article

An interactive weighted Tchebycheff procedure for multiple objective programming

Authors:

Ralph E. Steuer,

Eng-Ung ChooAuthors Info & Claims

Mathematical Programming: Series A and B, Volume 26, Issue 3

Pages 326 - 344

https://doi.org/10.1007/BF02591870

Published: 01 October 1983 Publication History

Abstract

The procedure samples the efficient set by computing the nondominated criterion vector that is closest to an ideal criterion vector according to a randomly weighted Tchebycheff metric. Using `filtering' techniques, maximally dispersed representatives of smaller and smaller subsets of the set of nondominated criterion vectors are presented at each iteration. The procedure has the advantage that it can converge to non-extreme final solutions. Especially suitable for multiple objective linear programming, the procedure is also applicable to integer and nonlinear multiple objective programs.

References

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V. J. Bowman, "On the relationship of the Tchebycheff norm and the efficient frontier of multiple-criteria objectives", Lecture Notes in Economics and Mathematical Systems 135 (1980) 76-85.

[2]

E. U. Choo, "Multicriteria linear fractional programming", Ph.D. dissertation, University of British Columbia, (Vancouver, B.C., 1980).

[3]

E. U. Choo and D. R. Atkins, "An interactive algorithm for multicriteria programming", Computers and Operations Research 7 (1980) 81-87.

[4]

W. Dinkelbach and W. Dürr, "Effizienzaussagen bei Ersatzprogrammen zum Vektormaximum-problem", in: R. Henn, H. P. Künzi and H. Schubert, eds., Operations Research Verfahren XII (Verlag Anton Hain, Meisenheim, 1972) pp. 117-123.

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J. G. Ecker and N. E. Shoemaker, "Selecting subsets from the set of nondominated vectors in multiple objective linear programming", SIAM Journal on Control and Optimization 19 (1981) 505-515.

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J. G. Ecker and M. Kupferschmid, "An ellipsoid algorithm for convex programming", Working Paper, Department of Mathematical Sciences, Rensselaer Polytechnic Institute (Troy, NY, 1982).

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A. M. Geoffrion, "Proper efficiency and the theory of vector maximization", Journal of Mathematical Analysis and Applications 22 (1968) 618-630.

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J. P. Ignizio, Linear programming in single and multiple objective systems (Prentice-Hall, Englewood Cliffs, NJ, 1982).

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S. M. Lee, Goal programming for decision analysis (Auerbach Publishers, Philadelphia, PA, 1972).

[10]

R. E. Steuer, "Operating manual for the ADBASE multiple objective linear programming computer package (release: 8/80)", College of Business Administration, University of Georgia (Athens, GA, 1980).

[11]

R. E. Steuer and F. W. Harris, "Intra-set point generation and filtering in decision and criterion space", Computers and Operations Research 7 (1980) 41-53.

[12]

R. E. Steuer, "On sampling the efficient set using weighted Tchbycheff metrics", Proceedings of the Task Force Meeting on Multiobjective and Stochastic Optimization, International Institute for Applied Systems Analysis (Laxenburg, Austria, 1982).

[13]

A. P. Wierzbicki, "The use of reference objectives in multiobjective optimization", Lecture Notes in Economics and Mathematical Systems 177 (1980) 468-486.

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P. L. Yu, "A class of solutions for group decision problems", Management Science 19 (1973) 936-946.

Digital Library

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M. Zeleny, "Compromise programming", in: J. L. Cochrane and M. Zeleny, eds., Multiple criteria decision making (University of South Carolina Press, Columbia, SC, 1973) pp. 262-301.

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cover image Mathematical Programming: Series A and B

Mathematical Programming: Series A and B Volume 26, Issue 3

October 1983

119 pages

ISSN:0025-5610

Issue’s Table of Contents

Copyright © Copyright © 1983 The Mathematical Programming Society, Inc.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 October 1983

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https://dl.acm.org/doi/10.3233/IDT-230608
Samanlioglu FTabassum NKaraca TBilge A(2024)A Bicriteria Model to Determine Pareto Optimal Pulse Vaccination StrategiesApplied Computational Intelligence and Soft Computing10.1155/2024/55310622024Online publication date: 1-Jan-2024
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Helfrich SPrinz KRuzika S(2024)The Weighted p-Norm Weight Set Decomposition for Multiobjective Discrete Optimization ProblemsJournal of Optimization Theory and Applications10.1007/s10957-024-02481-8202:3(1187-1216)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/s10957-024-02481-8
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Helfrich SPerini THalffmann PBoland NRuzika S(2023)Analysis of the weighted Tchebycheff weight set decomposition for multiobjective discrete optimization problemsJournal of Global Optimization10.1007/s10898-023-01284-x86:2(417-440)Online publication date: 2-May-2023
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Lin XYang ZZhang XZhang QKoyejo SMohamed SAgarwal ABelgrave DCho KOh A(2022)Pareto set learning for expensive multi-objective optimizationProceedings of the 36th International Conference on Neural Information Processing Systems10.5555/3600270.3601668(19231-19247)Online publication date: 28-Nov-2022
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