Abstract
A number of real life problems have multiple objectives and constraints that are truly nonlinear in nature. Many efficient interactive algorithms have been proposed to solve these problems. These procedures differ in the philosophy/approach they follow. Even within a given philosophy/approach, the algorithms differ in several details. In this paper, our objective is to give an overview of some of the available algorithms.
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References
Abadie, J. and Carpentier, J. (1969), “Generalization of the Wolfe reduced gradient method to the case of nonlinear constraints”, in R. Fletcher (ed.): Optimization, Academic Press, New York.
Benson, R. G. (1975), “Interactive multiple criteria optimization using satisfactory goals”, Doctoral thesis, University of Iowa, Iowa City.
Grauer, M. (1983), “Reference point optimization - the nonlinear case”, in P. Hansen (ed.): Essays and Surveys on Multiple Criteria Decision Making, Springer-Verlag, Berlin.
Haimes, Y. Y. and Hall, W. A. (1974), “Multiobjectives in water resources systems analysis: The surrogate worth trade off method”, Water Resources Research 10 (4), 615–623.
Lasdon, L., Fox, R. L., and Ratner, M. (1974), “Nonlinear optimization using the generalized reduced gradient method,” R.A.I.R.O. 3, 73–104.
Lewandowski, A. and Grauer, M. (1982), “The reference point optimization approach - methods of efficient implementation”, Working paper WP-82–019, IIASA, Laxenburg, Austria.
Lewandowski, A. and Wierzbicki, A. (1988), “Aspiration based decision analysis and support, Part I: Theoretical and methodological backgrounds”, Working paper WP-88–03,IIASA, Laxenburg, Austria.
Masud, A. S. and Hwang, C. L. (1981), “Interactive sequential goal programming”, Journal of the Operational Research Society 32, 391–400.
Narula, S. C. and Weistroffer, H. R. (1989), “A flexible method for nonlinear multicriteria decision making problems”, IEEE Transactions on Systems, Man, and Cybernetics SMC-19(4).
Roy, A. and Wallenius, J. (1988), “An algorithm and the supporting theory for nonlinear multiple objective optimization”, Working paper, Arizona State University and University of Jyvaskyla, Finland.
Sakawa, M. (1982), “Interactive multiobjective decision making by the sequential proxy optimization technique: SPOT”, European Journal of Operational Research 9 (4), 386–396.
Sakawa, M. (1986), “Interactive multiobjective decision-making using fuzzy satisficing intervals and its application to an urban water resources system”, Large Scale Systems 10, 203–213.
Simon, H. A. (1960). The New Science of Management Decision, Harper and Brothers, New York.
Spronk, J. (1981), Interactive Multiple Goal Programming, Martinus Nijhoff, Boston.
Weistroffer, H. R. (1982), “Multiple criteria decision making with interactive overachievement programming”, Operations Research Letters 1 (6), 241–245.
Weistroffer, H. R. (1983), “An interactive goal programming method for nonlinear multiple-criteria decision-making problems”, Computers and Operations Research 10 (4), 311–320.
Weistroffer, H. R. (1984), “A combined over-and under-achievement programming approach to multiple objectives decision making”, Large Scale Systems 7, 47–58.
Weistroffer, H. R. (1985). “Careful usage of pessimistic values is needed in multiple objectives optimization”, Operations Research Letters 4 (1), 23–25.
Weistroffer, H. R. (1987), “A flexible model for multi-objective optimization”, in J. Jahn and W. Krabs (eds): Recent Advances and Historical Development of Vector Optimization, Springer-Verlag, Berlin.
White, D. J. (1982), Optimality and Efficiency, John Wiley & Sons, Chichester.
Wierzbicki, A. P. (1982), “A mathematical basis for satisficing decision-making”, Mathematical Modelling 3, 391–405.
Yu, P. -L. (1985), Multiple-Criteria Decision Making, Plenum Press, New York.
Zionts, S. and Wallenius, J. (1976), “An interactive programming method for solving the multiple criteria problem”, Management Science 22, 652–663.
Zionts, S. and Wallenius, J. (1983), “An interactive multiple objective linear programming method for a class of underlying nonlinear utility functions”, Management Science 29, 519–529.
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© 1989 Springer-Verlag Berlin Heidelberg
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Narula, S.C., Weistroffer, H.R. (1989). Algorithms for Multi-Objective Nonlinear Programming Problems: An Overview. In: Lockett, A.G., Islei, G. (eds) Improving Decision Making in Organisations. Lecture Notes in Economics and Mathematical Systems, vol 335. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-49298-3_40
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DOI: https://doi.org/10.1007/978-3-642-49298-3_40
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