Labeling algorithms for multiple objective integer knapsack problems

Computers and Operations Research

Volumn 37, Issue 4, 2010, Pages 700-711

  Rui Figueira, José ^a   Tavares, Gabriel ^b   Wiecek, Margaret M ^c  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b RUTGERS UNIVERSITY   (United States)

^c CLEMSON UNIVERSITY   (United States)

Author keywords

Labeling algorithms; Multiple objective integer knapsack problem; Shortest path problem

Indexed keywords

BINARY VARIABLES; BOUNDED VARIABLES; EXACT ALGORITHMS; KNAPSACK PROBLEMS; LABELING ALGORITHMS; LAYER BY LAYER; MULTIPLE CONSTRAINT; MULTIPLE OBJECTIVE INTEGER KNAPSACK PROBLEM; MULTIPLE OBJECTIVES; NETWORK ALGORITHMS; NETWORK MODELS; NUMERICAL RESULTS; OBJECTIVE FUNCTIONS; SHORTEST PATH PROBLEM; TIME-DEPENDENT; UNDERLYING NETWORKS;

INTEGER PROGRAMMING; LABELING;

ALGORITHMS;

EID: 70350573951     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2009.06.026     Document Type: Article

References (38)

1. Ahuja R.K., Magnanti T.L., and Orlin J.B. Network flows (1993), Prentice-Hall, Englewood Cliffs, New Jersey
2. Arndt T., and Seelaender J. A method for solving a generalized knapsack problem with multiple objectives. In: Seelaender J., Goepfert A., and Tammer Ch. (Eds). Methods of multicriteria decision theory (1997), Haensel-Hohenhausen, Frankfurt 163-173
3. Barichard V., and Hao J.-K. Genetic tabu search for the multi-objective knapsack problem. Tsinghua Science and Technology 8 1 (2003) 8-13
4. Bazgan C., Hugot H., and Vanderpooten D. Solving efficiently the 0-1 multi-objective knapsack problem. Computers and Operations Research 36 (2009) 260-279
5. Ben Abdelaziz F., Krichen S., and Chaouadi J. A hybrid heuristic for multiobjective knapsack problems. In: Osman I., Voss S., Martello S., and Roucairol C. (Eds). Meta-heuristics: advances and trends in local search paradigms for optimization (1999), Kluwer Academic Publishers, Dordrecht 205-212
6. Bhaskar K. A multiple objective approach to capital budgeting. Accounting and Business Research 9 (1979) 25-46
7. Captivo M.E., Clímaco J., Figueira J., Martins E., and Santos J.L. Solving bicriteria 0-1 knapsack problems using a labeling algorithm. Computers and Operations Research 30 (2003) 1865-1886
8. Colombo G., and Mumford Ch. Comparing algorithms, representations and operators for the multi-objective knapsack problem. Proceedings of 2005 IEEE congress on evolutionary computation (2005) 1268-1275
9. Czyzak P., and Jaszkiewicz A. Pareto simulated annealing-a metaheuristic technique for multiple-objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis 7 (1998) 34-47
10. Ehrgott M. Multicriteria optimization. 3rd ed. (2005), Springer, Berlin
11. Gandibleux X., Mezdaoui N., and Freville A. A tabu search procedure to solve multiobjective combinatorial optimization problems. In: Ruiz F., Caballero R., and Steuer E. (Eds). Advances in multiple objective and goal programming (1997), Springer, Berlin 292-300
12. Garfinkel R.S., and Nemhauser G.L. Integer programming (1972), Wiley, New York
13. Gomes da Silva C., Clímaco J., and Figueira J. A scatter search method for bi-criteria { 0, 1 }-knapsack problems. European Journal of Operational Research 169 (2006) 373-391
14. Gomes da Silva C., Figueira J., and Clímaco J. Integrating partial optimization with scatter search for solving bi-criteria { 0, 1 }-knapsack problems. European Journal of Operational Research 177 (2007)
15. Grosan C., and Oltean M. Improving the performance of evolutionary algorithms for the multiobjective 0/1 knapsack problem using ε{lunate}-dominance. Lecture notes in computer science; computational science-ICCS 2004 vol. 3037 (2004), Springer, Berlin 674-677
16. Guder J. Discounted knapsack problems for pairs of items. Master Thesis, Universität Erlangen-Nürnberg, Germany; 2005.
