Solving multidimensional knapsack problems with generalized upper bound constraints using critical event tabu search

Computers and Operations Research

Volumn 32, Issue 4, 2005, Pages 825-848

  Li, V C ^a   Curry, G L ^b  

^a ITHACA COLLEGE   (United States)

^b Texas AandM University   (United States)

Author keywords

Critical event tabu search; GUB; Multidimensional knapsack; Strategic oscillation; Surrogate constraint

Indexed keywords

COMPUTATIONAL METHODS; HEURISTIC METHODS; INFORMATION RETRIEVAL; PROBLEM SOLVING; SET THEORY;

CRITICAL EVENT TABU SEARCH; GENERALIZED UPPER BOUND (GUB); MULTIDIMENSIONAL KNAPSACK; STRATEGIC OSCILLATION; SURROGATE CONSTRAINT;

OPERATIONS RESEARCH;

EID: 5644249597     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2003.08.021     Document Type: Article

References (55)

1. Beale E.M.L., Tomlin J.A. Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables. Lawrence J. Proceedings of the Fifth International Conference on Operational Research. 1970;p447-p454 Tavistock Publications, London.
2. Li V.C., Curry G.L., Boyd E.A. Towards the real time solution of strike force asset allocation problems. Computers and Operations Research. 31(2):2004;273-291.
3. Garey M.R., Johnson D.S. Computers and intractability: a guide to the theory of NP-completeness. 1979;Freeman, San Francisco.
4. Martello S., Toth P. Knapsack problems. 1990;Wiley, New York.
5. Moser M., Jokanovic D.P., Shiratori N. An algorithm for the multidimensional multiple-choice knapsack problem. IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences. E80-A(3):1997;582-589.
6. Everett III H. Generalized Lagrange multiplier method for solving problems of optimum allocation of resources. Operations Research. 11:1963;399-417.
7. Magazine M.J., Oguz O. A heuristic algorithm for the multidimensional 0-1 knapsack problem. European Journal of Operational Research. 16:1984;319-326.
8. Volgenant A., Zoon J.A. An improved heuristic for multidimensional 0-1 knapsack problems. Journal of the Operational Research Society. 41(10):1990;963-970.
9. Healy W.C. Jr. Multiple choice programming. Operations Research. 12:1964;122-138.
10. Lin E.Y.H. Multiple choice programming. a state-of-the-art review International Transactions in Operational Research. 1:1994;409-421.
11. Lin E.Y.H. A bibliographical survey on some well-known non-standard knapsack problems. INFOR. 36(4):1998;274-317.
12. Dyer M.E., Walker J. Dominance in multi-dimensional multiple-choice knapsack problems. Asia Pacific Journal of Operational Research. 15(2):1998;159-168.
13. Weingatner H.M. Capital budgeting of interrelated projects. survey and synthesis Operations Research. 12:1966;485-516.
14. Peterson C.C. Computational experience with variants of the Balas algorithm applied to the selection of research and development projects. Management Science. 13:1967;736-750.
15. Gilmore P.C., Gomory R.E. The theory and computation of knapsack functions. Operations Research. 14:1966;1045-1075.
16. Shih W. A branch and bound method for the multiconstraint zero-one knapsack problem. Journal of Operations Research Society. 30:1979;369-378.
17. Magazine M.J., Oguz O. A full polynomial approximation algorithm for the 0-1 knapsack problem. European Journal of Operational Research. 8:1981;270-273.
18. Magazine M.J., Chern M.S. A note on approximation schemes for multidimensional knapsack problems. Mathematics of Operations Research. 9:1984;244-247.
19. Geoffrion A.M. Lagrangian relaxation for integer programming. Mathematical Programming Study. 2:1974;82-114.
20. Glover F. Surrogate constraints. Operations Research. 16:1968;741-749.
21. Glover F. Heuristics for integer programming using surrogate constraints. Decision Sciences. 8:1977;156-166.
22. Chu P.C., Beasley J.E. A genetic algorithm for the multidimensional knapsack problem. Journal of Heuristics. 4:1998;63-86.
