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Adaptive Fitness Functions in Evolutionary Game Control Optimization Models in Structural-Complicated Systems

Authors: Serov V.A. Published: 12.04.2017
Published in issue: #2(113)/2017  
DOI: 10.18698/0236-3933-2017-2-111-122

 
Category: Informatics, Computer Engineering and Control | Chapter: System Analysis, Control, and Information Processing  
Keywords: multicriteria optimization, conflict, uncertainty, evolutionary computing technology, genetic algorithm, adaptive fitness function, Ekeland е-variational principle

The purpose of this work was to develop an evolutionary computing technology of multictiteria optimization of structural-complicated systems under conditions of conflict and uncertainty. Such technology allows us to find a variety of conflict-optimal solutions with required properties. The proposed computing technology is based on the adaptive fitness function mechanism, which uses Ekeland е-variational principle generalization in multicriteria conflict optimization problems.

References

[1] Voronov E.M. Metody optimizatsii upravleniya mnogoob’ektnymi mnogokriterial’nymi sistemami na osnove stabil’no-effektivnykh igrovykh resheniy [Optimization methods of control on multiobject mulricriteria systems based on stable-effective game solution]. Moscow, Bauman MSTU Publ., 2001. 576 p.

[2] Semenov S.S., Voronov E.M., Poltavskiy A.V., Kryanev A.V. Metody prinyatiya resheniy v zadachakh otsenki kachestva i tekhnicheskogo urovnya slozhnykh tekhnicheskikh system [Decision-making technique in quality and engineering level evaluation problems in complex technical systems]. Moscow, LENAND Publ., 2016. 520 p.

[3] Zhukovskiy V.I., Zhukovskaya L.V. Risk v mnogokriterial’nykh i konfliktnykh sistemakh pri neopredelennosti [Risk in multiobjective and conflict systems under uncertainty conditions]. Moscow, Editorial URSS Publ., 2004. 272 p.

[4] Harsanyi J.C. A general theory of equilibrium selection in games. MIT Press, 1988. 365 p. (Russ. ed.: Obshchaya teoriya vybora ravnovesiya v igrakh. Sankt-Petersburg, Ekonomicheskaya shkola Publ., 2001. 424 p.).

[5] Gusev M.I., Kurzhanskiy A.B. On equilibrium situations in multi-criteria game problems. Dokl. AN SSSR, 1976, vol. 229, no. 6, pp. 1295-1298 (in Russ.).

[6] Moiseev N.N. Matematicheskie metody sistemnogo analiza [Mathematical methods of system analysis]. Moscow, Nauka Publ., 1981. 487 p.

[7] Herve Moulin. Theorie des jeux pour l’economie et la politique. Hermann, Paris, Collection methodes, 1981. (Russ. ed.: Teoriya igr s primerami iz matematicheskoy ekonomiki. Moscow, Mir Publ., 1985. 200 p.).

[8] Karpenko A.P. Sovremennye algoritmy poiskovoy optimizatsii. Algoritmy, vdokhnovlennye prirodoy [Modern search optimization algorithms. Algorithms, inspired by nature]. Moscow, Bauman MSTU Publ., 2014. 446 p.

[9] Rutkovskaya D., Pilin’skiy M., Rutkovskiy L. Neyronnye seti, geneticheskie algoritmy i nechetkie sistemy [Neural networks, genetic algorithms and fuzzy systems]. Moscow, Goryachaya liniya-Telekom Publ., 2006. 452 p.

[10] Kureychik V.V., Kureychik V.M., Rodzin S.I. Teoriya evolyutsionnykh vychisleniy [Evolutionary computations theory]. Moscow, Fizmatlit Publ., 2012. 260 p.

[11] Ashlock D. Evolutionary computation for modeling and optimization. Berlin, Germany, Springer-Verlag, 2006. 571 p.

[12] Kita E., ed. Evolutionary algorithms. InTech, 2011. 596 p.

[13] Dos Santos W.P., ed. Evolutionary computation. InTech, 2009. 582 p.

[14] Zitzler E., Deb K., Thiele L. Comparison of multiobjective evolutionary algorithms: empirical results. Evolutionary Computation, 2000, vol. 8, no. 2, pp. 173-195. DOI: 10.1162/106365600568202 Available at: http://dl.acm.org/citation.cfm?id=1108876

[15] Serov V.A., Babintsev Yu.N., Kondakov N.S. Neyroupravlenie mnogokriterial’nymi konfliktnymi sistemami [Neurocontrol on multicriteria conflict systems]. Moscow, MosGU Publ., 2011. 136 p.

