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.

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  1. Ehrgott, Matthias; Löhne, Andreas; Shao, Lizhen: A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming (2012)
  2. Clemente, M.; Fernández, F.R.; Puerto, J.: Pareto-optimal security strategies in matrix games with fuzzy payoffs (2011)
  3. Mavrotas, George; Figueira, José Rui; Antoniadis, Alexandros: Using the idea of expanded core for the exact solution of bi-objective multi-dimensional knapsack problems (2011)
  4. Gutjahr, Walter J.; Katzensteiner, Stefan; Reiter, Peter; Stummer, Christian; Denk, Michaela: Multi-objective decision analysis for competence-oriented project portfolio selection (2010)
  5. Vera, Julio; González-Alcón, Carlos; Marín-Sanguino, Alberto; Torres, Néstor: Optimization of biochemical systems through mathematical programming: methods and applications (2010)
  6. Kozanidis, George: Solving the linear multiple choice knapsack problem with two objectives: Profit and equity (2009)
  7. Mavrotas, George; Figueira, José Rui; Florios, Kostas: Solving the bi-objective multi-dimensional knapsack problem exploiting the concept of core (2009)
  8. Neto, J.Quariguasi Frota; Walther, G.; Bloemhof, J.; van Nunen, J.A.E.E.; Spengler, T.: A methodology for assessing eco-efficiency in logistics networks (2009)
  9. Kim, Jaehee; Kim, Sheung-Kown: A CHIM-based interactive Tchebycheff procedure for multiple objective decision making (2006)
  10. Hinojosa, M.A.; Mármol, A.M.; Monroy, L.: Generalized maximin solutions in multicriteria bargaining (2005)
  11. Hinojosa, M.A.; Mármol, A.M.; Thomas, L.C.: Core, least core and nucleolus for multiple scenario cooperative games (2005)
  12. Mavrotas, G.; Diakoulaki, D.: Multicriteria branch and bound: a vector maximization algorithm for mixed 0-1 multiple objective linear programming (2005)
  13. Schechter, Murray; Steuer, Ralph E.: A correction to the connectedness of the evans-steuer algorithm of multiple objective linear programming (2005)
  14. Steuer, Ralph E.; Piercy, Craig A.: A regression study of the number of efficient extreme points in multiple objective linear programming (2005)
  15. Stummer, Christian; Sun, Minghe: MOAQ and ant-Q algorithm for multiple objective optimization problems (2005)
  16. Fernández, Elena; Puerto, Justo: Multiobjective solution of the uncapacitated plant location problem (2003)
  17. Gonçalves Gomes, Eliane; Lins, Marcos Pereira Estellita: Integrating geographical information systems and multi-criteria methods: A case study (2002)
  18. Wang, Hsiao-Fan; Huang, Zhi-Hao: Top-down fuzzy decision making with partial preference information (2002)
  19. Cherchye, Laurens; Van Puyenbroeck, Tom: Product mixes as objects of choice in non-parametric efficiency measurement (2001)
  20. T’kindt, V.; Billaut, J.-C.; Proust, C.: Solving a bicriteria scheduling problem on unrelated parallel machines occurring in the glass bottle industry (2001)

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