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An Approach for Simultaneous Finding of Multiple Efficient Decisions in Multi-objective Optimization Problems

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Mathematical Optimization Theory and Operations Research (MOTOR 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12755))

Abstract

This paper considers computationally intensive multi-objective optimization problems which require computing multiple Pareto-optimal decisions. It is also assumed that efficiency criteria may be multiextremal, and the cost of calculating function values may be quite high. The proposed approach is based on the reduction of multi-objective optimization problems to one-dimensional global optimization problems that can be solved using efficient information-statistical algorithms of global search. One key innovation of the developed approach consists in the possibility of solving several global optimization problems simultaneously, which allows multiple Pareto-optimal decisions to be obtained. Besides, such approach provides for reuse of the computed search information, which considerably reduces computational effort for solving multi-objective optimization problems. Computational experiments confirm the potential of the proposed approach.

This work was supported by the Russian Science Foundation, project No. 21-11-00204.

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References

  1. Miettinen, K.: Nonlinear Multiobjective Optimization. Springer, Boston (1999). https://doi.org/10.1007/978-1-4615-5563-6

    Book  MATH  Google Scholar 

  2. Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Heidelberg (2010). https://doi.org/10.1007/3-540-27659-9

    Book  MATH  Google Scholar 

  3. Collette, Y., Siarry, P.: Multiobjective Optimization: Principles and Case Studies. Decision Engineering, Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-662-08883-8

  4. Marler, R.T., Arora, J.S.: Multi-Objective Optimization: Concepts and Methods for Engineering. VDM Verlag, Saarbrücken (2009)

    Google Scholar 

  5. Pardalos, P.M., Žilinskas, A., Žilinskas, J.: Non-Convex Multi-Objective Optimization. Springer, Cham (2017)

    Google Scholar 

  6. Marler, R.T., Arora, J.S.: Survey of multi-objective optimization methods for engineering. Struct. Multidiscip. Optim. 26, 369–395 (2004)

    Article  MathSciNet  Google Scholar 

  7. Figueira, J., Greco, S., Ehrgott, M. (eds.): Multiple Criteria Decision Analysis: State of the Art Surveys. Springer, New York (2005). https://doi.org/10.1007/b100605

    Book  MATH  Google Scholar 

  8. Zavadskas, E.K., Turskis, Z., Kildienė, S.: State of art surveys of overviews on MCDM/MADM methods. Technol. Econ. Dev. Econ. 20, 165–179 (2014)

    Article  Google Scholar 

  9. Hillermeier, C., Jahn, J.: Multiobjective optimization: survey of methods and industrial applications. Surv. Math. Ind. 11, 1–42 (2005)

    MATH  Google Scholar 

  10. Collette, Y., Siarry, P.: Multiobjective Optimization: Principles and Case Studies. Decision Engineering. Springer, Heidelberg (2011) https://doi.org/10.1007/978-3-662-08883-8

  11. Eichfelder, G.: Scalarizations for adaptively solving multi-objective optimization problems. Comput. Optim. Appl. 44, 249–273 (2009)

    Article  MathSciNet  Google Scholar 

  12. Figueira, J., Liefooghe, A., Talbi, E., Wierzbicki, A.: A parallel multiple reference point approach for multi-objective optimization. Eur. J. Oper. Res. 205(2), 390–400 (2010). https://doi.org/10.1016/j.ejor.2009.12.027

    Article  MathSciNet  MATH  Google Scholar 

  13. Gergel, V.: An unified approach to use of coprocessors of various types for solving global optimization problems. In: 2nd International Conference on Mathematics and Computers in Sciences and in Industry, pp. 13–18 (2015). https://doi.org/10.1109/MCSI.2015.18

  14. Gergel, V.P., Kozinov, E.A.: Accelerating multicriterial optimization by the intensive exploitation of accumulated search data. In: AIP Conference Proceedings, vol. 1776, p. 090003 (2016). https://doi.org/10.1063/1.4965367

  15. Gergel, V., Kozinov, E.: Efficient multicriterial optimization based on intensive reuse of search information. J. Glob. Optim. 71(1), 73–90 (2018)

    Article  MathSciNet  Google Scholar 

  16. Gergel, V., Kozinov, E., Barkalov, K.: Computationally efficient approach for solving lexicographic multicriteria optimization problems. Optim. Lett. (2020). https://doi.org/10.1007/s11590-020-01668-y

    Article  Google Scholar 

  17. Zhigljavsky, A.A.: Theory of Global Random Search. Kluwer Academic Publishers, Dordrecht (1991)

    Google Scholar 

  18. Pintér, J.D.: Global Optimization in Action (Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications). Kluwer Academic Publishers, Dortrecht (1996)

    Google Scholar 

  19. Strongin, R., Sergeyev, Ya.: Global Optimization with Non-Convex Constraints. Sequential and Parallel Algorithms. Kluwer Academic Publishers, Dordrecht (2nd edn. 2013, 3rd edn. 2014)

    Google Scholar 

  20. Yang, X.-S.: Nature-inspired Metaheuristic Algorithms. Luniver Press, Frome (2008)

    Google Scholar 

  21. Locatelli, M., Schoen, F.: Global Optimization: Theory, Algorithms, and Applications. SIAM (2013)

    Google Scholar 

  22. Paulavičius, R., Žilinskas, J.: Simplicial Global Optimization. Springer, New York (2014). https://doi.org/10.1007/978-1-4614-9093-7

    Book  MATH  Google Scholar 

  23. Floudas, C.A., Pardalos, M.P.: Recent Advances in Global Optimization. Princeton University Press, Princeton (2016)

    Google Scholar 

  24. Sergeyev, Y.D., Kvasov, D.E.: Deterministic Global Optimization: An Introduction to the Diagonal Approach. Springer, New York (2017). https://doi.org/10.1007/978-1-4939-7199-2