17. Guo X.-P., Wu Z.-M., and Yang G.-K. A hybrid adaptive multi-objective memetic algorithm for 0/1 knapsack problem. Lecture notes in computer science; AI 2005: advances in artificial intelligence-18th Australian joint conference on artificial intelligence, proceedings vol. 3809 (2005), Springer, Berlin 176-185
18. Hansen M. Solving multiobjective knapsack problems using MOTS. Conference paper presented at MIC'97, Sophia, Antipolis, France, July, 1997.
19. Ibaraki T. Enumerative approaches to combinatorial optimization, part II. Annals of Operations Research 11 (1987) 343-602
20. Jaszkiewicz A. On the computational efficiency of multiple objective metaheuristics. The knapsack problem case study. European Journal of Operational Research 158 (2004) 418-433
21. Klamroth K., and Wiecek M.M. Dynamic programming approaches to the multiple criteria knapsack problem. Naval Research Logistics 77 (2000) 57-76
22. Kostreva M.M., Ogryczak W., and Tonkyn D.W. Relocation problems arising in conservation biology. Computers and Mathematics with Applications 37 (1999) 135-150
23. Kumar R., and Banerjee N. Analysis of a multiobjective evolutionary algorithm on the 0/1 knapsack problem. Theoretical Computer Science 358 1 (2006) 104-120
24. Kwak W., Shi Y., Lee H., and Lee C.F. Capital budgeting with multiple criteria and multiple decision makers. Review of Quantitative Finance and Accounting 7 (1996) 97-112
25. Laumanns M, Thiele L, Zitzler E. An adaptive scheme to generate the Pareto front based on the epsilon-constraint method. Technical Report 199, Institute für Technische Informatik und Kommunikationsnetze, ETH Zürich, Switzerland; 2004.
26. Laumanns M., Thiele L., and Zitzler E. Running time analysis of evolutionary algorithms on a simplified multiobjective knapsack problem. Natural Computing 3 1 (2004) 37-51
27. Laumanns M, Thiele L, Zitzler E. An adaptive scheme to generate the Pareto front based on the epsilon-constraint method. In: Practical approaches to multi-objective optimization, Dagstuhl seminar proceedings 04461, 2005 〈http://drops.dagstuhl.de/opus/volltexte/2005/246〉.
28. Laumanns M., Thiele L., and Zitzler E. An efficient adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method. European Journal of Operational Research 169 (2006) 932-942
29. Serafini P. Some considerations about computational complexity for multi objective combinatorial problems. In: Jahn J., and Krabs W. (Eds). Recent advances and historical development of vector optimization (1986), Springer, Berlin 222-232
30. Steuer R. Multiple criteria optimization: theory, computation, and application (1986), Wiley, New York
31. Teng J.-Y., and Tzeng G.-H. A multiobjective programming approach for selecting non-independent transportation investment alternatives. Transportation Research B 30 (1996) 291-307
32. Ulungu E.L., and Teghem J. Solving multi-objective knapsack problems by a branch-and-bound procedure. In: Climaco J.N. (Ed). Multicriteria analysis (1997), Springer, Berlin 269-278
33. Teghem J., Fortemps P.H., Ulungu E.L., and Tuyttens D. MOSA method: a tool for solving multiobjective combinatorial optimization problems. Journal of Multi-Criteria Decision Analysis 8 (1999) 221-236
34. Vetschera R. Time preferences in capital budgeting-an application of interactive multiobjective optimization. Methods of Operations Research 50 (1985) 649-660
35. Villarreal B., and Karwan M.H. Multicriteria integer programming: a (hybrid) dynamic programming recursive approach. Mathematical Programming 21 (1981) 204-223
36. Villarreal B., and Karwan M.H. Multicriteria dynamic programming with an application to the integer case. Journal of Mathematical Analysis and Applications 38 (1982) 43-69
37. Zhang B., Zhang X.-H., Gong M.-G., and Lu B. Immune system strength Pareto algorithm for multiobjective 0/1 knapsack problems. Journal of Harbin Engineering University 27 (2006) 214-218
38. Zitzler E., and Thiele L. Multiobjective evolutionary algorithms: a comparative study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation 3 4 (1999) 257-271