Solving the biobjective zero-one knapsack problem by an efficient LP-based heuristic

European Journal of Operational Research

Volumn 159, Issue 3, 2004, Pages 545-557

  Zhang, Cai Wen ^a   Ong, Hoon Liong ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Nondominated solution; Integer programming; Knapsack problem; LP based heuristic; Multiple objective programming

Indexed keywords

ANNEALING; APPROXIMATION THEORY; COMPUTATIONAL METHODS; DECISION MAKING; GENETIC ALGORITHMS; HEURISTIC PROGRAMMING; INTEGER PROGRAMMING; INVESTMENTS; OPTIMIZATION; PROBLEM SOLVING;

KNAPSACK PROBLEM; LP-BASED HEURISTIC; METAHEURISTICS; MULTIPLE OBJECTIVE PROGRAMMING;

OPERATIONS RESEARCH;

EID: 3343019200     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(03)00420-X     Document Type: Article

References (37)

1. Abbas M., Moulai M. Solving multiple objective integer linear programming. Recerca Operativa. 29(89):2000;15-38.
2. Aksoy Y. An interactive branch-and-bound algorithm for bicriterion nonconvex/mixed integer programming. Naval Research Logistics. 37:1990;403-417.
3. Alves M.J., Climaco J. An interactive reference point approach for multiobjective mixed-integer programming using branch-and-bound. European Journal of Operational Research. 124:2000;478-494.
4. Benders J.F., van Nunen J.A.E.E A property of assignment type mixed integer linear programming problems. Operations Research Letters. 2(2):1983;47-52.
5. Czyzak P., Jaszkiewicz A. Pareto simulated annealing - A metaheuristic technique for multiple-objective combinatorial optimization. Journal of Multi-Criteria Decision Analysis. 7:1998;34-47.
6. Dantzig G.B. Discrete-variable extremum problems. Operations Research. 5(2):1957;266-277.
7. Deckro R.F., Winkofsky E.P. Solving zero-one multiple objective programs through implicit enumeration. European Journal of Operational Research. 12:1983;362-374.
8. Ehrgott M., Gandibleux X. A survey and annotated bibliography of multiobjective combinatorial optimization. OR Spektrum. 22:2000;425-460.
9. Evans G.W. An overview of techniques for solving multiobjective mathematical programs. Management Science. 30(1):1984;1268-1282.
10. Gandibleux X., Freville A. Tabu search based procedure for solving the 0-1 multiobjective knapsack problem: The two objective case. Journal of Heuristics. 6:2000;361-383.
11. Hapke M., Jaszkiewicz A., Slowinski R. Interactive analysis of multiple-criteria project scheduling problems. European Journal of Operational Research. 107:1998;315-324.
12. Karasakal E.K., Koksalan M. A simulated annealing approach to bicriteria scheduling problems on a single machine. Journal of Heuristics. 6:2000;311-327.
13. Kiziltan G., Yucaoglu E. An algorithm for multiobjective zero-one linear programming. Management Science. 29(12):1983;1444-1453.
14. Klein D., Hannan E. An algorithm for the multiple objective integer linear programming problem. European Journal of Operational Research. 9:1982;378-385.
15. Lourenco H.R., Paixao J.P., Portugal R. Multiobjective metaheuristics for the bus driver scheduling problem. Transportation Science. 35(3):2001;331-343.
16. Marcotte O., Soland R.M. An interactive branch-and-bound algorithm for multiple criteria optimization. Management Science. 32(1):1986;61-75.
17. Marett R., Wright M. A comparison of neighborhood search techniques for multi-objective combinatorial problems. Computers & Operations Research. 23(5):1996;465-483.
18. Martello S., Toth P. Knapsack Problems: Algorithm and Computer Implementations. 1990;John Wiley & Sons, New York.
19. Ramesh R., Zionts S., Karwan M.H. A class of practical interactive branch and bound algorithms for multicriteria integer programming. European Journal of Operational Research. 26:1986;161-172.
20. Rasmussen L.M. Zero-one programming with multiple criteria. European Journal of Operational Research. 26:1986;83-95.
21. Steuer R.E. Multiple Criteria Optimization: Theory, Computation, and Application. 1986;John Wiley & Sons, New York.
22. Teghem J., Kunsch P.L. A survey of techniques for finding efficient solutions to multiobjective integer linear programming. Asia-Pacific Journal of Operational Research. 3:1986;95-108.
23. Teghem J., Kunsch P.L. Interactive methods for multi-objective integer linear programming. Fandel G., Graver M., Kurzhanski W. Lecture Notes in Economics and Mathematical Systems. vol. 273:1986;75-86 Springer, Berlin.
24. Teghem J., Tuyttens D., Ulungu E.L. An interactive heuristic method for multiobjective combinatorial optimization. Computers & Operations Research. 27:2000;621-634.
25. Trick M.A. A linear relaxation heuristic for the generalized assignment problem. Naval Research Logistics. 39:1992;137-151.
26. Tuyttens D., Teghem J., Fortemps Ph., Van Nieuwenhuyze K. Performance of the MOSA method for the bicriteria assignment problem. Journal of Heuristics. 6:2000;295-310.
27. Ulungu E.L., Teghem J. Multiobjective combinatorial optimization problems: a survey. Journal of Multi-Criteria Decision Analysis. 3:1994;83-104.
28. Ulungu E.L., Teghem J. The two-phases method: An efficient procedure to solve biobjective combinatorial optimization problems. Foundations of Computing and Decision Sciences. 20(2):1995;149-165.
29. Ulungu E.L., Teghem J., Fortemps Ph., Tuyttens D. MOSA method: A tool for solving multiobjective combinatorial optimization problems. Journal of Multi-Criteria Decision Analysis. 8:1999;221-236.
30. Viana A., Sousa J.P. Using metaheuristics in multiobjective resource constrained project scheduling. European Journal of Operational Research. 120:2000;359-374.
31. Visee M., Teghem J., Pirlot M., Ulungu E.L. Two-phase method and branch and bound procedures to solve the bi-objective knapsack problem. Journal of Global Optimization. 12:1998;139-155.
32. White D.J. A multiple objective interactive Lagrangean relaxation approach. European Journal of Operational Research. 19:1985;82-90.
33. White D.J. A bibliography on the applications of mathematical programming multiple-objective methods. The Journal of the Operational Research Society. 41(8):1990;669-691.
34. Zeleny M. Multiple Criteria Decision Making. 1982;McGraw-Hill, New York.
35. Zionts S. Integer linear programming with multiple objectives. Annals of Discrete Mathematics. 1:1977;551-562.
36. Zionts S. A survey of multiple criteria integer programming methods. Annals of Discrete Mathematics. 5:1979;389-398.
37. Zionts, S., 1992. Multiple criteria decision making: The challenge that lies ahead. In: Proceedings of the 10th International Conference on Multiple Criteria Decision Making, Taipei, Taiwan, 1992.