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A correction to the connectedness of the Evans-Steuer algorithm of multiple objective linear programming

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The Evans-Steuer algorithm (and its ADBASE computerized implementation) for finding all efficient extreme points of a multiple objective linear program (MOLP) is based on efficient pivots. The justification of the algorithm rests on the assumption that the set of efficient basic index sets is connected with respect of efficient pivots. This assumption is incorrect. Nevertheless, the algorithm is valid and is, in fact, more efficient than originally believed.
Rocznik
Strony
351--359
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
  • Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18105 USA
autor
  • Terry College of Business, University of Georgia, Athens, Georgia 30602-6253 USA
Bibliografia
  • [1] P. Armand and С. Malivert. Determination of the efficient set in multiobjective linear programming. Journal of Optimization Theory and Applications, 70(3):467-489, 1991.
  • [2] A. Cakravastia and K. Takahashi. Integrated model for supplier selection and negotiation in a make-to-order environment. International Journal of Production Research, 41(21):4457-4474, 2004.
  • [3] J.G. Ecker and I. A. Kouada. Finding all efficient extreme points for multiple objective linear programs. Mathematical Programming, 5(l):54-72, 1978.
  • [4] M. Ehrgott. An optimisation model for intensity modulated radiation therapy. In M. Ehrgott, editor, Proceedings of the 37th Annual Conference of the Operational Research Society of New Zealand, pages 23-31. University of Auckland, New Zealand, 2003.
  • [5] J. P. Evans and R. E. Steuer. A revised simplex method for multiple objective programs. Mathematical Programming, 5(l):54-72, 1973.
  • [6] E. Fernandez and J. Puerto. Multiobjective solution of the uncapacitated plant location problem. European Journal of Operational Research, 145(3):509-529, 2003.
  • [7] J. Fliege. Gap-free computation of Pareto-points by quadratic scalarizations. Mathematical Methods of Operations Research, 59(l):69-89, 2004.
  • [8] T. Gal. A general method for determining the set of all efficient solutions to a linear vectormaximum problem. European Journal of Operational Research, l(5):307-322, 1977.
  • [9] R. Hartley. Survey of algorithms for vector optimization problems. In S. French, R. Hartley, L. C. Thomas, and D. J. White, editors, Multi-Objective Decision Making, pages 1-34. Academic Press, New York, 1983.
  • [10] H. Isermann. The enumeration of the set of all efficient solutions for a linear multiple objective program. Operational Research Quarterly, 28(3):711-725, 1977.
  • [11] M. P. E. Lins, L. Angulo-Meza, and A. C. M. da Silva. A multi-objective approach to determine alternative targets in data envelopment analysis. Journal of the Operational Research Society, 55(10):1090-1101, 2004.
  • [12] M. Mañas and J. Nedoma. Finding all vertices of a convex polyhedron. Numerische Mathematik, 12:226-229, 1968.
  • [13] B. Martos. Nonlinear Programming. American Elsevier, New York, 1975.
  • [14] G. Naujoks. "Operating manual for the EFFACET multiple objective linear programming package," Masters Thesis, Fakultät für Wirtschaftswissenschaften, Universität Bielefeld, Germany, 1984.
  • [15] R. E. Steuer. "ADBASE: A multiple objective linear programming solver for all efficient extreme points and all unbounded efficient edges," Terry College of Business, University of Georgia, Athens, Georgia, 2004.
  • [16] R. E. Steuer. Multiple Criteria Optimization: Theory, Computation and Application. John Wiley, New York, 1986.
  • [17] M. Sun. Procedures for finding nondominated solutions for multiple objective network programming problems. Transportation Science, 37(2): 139-152, 2003.
  • [18] J. Vera, P. de Atauri, M. Cascante, and N. V. Torres. Multicriteria optimization of biochemical systems by linear programming: Application to production of ethanol by Saccharomyces cerevisiae. Biotechnology and Bioengineering, 83(3):335-343, 2003.
  • [19] J. Vera, N. V. Torres, C. G. Moles, and J. Banga. Integrated nonlinear optimization of bioprocesses via linear programming. AIChE Journal, 49(12):3173-3187, 2003.
  • [20] P. L. Yu. Linear Multi-Objective Programming. Pergamon Press, New York, 1985.
  • [21] M. Zeleny. Linear Multi-Objective Programming. Springer Verlag, New York, 1974.
  • [22] L. Zhu and D. Kazmer. An extensive simplex method for mapping global feasibility. Engineering Optimization, 35(2):165-176, 2003.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPP1-0053-0100
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