ADBASE

Random problem genertion and the computation of efficient extreme points in multiple objective linear programming. This paper looks at the task of computing efficient extreme points in multiple objective linear programming. Vector maximization software is reviewed and the ADBASE solver for computing all efficient extreme points of a multiple objective linear program is described. To create MOLP test problems, models for random problem generation are discussed. In the computational part of the paper, the numbers of efficient extreme points possessed by MOLPs (including multiple objective transportation problems) of different sizes are reported. In addition, the way the utility values of the efficient extreme points might be distributed over the efficient set for different types of utility functions is investigated. Not surprisingly, results show that it should be easier to find good near- optimal solutions with linear utility functions than with, for instance, Tchebycheff types of utility functions.


References in zbMATH (referenced in 64 articles )

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  1. Mavrotas, G.; Diakoulaki, D.: Multicriteria branch and bound: a vector maximization algorithm for mixed 0-1 multiple objective linear programming (2005)
  2. Schechter, Murray; Steuer, Ralph E.: A correction to the connectedness of the evans-steuer algorithm of multiple objective linear programming (2005)
  3. Steuer, Ralph E.; Piercy, Craig A.: A regression study of the number of efficient extreme points in multiple objective linear programming (2005)
  4. Stummer, Christian; Sun, Minghe: MOAQ and ant-Q algorithm for multiple objective optimization problems (2005)
  5. Cakravastia, A.; Takahashi, K.: Integrated model for supplier selection and negotiation in a make-to-order environment (2004)
  6. Fernández, Elena; Puerto, Justo: Multiobjective solution of the uncapacitated plant location problem (2003)
  7. Gonçalves Gomes, Eliane; Lins, Marcos Pereira Estellita: Integrating geographical information systems and multi-criteria methods: A case study (2002)
  8. Wang, Hsiao-Fan; Huang, Zhi-Hao: Top-down fuzzy decision making with partial preference information (2002)
  9. Cherchye, Laurens; Van Puyenbroeck, Tom: Product mixes as objects of choice in non-parametric efficiency measurement (2001)
  10. T’kindt, V.; Billaut, J.-C.; Proust, C.: Solving a bicriteria scheduling problem on unrelated parallel machines occurring in the glass bottle industry (2001)
  11. Benson, H. P.; Sun, E.: Outcome space partition of the weight set in multiobjective linear programming (2000)
  12. Ringuest, Jeffrey L.; Graves, Samuel B.: A sampling-based method for generating nondominated solutions in stochastic MOMP problems (2000)
  13. Romero, Carlos: Risk programming for agricultural resource allocation: A multidimensional risk approach (2000)
  14. Sun, Minghe; Stam, Antonie; Steuer, Ralph E.: Interactive multiple objective programming using Tchebycheff programs and artificial neural networks (2000)
  15. Mateos, A.; Rios-Insua, S.; Prieto, L.: Computational study of the relationships between feasible and efficient sets and an approximation (1999)
  16. Reeves, Gary R.; MacLeod, Kenneth R.: Robustness of the interactive weighted Tchebycheff procedure to inaccurate preference information (1999)
  17. Downing, C. E.; Ringuest, J. L.: An experimental evaluation of the efficacy of four multi-objective linear programming algorithms (1998)
  18. Tamiz, Mehrdad; Jones, Dylan; Romero, Carlos: Goal programming for decision making: An overview of the current state-of-the-art (1998)
  19. Aurovillian, Alok; Zhang, Hong; Wiecek, Malgorzata M.: A bookkeeping strategy for multiple objective linear programs (1997)
  20. Benson, H. P.; Boger, G. M.: Multiplicative programming problems: Analysis and efficient point search heuristic (1997)