Abstract
This paper examines the state of the art in multicriteria optimization. For this purpose, multicriteria problems are classified in terms of complexity as finite and small, finite and large, and infinite. The relative merits of typical methods for solving each of these classes are discussed and some suggestions for future work are made.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abelson, R. P., “The Choice of Choice Theories,” in S. Messick and A. H. Brayfield (eds.), Decision and Choice, New York: McGraw-Hill, pp. 257–266, 1964.
Athans, M., “The Role and Use of the Stochastic Linear-Quadratic-Gaussian Problem in Control System Design,” IEEE Trans. Automat. Contr., vol. AC-16, pp. 529–552, Dec. 1971.
Briskin, L. E., “A Method Unifying Multiple Objective Functions,” Management Science, Vol. 12, pp. B406–B416, June 1966.
Briskin, L. E., “Establishing a Generalized Multi-Attribute Utility Function,” in J. L. Cochrane and M. Zeleny (eds.), Multiple Criteria Decision Making, Columbia, S. C.: USC Press, pp. 236–245, 1973.
Charnes, A. and W. W. Cooper, Management Models and Industrial Application of Linear Programming, Vol. I, New York: Wiley, 1961.
Consumer Reports, Vol. 39, pp. 164–171, Feb. 1974.
Da Cunha, N. O. and E. Polak, “Constrainted Minimization Under Vector-Valued Criteria in Linear Topological Spaces,” in A. V. Balakrishnan and L. W. Neustadt (eds.), Mathematical Theory of Control, New York: Academic Press, pp. 96–108, 1967.
Dawes, R. M., “A Case Study of Graduate Admissions,” American Psychologist, Vol. 26, pp. 180–188, Feb. 1971.
Dinkelbach, W. and H. Isermann, “On Decision Making Under Multiple Criteria and Under Incomplete Information,” in J. L. Cochrane and M. Zeleny (eds.), Multiple Criteria Decision Making, Columbia, S. C.: USC Press, pp. 302–312, 1973.
Geoffrion, A., “Vector Maximal Decomposition Programming,” Western Management Science Institute, Univ. of California, Los Angeles, Working Paper No. 164, Sept. 1970.
Geoffrion, A. M., J. S. Dyer and A. Feinberg, “An Interactive Approach for Multi-Criterion Optimization with an Application to the Operation of an Academic Department, ” Management Science, Vol. 19, pp. 357–368, Dec. 1972.
Hanieski, J. F., “Technological Change as the Optimization of a Multidimensional Product,” in J. L. Cochrane and M. Zeleny (eds.), Multiple Criteria Decision Making, Columbia, S. C.: USC Press, pp. 550–569, 1973.
Huang, S. C., “Note on the Mean-Square Strategy of Vector Valued Objective Functions,” JOTA, Vol. 9, pp. 364–366, May 1972.
Kung, H. T., “On the Computational Complexity of Finding the Maxima of a Set of Vectors, ” Proc. 15th Annual IEEE Symp. on Switching and Automata Theory, pp. 117–121, Oct. 1974.
Kung, H. T., F. Luccio and F. P. Preparata, “On Finding the Maxima of a Set of Vectors,” J. ACM, Vol. 22, pp. 469–476, Oct. 1975.
Luccio, F. and F. P. Preparata, “On Finding the Maxima of a Set of Vectors,” Istituto di Scienze dell’Informazione, Università di Pisa, Pisa, Italy, Dec. 1973.
Luenberger, D. G., Introduction to Linear and Nonlinear Programming, Reading, Mass.: Addison-Wesley, 1973.
MacCrimmon, K. R., “An Overview of Multiple Objective Decision Making,” in J. L. Cochrane and M. Zeleny (eds.), Multiple Criteria Decision Making, Columbia, S. C.: USC Press, pp. 18–44, 1973.
Meisel, W. S., “Trade off Decisions in Multiple Criteria Decision Making,” in J. L. Cochrane and M. Zeleny (eds.), Multiple Criteria Decision Making, Columbia, S. C.: USC Press, pp. 461–476, 1973.
Payne, H. J., E. Polak, D. C. Collins and W. S. Meisel, “An Algorithm for Bicriteria Optimization Based on the Sensitivity Function,” IEEE Trans. Automat. Contr., Vol. AC-20, pp. 546–548, Aug. 1975.
Polak, E., “On the Approximation of Solutions to Multiple Criteria Decision Making Problems,” Presented at XXII International Meeting of The Institute of Management Sciences, Kyoto, Japan, July 24–26, 1975.
Russ, F., “Consumer Evaluation of Alternative Product Models,” Ph.D. Dissertation, Carnegie-Mellon University, 1971.
Salukvadze, M. E., “Optimization of Vector Functionals. I. The Programming of Optimal Trajectories, ” Automation and Remote Control, Vol. 32, pp. 1169–1178, Aug. 1971.
Smale, S., “Global Analysis and Economics I. Pareto Optimum and a Generalization of Morse Theory,” in M. Peixoto (ed.), Dynamical Systems, New York: Academic Press, pp. 531–544, 1973.
Wan, Y. H., “Morse Theory for Two Functions,” Ph.D. Dissertation, Univ. of California, Berkeley, 1973.
Wolfe, P., “Convergence Theory in Nonlinear Programming,” in J. Abadie (ed.), Integer and Nonlinear Programming, New York: American Elsevier, pp. 1–36, 1970.
Yao, F. F., “On Finding the Maximal Elements in a Set of Plane Vectors,” Comput. Sci. Dep. Rep., University of Illinois at Urbana-Champaign, Urbana, 111., July 1974.
Yu, P. L., “A Class of Solutions for Group Decision Problems,” Management Science, Vol. 19, pp. 936–946, April 1973.
Yu, P. L. and G. Leitmann, “Compromise Solutions, Domination Structures and Salukvadze’s Solution, ” JOTA, Vol. 13, pp. 362–378, Mar. 1974.
Zeleny, M., “Compromise Programming,” in J. L. Cochrane and M. Zeleny (eds.), Multiple Criteria Decision Making, Columbia, S. C.: USC Press, pp. 262–301, 1973.
Zeleny, M., Linear Multiobjective Programming, Berlin: Springer-Verlag, 1974.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1976 Plenum Press, New York
About this chapter
Cite this chapter
Polak, E., Payne, A.N. (1976). On Multicriteria Optimization. In: Ho, Y.C., Mitter, S.K. (eds) Directions in Large-Scale Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2259-7_7
Download citation
DOI: https://doi.org/10.1007/978-1-4684-2259-7_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-2261-0
Online ISBN: 978-1-4684-2259-7
eBook Packages: Springer Book Archive