Quantitative parametric connections between methods for generating noninferior solutions in multiobjective optimization

In multiobjective optimization, the trade-oA information between diAerent objective functions is probably the most important piece of information in a solution process to reach the most preferred solution. Generating methods are the methods in generating noninferior solutions. DiAerent generating methods provide decision makers trade-oA information in diAerent forms. Various generating methods are characterized in this paper and the quantitative parametric connections between these generating methods are established. The result in this paper is then used to consolidate tradeoA information with diAerent formats associated with diAerent generating methods. ” 1999 Elsevier Science B.V. All rights reserved.

[1]  A. Wierzbicki On the completeness and constructiveness of parametric characterizations to vector optimization problems , 1986 .

[2]  H. P. Benson,et al.  Optimization over the efficient set: Four special cases , 1994 .

[3]  H. P. Benson,et al.  Optimization over the efficient set , 1984 .

[4]  Johannes Jahn,et al.  Some characterizations of the optimal solutions of a vector optimization problem , 1985 .

[5]  Joseph G. Ecker,et al.  Finding all efficient extreme points for multiple objective linear programs , 1978, Math. Program..

[6]  M. Lightner,et al.  Multiple criterion optimization for the design of electronic circuits , 1981 .

[7]  J. Ecker,et al.  Optimizing a linear function over an efficient set , 1994 .

[8]  Yacov Y. Haimes,et al.  On the characterization of noninferior solutions of the vector optimization problem , 1982, Autom..

[9]  Simon French,et al.  Multi-Objective Decision Analysis with Engineering and Business Applications , 1983 .

[10]  R. Reid,et al.  On noninferior performance index vectors , 1971 .

[11]  D. White The maximization of a function over the efficient set via a penalty function approach , 1996 .

[12]  Eric Jacquet-Lagrèze,et al.  Multiobjective decision analysis with engineering and business applications: A. GOICOECHEA, D.R. HANSEN and L. DUCKSTEIN Wiley, New York, 1982, xvii + 519 pages, £26.50 , 1983 .

[13]  Marc Despontin,et al.  Multiple Criteria Optimization: Theory, Computation, and Application, Ralph E. Steuer (Ed.). Wiley, Palo Alto, CA (1986) , 1987 .

[14]  Duan Li,et al.  Iterative Parametric Minimax Method for a Class of Composite Optimization Problems , 1996 .

[15]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[16]  Harold P. Benson,et al.  Outcome-based algorithm for optimizing over the efficient set of a bicriteria linear programming problem , 1996 .

[17]  Duan Li Iterative Parametric Dynamic Programming and Its Application in Reliability Optimization , 1995 .

[18]  Duan Li,et al.  Convexification of a noninferior frontier , 1996 .