Evolutionary Algorithms of Stable-Effective Compromises Search in Multi-object Control Problems

  • Vladimir A. SerovEmail author
  • Evgeny M. Voronov
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 174)


In the article the main principles of adaptive evolutionary computing technology of smart electromechanical systems (SEMS) group control optimization under conflict and uncertainty, based on stable-effective compromises (STEC), are discussed. The necessary conditions of STEC existence are formulated in the form of variational principles generalizing the known Ekeland variational principle for a class of multicriteria conflict optimization under uncertainty problems. On the basis of the formulated variational principles the mechanism of adaptive fitness functions formation is developed for using in adaptive genetic algorithms, which allows to search STEC for different types of SEMS conflict group interaction.


Conflict group interaction Smart electromechanical system (SEMS) Uncertainty Multi-object multi-criteria system (MMS) Stable-effective compromise (STEC) Genetic algorithm (GA) Adaptive fitness function (AFF) 


  1. 1.
    Voronov, E.M.: Methods of optimization of management of multi-object multi-criteria systems on the basis of stable-effective gaming solutions. E.Egupova. M.: Publishing house of BMSTU. - 576c (2001)Google Scholar
  2. 2.
    Voronov, E.M., Serov, V.A.: A coordinated stable-effective compromises based methodology of design and control in multi-object systems, in this collectionGoogle Scholar
  3. 3.
    Serov, V.A., Klishin, M.A., Borisov, A.B., Kozlov, D.A.: Program complex for implementation of evolutionary algorithms of multicriteria optimization under conflict and uncertainty. Certificate of state registration of computer program No. 2018614102 of 29.03.2018—Federal service for intellectual property (ROSPATENT)—The register of computer programsGoogle Scholar
  4. 4.
    Serov, V.A.: The conditions of ε-cone optimality in the multicriteria optimization problem. Vestnik RUDN. Ser. Cybernetics, no: 1, pp. 49–54 (1998)Google Scholar
  5. 5.
    Karpenko, A.P.: Modern algorithms of search optimization. Algorithms inspired by nature, 446p. M.: Publishing house of BMSTU (2014)Google Scholar
  6. 6.
    Greiner, D., Periaux, J., Emperador, J., Galván, B., Winter, G.: Game theory based evolutionary algorithms: a review with Nash applications in structural engineering optimization problems. Arch. Comput. Methods Eng. 24(4), 703–750 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Rutkovskaya, D.: Neural networks, genetic algorithms and fuzzy systems, 452p. In: Rutkovskaya, D., Pilinsky, M., Rutkovsky, L.M., Hotline-Telecom (2006)Google Scholar
  8. 8.
    Kureychik, V.V., Kureychik, V.M., Rodzin, S.I.: Theory of evolutionary computation, 260s. – M.: FIZMATLIT (2012)Google Scholar
  9. 9.
    Ashlock, D.: Evolutionary Computation for Modeling and Optimization, p. 571. Springer, Berlin, Germany (2006)zbMATHGoogle Scholar
  10. 10.
    Kita, E. (ed.): Evolutionary Algorithms. InTech, 596p (2011)Google Scholar
  11. 11.
    Dos Santos, W.P. (ed.): Evolutionary Computation. InTech, 582p (2009)Google Scholar
  12. 12.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)CrossRefGoogle Scholar
  13. 13.
    Serov, V.A.: Adaptive fitness functions in evolutionary game control optimization models in structure complicated systems. Vestnik BMSTU. Ser. Instrument Making 2(113), 111–122 (2017)Google Scholar
  14. 14.
    Serov, V.A.: Genetic algorithms of conflict equilibriums-based multicriteria systems control optimization under uncertainty. Vestnik BMSTU. Ser. Instrument Making. 4(69), 70–80 (2007)Google Scholar
  15. 15.
    Lung, R.I., Dumitrescu, D.: Computing Nash equilibria by means of evolutionary computation. Int. J. Comput. Commun. 3, 364–368 (2008)Google Scholar
  16. 16.
    El Majd, B., Desideri, J., Habbal, A.: Aerodynamic and structural optimization of a business-jet wingshape by a Nash game and an adapted split of variables. Mec. Ind. 1(3–4), 209–214 (2010)Google Scholar
  17. 17.
    Gonzalez, L., Srinivas, K., Seop, D., Lee, C., Periaux, J.: Coupling hybrid-game strategies with evolutionary algorithms for multi-objective design problems in aerospace. In: Evolutionary and deterministic methods for design, optimization and control with applications to industrial and societal problems, CIMNE, pp. 221–248 (2011)Google Scholar
  18. 18.
    D’Amato, E., Daniele, E., Mallozzi, L., Petrone, G.: Equilibrium strategies via GA to Stackelberg games under multiple follower’s best reply. Int. J. Intell. Syst. 27, 74–85 (2012)CrossRefGoogle Scholar
  19. 19.
    Arias-Montano, A., Coello, C.C., Mezura-Montes, E.: Multiobjective evolutionary algorithms in aeronautical and aerospace engineering. IEEE T Evolut. Comput. 16(5), 662–694 (2012)CrossRefGoogle Scholar
  20. 20.
    Coelho, R.: Co-evolutionary optimization for multi-objective design under uncertainty. J. Mech. Des. T. ASME 135(2), 1–8 (2013)Google Scholar
  21. 21.
    Periaux, J., Gonzalez, F., Lee, D.: Multi-objective EAs and game theory. In: Evolutionary Optimization and Game Strategies for Advanced Multi-Disciplinary Design. Intelligent Systems, Control and Automation: Science and Engineering, vol 75, pp. 21–38. Springer, Dordrecht (2015)Google Scholar
  22. 22.
    Greiner, D., Periaux, J., Emperador, J.M., Galvan, B., Winter, G.: A study of Nash-evolutionary algorithms for reconstruction inverse problems in structural engineering. In: Greiner, D. et al. (eds.) Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences. Computational Methods in Applied Sciences, vol 36. Springer, New York, pp. 321–333 (2015)Google Scholar
  23. 23.
    Lee, D.S., Gonzalez, F., Periaux, J., Srinivas, K.: Efficient hybrid-game strategies coupled to evolutionary algorithms for robust multidisciplinary design optimization in aerospace engineering. IEEE T. Evolut. Comput. 15(2), 133–150 (2011)CrossRefGoogle Scholar
  24. 24.
    Leskinen, J., Périaux, J.: Distributed evolutionary optimization using Nash games and GPUs-applications to CFD design problems. Comput. Fluids, 80, 190–201 (2013)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Sinha, A., Malo, P., Frantsev, A., Deb, K.: Finding optimal strategies in a multi-period multi-leader-follower Stackelberg game using an evolutionary algorithm. Comput. Oper. Res. 41, 374–385 (2014)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Tang, Z., Desideri, J.A., Periaux, J.: Multi-criteria aerodynamic shape design optimization and inverse problems using control theory and Nash games. J. Optimiz. Theory App. 135(1), 599–622 (2007)CrossRefGoogle Scholar
  27. 27.
    Serov, V.A.: On the variational principle in of multicriteria optimization and decision-making problems. Actual problems of the theory and applications of engineering research: SB. scientific papers. – M.: Mechanical Engineering, pp. 18–22 (1999)Google Scholar
  28. 28.
    Auben, J.-P., Ekland, I.: Applied nonlinear analysis. M. World, 512p (1988)Google Scholar
  29. 29.
    Ekeland, I.: On the variational principle. J. Math. Anal. Appl. 47(2), 324 (1974)MathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Russian Technological University (MIREA)MoscowRussia
  2. 2.Bauman Moscow State Technical UniversityMoscowRussia

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