ISSN 2071-8594

Russian academy of sciences

Editor-in-Chief

Gennady Osipov

A.V. Lotov, A.I. Riabikov, A.L. Buber Multi-criteria decision making procedure with an inherited set of startingpoints of local optimization of scalar functions of criteria

Abstract.

The paper is devoted to a new dialogue iterative procedure of search for a preferred solution of a complicated non-linear multi-criteria optimization problem, in the framework of which global optimization of a scalar function of criteria is too complicated because of numerous local extrema of the function and for other reasons. In the procedure proposed in the paper, instead of global optimization of a scalar function of criteria, a large number of local optimization problems is solved on each iteration, while the set of starting points of local optimization processes is generated in a small neighborhood of the decision inherited from the previous iteration. Moreover, the type of the scalar function of criteria varies from iteration to iteration. The proposed procedure has got the name "Method of the Heritable Decision" (MHD). Experience of application of the MHD procedure in the framework of multi-criteria development of control rules of the water reservoir cascade located at the main flow of the Angara River is described. The problem of control rule development contains as a part the task of regulation of the level of the Lake Baikal and is described by the model which includes hundreds of parameters of control rules and is related to more, than two dozen of decision criteria.

Keywords:

decision making, non-linear multi-criteria optimization, local scalar optimization, variation of a type of a scalar function of criteria, heritable set of starting points

PP. 100-111.

DOI 10.14357/20718594180320

References

1. Larichev, O.I. 2006. Teoriya i metody prinitiya reshenij [Theory and methods of decision making]. Moscow: Logos. 391 p.
2. Poidinivskij, V.V., and Nogin, V.D. 2007. Pareto-optimalnye resheniya mnogokriterialnykh zadach [Pareto-optimal solutions of multi-criteria problems]. Moscow: Physmatlit. 255 p.
3. K. Miettinen, F. Ruiz, and A.P. Wierzbicki. Introduction to multiobjective optimization: Interactive approaches // In: Branke J., Deb K., Miettinen K., Slowinski R. (eds.) Multiobjective Optimization. Interactive and Evolutionary Approaches, Lecture Notes in Computer Science, V. 5252, Berlin-Heidelberg: Springer, 2008, p. 27-58.
4. Lotov, A.V., and Pospelova, I.I. 2008. Mnogokriterialnye zadachi prinyatiya reshenij [Multicriteria decision making problems]. Moscow: MAKS Press. 197 p.
5. Horst, R., and Pardalos, P.M. Handbook of global optimization. Dordrecht, NL: Kluwer, 1995. 455p
6. Lotov, A.V., Ryabikov A.I., and Buber, A.L. Pareto Frontier Visualization in the Development of Release Rules for Hydro_ Electrical Power Stations // Scientific and Technical Information Processing. 2014. Vol. 41. No. 5. P. 314-324.
7. Lotov, A.V., and Ryabikov A.I. 2014. Mnogokriterial’nyj sintez optimalnogo upravleniya I ego primenenie pri postroenii pravil upravleniya kaskadom gidrostanzij [Multicriteria feedback control and its application to the construction of the control rules for the cascade of hydroelectric power plants]. Trudy Instituta Matematiki i Mekhaniki UrO RAN [Proceedings of the Institute of Mathematics and Mechanics of Ural Branch of Russian Academy of Sciences]. V.20. № 4. P. 187-203.
8. Evtushenko, Yu.G. 1982. Metody resheniya ekstremalnykh zadach [Methods for solution of the extremal problems]. Moscow: Nauka. 432 p.
9. Pryazhinskaya, V.G., Yaroshevskij, D.M., and Levit-Gurevich, L.K. 2002. Kompyuternoe modelirovanie v upravlenii vodnymi resursami [Computer modeling in water resources control]. Moscow: Physmatlit. 496 p.
10. Asarin, A.E., and Bestuzheva, K.N. 1986 Vodnoenergeticheskie raschety [Water energy calculation]. Moscow: Energoatomizdat. 224 p.
11. Loucks D.P, van Beek E. Water Resources Systems Planning and Management. An Introduction to Methods, Models and Applications. Paris: UNESCO and Delft, the Netherlands: Delft Hydraulics, 2005. 680 p.
12. Bolgov, M.V., Sarmanov, I.O., and Sarmanov, O.V. 2009. Markowskie processy v gidrologii [Markov processes in hydrology]. Moscow: Institute for Water Problems, Russian Academy of Sciences. 211 p.
13. Riabikov, A.I. Ersatz Function Method for Minimizing a Finite-Valued Function on a Compact Set // Computational Mathematics and Mathematical Physics. Vol. 54, No. 2. P. 206-1218.