Abstract
The aim of the chapter is to expose its readers to some basic and generic ideas associated with interior algorithms and develop approaches for using these algorithms to address MOLP problems. In doing so, we discuss basic MOLP questions associated with interior algorithms, develop some specific interior MOLP approaches and illustrated them with examples.
This is a preview of subscription content, log in via an institution to check access.
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
Arbel, A., Exploring Interior Point Linear Programming: Algorithms and Software, MIT Press, Cambridge, MA, 1993
Arbel, A.: An Interior Multiobjective Linear Programming Algorithm. Computers and Operations Research 20(1993)723–735
Arbel, A., S. S. Oren: Generating Interior Search Directions for Multiobjective Linear Programming. Journal of Multicriteria Decision Analysis 2(1993)73–86
Arbel, A.: Anchoring Points and Cones of Opportunities in Interior Multiobjective Linear Programming Problems. Journal of the Operational Research Society 45(1994)83–96
Arbel, A.: A Multiobjective Interior Primal-Dual Linear Programming Algorithm. Computers and Operation Research, 21(1994)433–445
Arbel, A., P. Korhonen: Using Aspiration Levels in an Interactive Interior Multiobjective Linear Programming Algorithm. European Journal of Operational Research 89(1996)193–201
Arbel, A., P. Korhonen: Using Aspiration Levels in an Interior Primal-Dual Multiobjective Linear Programming Algorithm. Journal of Multicriteria Decision Analysis 5(1996)61–71
Chankong, V., Y. Y. Haimes: Multiobjective Decision Making: Theory and Methodology, North-Holland, 1983
Gal, T.: Postoptimal Analyses, Parametric Programming, and Related Topics, 2nd/3rd edition, de Gruyter, Berlin 1996, Chapter 9
Karmarkar, N. K.: A new polynomial time algorithm for linear programming. Combinatorica 4(1984)373–395
J. Laakso: A Visual Interactive Method for Solving the Multiple Criteria Problem. European Journal of Operational Research 24(1986)277–287
Korhonen, P., J. Wallenius: A Pareto Race. Naval Research Logistics 35(1988)615–623
Shin, W. S., A. Ravindran: Interactive Multiobjective Optimization Survey I — Continuous Case. Computers and Operations Research 18(1991)97–114
Steuer, R. E.: Multiple Criteria Optimization: Theory, Computation, and Application, Wiley and Sons, New York, 1986
Vanderbei, R. J., M. S. Meketon, B. A. Freedman: A modification of Karmarkar’s linear programming algorithm. Algorithmica 1(1986)395–407
Vanderbei, R. J.: Linear Programming, Kluwer, 1996
Wierzbicki, A.: “The Use of Reference Objectives in Multiobjective Optimization.” In: G. Fandel, T. Gal, (Eds.): Multiple Criteria Decision Making: Theory and Application. Springer-Verlag, Berlin, 1980, pp}. 468–486
Wierzbicki, A.: On the Completeness and Constructiveness of Parametric Characterizations to Vector Optimization Problems, OR-Spectrum, 8(1986)73–87
Zeleny, M.: Multiple Criteria Decision Making, McGraw-Hill Book Co., New York, 1982
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Arbel, A. (1999). Fundamentals of Interior Multiple Objective Linear Programming Algorithms. In: Gal, T., Stewart, T.J., Hanne, T. (eds) Multicriteria Decision Making. International Series in Operations Research & Management Science, vol 21. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5025-9_13
Download citation
DOI: https://doi.org/10.1007/978-1-4615-5025-9_13
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7283-7
Online ISBN: 978-1-4615-5025-9
eBook Packages: Springer Book Archive