[16] Serov V.A., Babintsev Yu.N., Chechurin A.V. Programmnoe sredstvo obucheniya iskusstvennykh neyronnykh setey na osnove kompleksa geneticheskikh algoritmov mnogokriterial’noy optimizatsii v usloviyakh konflikta i neopredelennosti (MONS) [Software educational tool for artificial neural networks based on complex of multicriteria optimization genetic algorithms under conditions of conflict and uncertainty (MONS)]. Svidetel’stvo o gosudarstvennoy registratsii programmy dlya EVM № 2011618436 ot 26.10.2011 g. [Computer program certificate of registration № 2011618436 dated 26.10.2011] (in Russ.).

[17] Serov V.A., Khitrin V.V. Neurogenetic technology of multicriteria stabilization of technological process operating mode under uncertainty conditions. Promyshlennye ASU i kontrollery, 2011, no. 6, pp. 38-42 (in Russ.).

[18] Serov V.A., Khitrin V.V. Hybrid evolutionary algorithm for multicriteria optimization of biotechnological process software mode. Promyshlennye ASU i kontrollery, 2010, no. 8, pp. 13-16 (in Russ.).

[19] Serov V.A., Babintsev Yu.N., Chechurin A.V. Neurogenetic technology of technological process multi-criteria stabilization under uncertainty. Neyrokomp’yutery: razrabotka i primenenie [Industrial Automatic Control Systems and Controllers], 2008, no. 9, pp. 65-71 (in Russ.).

[20] Serov V.A. Genetic algorithms of optimizing control of multiobjective systems under condition of uncertainty based on conflict equilibrium. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Priborostr. [Herald of the Bauman Moscow State Tech. Univ., Instrum. Eng.], 2007, no. 4, pp. 70-80.

[21] Serov V.A. Osobennosti vychislitel’noy tekhnologii poiska mnozhestva stabil’nykh ravnovesiy v koalitsionnoy igrovoy modeli funktsionirovaniya strukturno-slozhnoy sistemy v usloviyakh neopredelennosti [Features of search computational technologies of the many stable equilibriums in cooperative game model of the structural-complicated system functioning under uncertainty conditions]. Trudy ISA RAN. Dinamika neodnorodnykh system. T. 10. Vyp. 2 [Proceedings of ISP RAS. Geterogeneous system dynamics. Vol. 10. Iss. 2]. Moscow, Komkniga Publ., 2006, pp. 57-65.

[22] Serov V.A., Ivanova G.I., Sukhanova N.I. Investigation of ecosystem exploitation of theoretical game model with vector valued goal functional. Vestnik RUDN. Ser. Inzhenernye issledovaniya [RUDN Journal of Engineering Researches], 2003, no. 2, pp. 99-103 (in Russ.).

[23] Serov V.A. On conditions e-optimality on cone in multicriteria optimization problem. Vestnik RUDN. Ser. Kibernetika, 1998, no. 1, pp. 49-54 (in Russ.).

[24] Serov V.A. O variatsionnom printsipe v zadachakh mnogokriterial’noy optimizatsii i prinyatiya resheniy. Aktual’nye problemy teorii i praktiki inzhenernykh issledovaniy: Sb. nauch. trudov. [On variational principle in multicriteria optimization and decision making problems. In: Contemporary problems of theory and practice of engineering research]. Moscow, Mashinostroenie, 1999, pp. 18-22.

[25] Serov V.A. e-variational principles in game-theoretical problems of complex-structure systems. Vestnik RUDN. Ser. Kibernetika, 1999, no. 1, pp. 3-11 (in Russ.).

[26] Ekeland I. On the variational principle. Journal of Mathematical Analysis and Applications, 1974, vol. 47, no. 2, pp. 324-353. DOI: 10.1016/0022-247X(74)90025-0 Available at: http://www.sciencedirect.com/science/article/pii/0022247X74900250

[27] Aubin J.-P., Ekeland I. Applied nonlinear analysis. New York, Wiley. 1984 (Russ. ed.: Prikladnoy nelineynyy analiz. Moscow, Mir Publ., 1988. 512 p.).

[28] Isac G. The Ekeland principle and Pareto e-efficiency. In: Multiobjective programming and goal programming: theory and applications. Ser: Lecture notes in economics and mathematical systems. Vol. 432. Berlin, Germany, Springer Verlag, 1996, pp. 148-163.

[29] Loridan P. e-solutions in vector minimization problems. JOTA, 1984, vol. 43, no. 2, pp. 265-276.

[30] Chen G.Y., Huang X.X., Hou S.H. General Ekeland’s variational principle for set-valued mappins. JOTA, 2000, vol. 106, no. 1, pp. 151-164.

[31] Zhu J., Zhong C., Cho Y. Generalized variational principle and vector optimization. JOTA, 2000, vol. 10, no. 1, pp. 201-217.