Smooth Relations in Multiple Criteria Programming
This paper addresses some methodological aspects of multiple criteria (MC) programming. Special attention is paid to smooth (binary) relations as a model of decision maker’s (DM) preference structure (PS). The theoretical results are presented that allow correct utilization of mighty means of mathematical programming in much wider a context than that of smooth value function.
Also the classification of MC-problems from the viewpoint of PS modelling is proposed. In the framework of this classification a number of approximational MC-methods for solving problems with “smooth-relation” preferences are discussed.
KeywordsDecision Maker Binary Relation Multiple Criterion Choice Function Preference Structure
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- Berezovskiy, B. A., Borzenko, V. I. and Kempner, L. M. (1981). Binary relations in multicriteria optimization. Nauka Pbl., Moscow (in Russian).Google Scholar
- Berezovskiy, B. A., Borzenko, V. I. and Polyashuk, M. V. (1987). Modelling DM’s preference structure (models and methods of multicriteria optimization), Informat-syonnyie matierialy: Kibernetika, No.6, (in Russian).Google Scholar
- Borzenko, V. I. (1989). Approximational Approach to Multicriteria Problems, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, vol.337.Google Scholar
- Frank, M. and Wolf, P. (1956). An algorithm for quadratic programming. Nav. Res. Logist. Quat., vol. 3., No. 1,2.Google Scholar
- Geoffrion A. M. (1979). Vector maximal decomposition programming. In: 7th Mathematical Programming Symp., The Hague.Google Scholar
- Iserman, M. A. and Malishevskiy, A. V. (1982). General choice theory: some aspects. Avtomatika i Telemekhanika, No. 2.Google Scholar
- Polyashuk, M. V. (1990). An interactive procedure for choosing adequate methods for multicriteria problems. Ph.D. Thesis, Moscow, Pbl. of the Institute of Control Sciences (in Russian).Google Scholar
- Wierzbicki A. P. (1979). The use of reference levels in group assessment of solutions of multiobjective optimization. IIASA Working Paper, Austria: Laxenburg.Google Scholar