Bound sets for biobjective combinatorial optimization problems

Computers and Operations Research

Volumn 34, Issue 9, 2007, Pages 2674-2694

  Ehrgott, Matthias ^a   Gandibleux, Xavier ^b  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b UNIVERSITÉ DE NANTES   (France)

Author keywords

Heuristics; Lower bound; Multiobjective discrete optimization; Relaxation; Upper bound

Indexed keywords

ALGORITHMS; COMBINATORIAL MATHEMATICS; HEURISTIC METHODS; OPTIMIZATION; RELAXATION PROCESSES;

BIOBJECTIVE PROBLEMS; LOWER BOUND; MULTIOBJECTIVE DISCRETE OPTIMIZATION; UPPER BOUND;

PROBLEM SOLVING;

EID: 33846575257     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2005.10.003     Document Type: Article

References (26)

1. Ehrgott M., and Gandibleux X. A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum 22 (2000) 425-460
2. Ehrgott M, Gandibleux X. editors. Multiple criteria optimization-state of the art annotated bibliographic surveys, Kluwer's international series in operations research and management science, vol. 52. Boston, MA: Kluwer Academic Publishers, 2002.
3. Sawaragi Y., Nakayama H., and Tanino T. Theory of multiobjective optimization (1985), Academic Press, Orlando
4. Ausiello G., Crescenzi P., Gambosi G., Kann V., Marchetti-Spaccamela A., and Protasi M. Complexity and approximation-combinatorial optimization problems and their approximability properties (1999), Springer, Berlin
5. Ehrgott M., and Tenfelde-Podehl D. Computation of ideal and nadir values and implications for their use in MCDM methods. European Journal of Operational Research 151 1 (2003) 119-131
6. Korhonen P., Salo S., and Steuer R.E. A heuristic for estimating nadir criterion values in multiple objective linear programming. Operations Research 45 5 (1997) 751-757
7. Villarreal B., and Karwan M.H. Multicriteria dynamic programming with an application to the integer case. Journal of Optimization Theory and Applications 38 1 (1982) 43-69
8. Bitran G.R., and Rivera J.M. A combined approach to solve binary multicriteria problems. Naval Research Logistics Quarterly 29 (1982) 181-201
9. Visée M., Teghem J., Pirlot M., and Ulungu E.L. Two-phases method and branch-and-bound procedures to solve the bi-objective knapsack problem. Journal of Global Optimization 12 (1998) 139-155
10. Mavrotas G., and Diakoulaki D. A branch and bound algorithm for mixed zero-one multiple objective linear programming. European Journal of Operational Research 107 3 (1998) 530-541
11. Kaliszewski I. Dynamic parametric bounds on efficient outcomes in interactive multiple criteria decision making problems. European Journal of Operational Research 147 (2003) 94-107
12. Ehrgott M, Gandibleux X. Bounds and bound sets for biobjective combinatorial optimization problems. In: Köksalan M, Zionts S. editors. Multiple criteria decision making in the new millenium, Lecture notes in economics and mathematical systems, vol. 507, Berlin: Springer, 2001. p. 242-53.
13. Ehrgott M., and Tam B. A heuristic for the discrete biobjective p-median location problem. Proceedings of the 39th annual conference of the operational research society of New Zealand. ORSNZ, Auckland (2004) 228-237
14. Tenfelde-Podehl D. Facilities layout problems: polyhedral structure, multiple objectives and robustness, PhD thesis, University of Kaiserslautern, Department of Mathematics; 2002.
15. Ehrgott M. Approximation algorithms for combinatorial multicriteria optimization problems. International Transcations in Operational Research 7 (2000) 5-31
16. Ruhe G. Complexity results for multicriteria and parametric network flows using a pathological graph of Zadeh. Zeitschrift für Operations Research 32 (1988) 27-59
17. Ulungu EL. Optimisation combinatoire multicritère: Détermination de l'ensemble des solutions efficaces et méthodes interactives. PhD thesis, Faculté des Sciences, Université de Mons-Hainaut. Mons, Belgium; 1993.
18. Ulungu E.L., and Teghem J. The two-phases method: An efficient procedure to solve biobjective combinatorial optimization problems. Foundations of Computing and Decision Sciences 20 2 (1994) 149-165
19. Gandibleux X. MCDM numerical instances library. Available online at www.terry.uga.edu/mcdm; 1998-2005.
20. Hansen MP, Jaszkiewicz A. Evaluating the quality of approximations to the non-dominated set. Technical Report IMM-REP-1998-7, Institute of Mathematical Modelling, Technical University of Denmark, Lyngby; 1998.
21. Ziztler E., Thiele L., Laumanns M., Fonseca C.M., and Grunert da Fonseca V. Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7 2 (2003) 117-132
22. Sayin S. Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming. Mathematical Programming 87 (2000) 543-560
23. Martello S., and Toth P. Knapsack problems. Algorithms and computer implementations (1990), Wiley, Chichester
24. Beasley J.E. Lagrangean relaxation. In: Reeves C.R. (Ed). Modern heuristic techniques for combinatorial problems (1993), McGraw-Hill Book Company, London 243-303
25. Lawler EL, Lenstra JK, Rinooy Kan AG, Shmooys DB. editors. The traveling salesman problem: a guided tour of combinatorial optimization, Wiley interscience series in pure and applied mathematics. Chichester: Wiley; 1985.
26. Chankong V., and Haimes Y.Y. Multiobjective decision making theory and methodology (1983), Elsevier Science, New York