    Book  MATH  Google Scholar 

  25. Sergeyev, Y.D., Strongin, R.G., Lera, D.: Introduction to Global Optimization Exploiting Space-Filling Curves. Springer, New York (2013). https://doi.org/10.1007/978-1-4614-8042-6

    Book  MATH  Google Scholar 

  26. Piyavskij, S.: An algorithm for finding the absolute extremum of a function. Comput. Math. Math. Phys. 12, 57–67 (1972)

    Article  Google Scholar 

  27. Shubert, B.O.: A sequential method seeking the global maximum of a function. SIAM J. Numer. Anal. 9, 379–388 (1972)

    Article  MathSciNet  Google Scholar 

  28. Strongin, R.G.: Multiextremal minimization. Autom. Remote. Control. 7, 1085–1088 (1970)

    MathSciNet  MATH  Google Scholar 

  29. Galperin, E.A.: The cubic algorithm. J. Math. Anal. Appl. 112, 635–640 (1985)

    Article  MathSciNet  Google Scholar 

  30. Breiman, L., Cutler, A.: A deterministic algorithm for global optimization. Math. Program. 58, 179–199 (1993)

    Article  MathSciNet  Google Scholar 

  31. Baritompa, W.: Accelerations for a variety of global optimization methods. J. Glob. Optim. 4, 37–45 (1994)

    Article  MathSciNet  Google Scholar 

  32. Gergel, V.P.: A method of using derivatives in the minimization of multiextremum functions. Comput. Math. Math. Phys. 36(6), 729–742 (1996)

    MathSciNet  MATH  Google Scholar 

  33. Sergeyev, Y.D.: Global one-dimensional optimization using smooth auxiliary functions. Math. Program. 81, 127–146 (1998)

    MathSciNet  MATH  Google Scholar 

  34. Sergeyev, Ya.D., Grishagin, V.A.: Sequential and parallel global optimization algorithms. Optim. Methods Softw. 3, 111–124 (1994)

    Google Scholar 

  35. Sergeyev, Y.D.: An information global optimization algorithm with local tuning. SIAM J. Optim. 5(4), 858–870 (1995)

    Article  MathSciNet  Google Scholar 

  36. Sergeyev, Y.D., Grishagin, V.A.: Parallel asynchronous global search and the nested optimization scheme. J. Comput. Anal. Appl. 3(2), 123–145 (2001)

    MathSciNet  MATH  Google Scholar 

  37. Lera, D., Sergeyev, Ya.D.: Deterministic global optimization using space-filling curves and multiple estimates of Lipschitz and Holder constants. Commun. Nonlinear Sci. Numer. Simul. 23, 328–342 (2015)

    Google Scholar 

  38. Grishagin, V., Israfilov, R., Sergeyev, Y.: Comparative efficiency of dimensionality reduction schemes in global optimization. In: AIP Conference Proceedings, vol. 1776 (2016)

    Google Scholar 

  39. Gergel, V., Barkalov, K., Sysoyev, A.: Globalizer: a novel supercomputer software system for solving time-consuming global optimization problem. Numer. Algebra Control Opt. 8(1), 47–62 (2018)

    Article  MathSciNet  Google Scholar 

  40. Žilinskas, A., Zilinskas, J.: Adaptation of a one-step worst-case optimal univariate algorithm of bi-objective Lipschitz optimization to multidimensional problems. Commun. Nonlinear Sci. Numer. Simul. 21(1–3), 89–98 (2015). https://doi.org/10.1016/j.cnsns.2014.08.025

    Article  MathSciNet  MATH  Google Scholar 

  41. Evtushenko, Y., Posypkin, M.: A deterministic algorithm for global multiobjective optimization. Optim. Methods Softw. 29(5), 1005–1019 (2014) https://doi.org/10.1080/10556788.2013.854357

  42. Evtushenko, Y., Posypkin, M.: Method of non-uniform coverages to solve the multicriteria optimization problems with guaranteed accuracy. Autom. Remote Control 75(6), 1025–1040 (2014)

    Article  MathSciNet  Google Scholar 

  43. Bleuler, S., Laumanns, M., Thiele, L., Zitzler, E.: PISA—a platform and programming language independent interface for search algorithms. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Thiele, L., Deb, K. (eds.) EMO 2003. LNCS, vol. 2632, pp. 494–508. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36970-8_35

    Chapter  Google Scholar 

  44. Gaviano, M., Kvasov, D.E., Lera, D., Sergeyev, Ya.D.: Software for generation of classes of test functions with known local and global minima for global optimization. ACM Trans. Math. Softw. 29(4), 469–480 (2003)

    Google Scholar 

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Authors and Affiliations

  1. Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia

    Konstantin Barkalov, Victor Gergel, Vladimir Grishagin & Evgeniy Kozinov

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  1. Konstantin Barkalov
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  2. Victor Gergel
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  3. Vladimir Grishagin
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  4. Evgeniy Kozinov
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Correspondence to Evgeniy Kozinov .

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Editors and Affiliations

  1. University of Florida, Gainesville, FL, USA

    Panos Pardalos

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Matrosov Institute for System Dynamics and Control Theory, Irkutsk, Russia

    Alexander Kazakov

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Barkalov, K., Gergel, V., Grishagin, V., Kozinov, E. (2021). An Approach for Simultaneous Finding of Multiple Efficient Decisions in Multi-objective Optimization Problems. In: Pardalos, P., Khachay, M., Kazakov, A. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2021. Lecture Notes in Computer Science(), vol 12755. Springer, Cham. https://doi.org/10.1007/978-3-030-77876-7_9

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  • DOI: https://doi.org/10.1007/978-3-030-77876-7_9

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