for various classes of problems.
The final part of the paper presents a broader description of a relatively new approach based on reference objective levels, not fully developed yet but applicable in many classes of problems. A new notion of extended threshold utility functions, other basic theoretical results, applicational examples and directions of further research related to this approach are presented.
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References
Ackoff, R.L., The Future of Operation Research is Past, Operational Research Society, Vol.30, 93–104, 1979.
Bell, D.E., R.L. Keeney and H. Raiffa, Conflicting Objectives in Decisions, Wiley/IIASA International Series on Applied Systems Analysis, New York.
O'Neill, V.R. and B. Rust, Aggregation error in Ecological Models, Journal of Ecological Modelling, Vol. 7, 90–105, 1979.
Cohn, J.L. and D.H. Marks, A Review and Evaluation of Multiobjective Programming Techniques, Water Resources Research, Vol.11, 208–220, April 1975.
Da Cunha, N.O. and E. Polak, Constrained Minimisation under Vector-Valued Criteria in Finite Dimensional Space, Journal of Mathematical Analysis and Applications, Vol. 19, 103–124, 1967.
Debreu, G., Theory of Value, Wiley, New York, 1959.
Dyer, J.S., Interactive Goal Programming, Management Science, Vol. 19(1), 62–70, March 1972.
Elster, K.H. and R. Nehse, Necessary and Sufficient Conditions for Order Completeness of Partially Ordered Vector Space, Mathematische Nachrichten, Vol. 81, 301–311, 1978.
Evans, J.P. and R.E. Steuer, A Revised Simplex Method for Linear Multiple Objective Programs, Mathematical Programming, Vol.5, 54–72, 1973.
Fishburn, P.C., Utility Theory for Decision Making, Wiley, New York, 1970.
Geoffrion, A.M. Proper Efficiency and the Theory of Vector Maximization, Journal of Mathematical Analysis and Applications, Vol.22, 816–630, 1968.
Haimes, Y.Y., W.A. Hall and H.T. Freedman, Multiobjective Optimization in Water Resources Systems: The Surrogate Worth Trade-off Method, Elsevier, New York, 1975.
Hogarth, R., Cognitive Process and the Assessment of Subjective Probability Distributions, Journal of the American Statistical Association, Vol.70, 271–289, 1975.
Keeney, R.L. and H. Raiffa, Decisions with Multiple Objectives: Preferences and Value Trade-offs, Wiley, New York, 1976.
Kornbluth, J.H.S., A Survey of Goal Programming, Omega, Vol.1, 193–205, 1973.
Kallio, M. and A. Lewandowski, Reference point optimization for compromise finding in the development of the Finnish forestry industrial sector, IIASA WP, 1979, in preparation.
Leitmann, G., and W. Schmitendorf, Some Sufficient Conditions for Pareto-Optimal Control, Journal of Dynamical Systems, Measurement and Control, Vol.95(3), 1973.
Pareto, V. Cours d'Economie Politiqe, Rouge, Lausanne, 1896.
Peschel, M. and C. Riedel, Polyoptimization — a Decision Making Aid for Technical Engineering Compromise Solutions, (in German), VEB Verlag Technik, Berlin.
Sakluvadze, M.E., Optimization of Vector Functionals. Part I: Programming of Optimal Trajectories, Automatika i Telemekjanika, No.8, 5–15, Part III: The Analytic Construction of Optimal Controls, Ibidem, No.9, 5. 15, (in Russian) 1971.
Sakluvadze, M.E., On the Existence of Solutions in Problems of Optimization under Vector-Valued Criteria, Journal of Optimization Theory and Applications, Vol.13(2), 1974.
Wierzbicki, A.P., Penalty Methods in Solving Optimization Problems with Vector Performance Criteria, Proceedings of VI-th IFAC World Congress, Cambridge, Boston, 1975.
Wierzbicki, A.P., Basic Properties of Scalarizing Functionals for Multiobjective Optimization, Mathematische Operationsforschung and Statistik, Ser. Optimization, Vol.8(1), 55–60, 1977.
Wierzbicki, A.P. and St. Kurcyusz, Projection on a Cone, Penalty Functional and Duality Theory for Problems with Inequality Constraints in Hilbert Space, SIAM Journal Control and Optimization, Vol. 15, 25–26, 1977.
Wierzbicki, A.P., On the Use of Penlty Functions in Multiobjective Optimization, Proceedings of the International Symposium on Operations Research, Mannheim, 1978.
Wierzbicki, A.P., Reference Objective Levels in Multiobjective Decision Theory and Optimization, International Institute for Applied Systems Analysis, WP-66-1979.
Yu, P.L. and G. Leitmann, Compromise Solutions, Domination Structures and Savlukadze's Solution, Journal of Optimization Theory and Applications, Vol.13, 362–378, 1974.
Zeleny, M., Linear Multiobjective Programming, Springer Verlag, Berlin, 1974.
Zeleny, M., Multicriterion Decision-Making Bibliography, in Multiple Criteria Decision Making, Kyoto, 1975, ed. M. Zeleny, Springer Verlag, Berlin, 1976.
Zionts, Z., ed., Multiple Criteria Problem Solving, Springer Verlag, Berlin, 1978.
Zowe, J., A Quality Theorem for Convex Programming Problem in Order Complete Vector Lattices, J. Math, Analysis Appl., Vol.50, 273–287, 1975.
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Wierzbicki, A.P. (1980). A methodological guide to multiobjective optimization. In: Iracki, K., Malanowski, K., Walukiewicz, S. (eds) Optimization Techniques. Lecture Notes in Control and Information Sciences, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036382
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DOI: https://doi.org/10.1007/BFb0036382
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