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Using Multiobjective Optimization As a Separation Strategy for Nonseparable Problems

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Multiple Criteria Decision Making
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Abstract

The purpose of this paper is to investigate efficient solution schemes for a class of nonseparable optimization problems using multiobjective optimization as a separation strategy. The general conditions are provided for characterizing an optimal solution of a nonseparable problem from among the set of noninferior solutions of the corresponding multiobjective optimization problem. Multilevel solution schemes are discussed. Applications are presented in the areas of general multiple linear-quadratic control, network reliability optimization, and optimal maintenance policies for large-scale deteriorating water distribution systems.

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References

  • Bellman, R. 1961. Adaptive Control Process: A Guided Tour. Princeton, New Jersey: Princeton University Press.

    Google Scholar 

  • Bryson, A. E. and Y.-C. Ho. 1975. Applied Optimal Control. New York: John Wiley.

    Google Scholar 

  • Chankong, V., and Y. Y. Haimes. 1983. Multiobjective Decision Making: Theory an Methodology. New York: Elsevier-North Holland.

    Google Scholar 

  • Geoffrion, A. M. 1967. Solving bicriterion mathematical problems. Operations Research 15: 39 - 54.

    Article  MathSciNet  MATH  Google Scholar 

  • Haimes, Y. Y., K. Tarvainen, T. Shima, and J. Thadathil. 1990. Hierarchical Multiobjective Analysis of Large-Scale Systems. New York: Hemisphere Publishing Company.

    Google Scholar 

  • Krasnoshchekov, P. C., V. V. Morozov, and V. V. Fedorov. 1979. Decomposition in planning problems, I. Engineering Cybernetics 17: 1 - 10.

    MATH  Google Scholar 

  • Li, D. 1990a. Multiple objectives and nonseparability in stochastic dynamic programming. Int. J. Systems Science 21: 933-50.

    Google Scholar 

  • Li, D. 1990b. A new solution approach to Salukvadze’s problem. Proceedings of 1990 American Control Conference, May 23-25, 1990. San Diego, California, pp. 409 - 14.

    Google Scholar 

  • Li, D. 1992. Multilevel dynamic programming in nonseparable reliability optimization problems. Submitted for publication.

    Google Scholar 

  • Li, D. 1993a. On general multiple linear-quadratic control problems, to appear in IEEE Trans, on Automatic Control, December, 1993.

    Google Scholar 

  • Li, D. 1993b. Hierarchical control for large-scale systems with general multiple linear-quadratic structure, to appear in Automatica, November, 1993.

    Google Scholar 

  • Li, D. and Y. Y. Haimes. 1987. The envelope approach for multiobjective optimization problems. IEEE Trans. Syst., Man, and Cybern. SMC-17: 1026 - 38.

    Google Scholar 

  • Li, D. and Y. Y. Haimes. 1989. Multiobjective dynamic programming: The state of the art. Control - Theory and Advanced Technology 5: 471-483.

    Google Scholar 

  • Li, D. and Y. Y. Haimes. 1990a. New approach for nonseparablem dynamic programming. J. Optimization Theory and Applications 64: 311 - 30.

    Article  MathSciNet  MATH  Google Scholar 

  • Li, D. and Y. Y. Haimes. 1990b. Multilevel methodology for a class of nonseparable optimization problems. Int. J. Systems Science 21: 2351-60.

    Google Scholar 

  • Li, D. and Y. Y. Haimes. 1991. Extension of dynamic programming to nonseparable problems. Computer and Mathematics with Applications 21: 51 - 6.

    Article  MathSciNet  MATH  Google Scholar 

  • Li, D. and Y. Y. Haimes. 1992a. Optimal maintenance-related decisionmaking for deteriorating water distribution systems 2. Multilevel decomposition approach. Water Resources Research 28: 1063-70.

    Google Scholar 

  • Li, D. and Y. Y. Haimes. 1992b. A decomposition method for optimization of large system reliability. IEEE Trans, on Reliability 41: 183 - 9.

    Article  MATH  Google Scholar 

  • Lightner, M. R. and S. W. Director. 1981. Multiple criterion optimization for the design of electronic circuits. IEEE Trans, on Circuits and Systems CAS-28: 169 - 79.

    Google Scholar 

  • Mesarovic, M. D., D. Macko, and Y. Takahara. 1970. Theory of Hierarchical Multilevel Systems. New York: Academic Press.

    MATH  Google Scholar 

  • Singh, M. G. and A. Titli. 1978. Systems: Decomposition, Optimisation and Control. Oxford: Pergamon Press.

    Google Scholar 

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© 1994 Springer-Verlag New York, Inc.

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Li, D., Haimes, Y.Y. (1994). Using Multiobjective Optimization As a Separation Strategy for Nonseparable Problems. In: Tzeng, G.H., Wang, H.F., Wen, U.P., Yu, P.L. (eds) Multiple Criteria Decision Making. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2666-6_12

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  • DOI: https://doi.org/10.1007/978-1-4612-2666-6_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7626-5

  • Online ISBN: 978-1-4612-2666-6

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