On the Approximation of Solutions to Multiple Criteria Decision Making Problems

This paper presents an adaptive precision method based on cubic splines and a new scalarization procedure, which constructs approximations to the surface of noninferior points. It is particularly well suited for the two or three criteria optimization problems, but it can also be used to some extent for high dimensional problems. An important aspect of this method is that it is quite efficient, since it computes no more points than necessary to ensure a prescribed level of precision of approximation.

[1]  H. Keller,et al.  Analysis of Numerical Methods , 1969 .

[2]  E. Polak,et al.  Constrained minimization under vector-valued criteria in finite dimensional spaces☆ , 1967 .

[3]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[4]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

[5]  Klaus Ritter,et al.  Optimization theory in linear spaces. I , 1969 .

[6]  K. Ritter.  Optimization theory in linear spaces , 1969 .

[7]  K. Chu.  On the noninferior set for the systems with vector-valued objective function , 1970 .

[8]  K. Ritter,et al.  Optimization theory in linear spaces , 1970 .

[9]  A. M. Geoffrion.  Duality in Nonlinear Programming: A Simplified Applications-Oriented Development , 1971 .

[10]  W. Meisel,et al.  The optimization of complex systems with respect to multiple criteria. , 1971 .

[11]  E. Polak,et al.  Computational methods in optimization : a unified approach , 1972 .

[12]  W. Schmitendorf,et al.  Cooperative games and vector-valued criteria problems , 1972, CDC 1972.

[13]  E. Polak,et al.  A Dual Method for Optimal Control Problems with Initial and Final Boundary Constraints , 1973 .

[14]  E. Polak.  Introduction to linear and nonlinear programming , 1973 .

[15]  M. Athans,et al.  Necessary and sufficient conditions for differentiable nonscalar-valued functions to attain extrema , 1973 .

[16]  George Leitmann,et al.  Nondominated Decisions and Cone Convexity in Dynamic Multicriteria Decision Problems , 1974 .

[17]  E. Polak,et al.  An algorithm for bicriteria optimization based on the sensitivity function , 1974, CDC 1974.

[18]  P. Yu.  Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives , 1974 .

[19]  Y. Wan,et al.  Morse theory for two functions , 1975 .

[20]  S. Smale,et al.  Global Analysis and Economics I: Pareto Optimum and a Generalization of Morse Theory† , 1975 .

[21]  Elijah Polak,et al.  An algorithm for bicriteria optimization based on the sensitivity function , 1975 .