23. Bertsimas D., Demir R. An approximate dynamic programming approach to multidimensional knapsack problems. Management Science. 48(4):2002;550-565.
24. Glover F. Future paths for integer programming and links to artificial intelligence. Computers and Operations Research. 19:1986;533-549.
25. Aarts E.H.L., Lenstra J.K. Local search in combinatorial optimization. 1997;Wiley, Chichester, UK.
26. Glover F., Kochenberger G.A. Handbook of metaheuristics. 2002;Kluwer Academic Publishers, Boston.
27. Osman I.H., Laporte G. Metaheuristics: A bibliography. Annals of Operations Research. 63:1996;513-623.
28. Osman I.H., Kelly J.P. Metaheuristics: an overview. Osman I.H., Kelly J.P. Metaheuristics: theory and applications. 1996;p1-21 Kluwer Academic Publishers, Boston.
29. Haul C., Voss S. Using surrogate constraints in genetic algorithms for solving multidimensional knapsack problems. Woodruff D.L. Advances in computational and stochastic optimization, logic programming, and heuristic search. 1998;p235-p251 Kluwer Academic Publishers, Boston.
30. Drexl A. A simulated annealing approach to the multiconstraint zero-one knapsack problem. Computing. 40:1988;1-8.
31. Glover F., Kochenberger G.A. Critical event tabu search for multidimensional knapsack problems. Osman I.H., Kelly J.P. Metaheuristics: theory and applications. 1996;p407-p427 Kluwer Academic Publishers, Boston.
32. Hansen P. The steepest ascent mildest descent heuristic for combinatorial programming. Presented at the Congress on Numerical Methods in Combinatorial Optimization, Capri, Italy, 1986.
33. Glover F. Tabu search - part I. ORSA Journal on Computing. 1(3):1989;190-206.
34. Glover F. Tabu search - part II. ORSA Journal on Computing. 2(1):1990;4-32.
35. de Werra D., Hertz A. Tabu search techniques. a tutorial and an application to neural networks OR Spektrum. 11:1989;131-141.
36. Glover F. Tabu search fundamentals and uses. Birge J.R., Murty K.G. Mathematical programming: state of the art. 1994;p64-p92 University of Michigan, Ann Arbor, MI.
37. Glover F., Laguna M. Tabu search. 1998;Kluwer Academic Publishers, Boston.
38. Kirkpatrick S., Gelatt C.D. Jr., Vecchi M.P. Optimization by simulated annealing. Science. 220(4598):1983;671-680.
39. Dammeyer F., Voss S. Dynamic tabu list management using the reverse elimination method. Annals of Operations Research. 41:1993;31-46.
40. Hanafi S., Freville A. Extension of reverse elimination method through a dynamic management of the tabu list. RAIRO-Operations Research. 35(2):2001;251-267.
41. Aboudi R., Jörnsten K. Tabu search for general zero-one integer programs using the pivot and complement heuristic. ORSA Journal on Computing. 6(1):1992;82-93.
42. Lokketangen A., Jörnsten K., Storoy S. Tabu search within a pivot and complement framework. International Transactions of Operations Research. 1(3):1994;305-316.
43. Balas E., Martin C.H. Pivot and complement - a heuristic for zero-one programming. Management Science. 26:1980;86-96.
44. Battiti R., Tecchiolli G. The reactive tabu search. ORSA Journal on Computing. 6(2):1994;126-140.
45. Lokketangen A., Glover F. Solving zero-one mixed integer programming problems using tabu search. European Journal of Operational Research. 106(2-3):1998;624-658.
46. Hanafi S., Freville A. An efficient tabu search approach for the 0-1 multidimensional knapsack problem. European Journal of Operational Research. 106(2-3):1998;659-675.
47. Carlton W.B., Barnes J.W. A note on hashing functions and tabu search algorithms. European Journal of Operational Research. 95:1996;237-239.
48. Woodruff D.L., Zemel E. Hashing vectors for tabu search. Annals of Operations Research. 41:1993;123-138.
49. Fisher M.L. The Lagrangian relaxation method for solving integer programming problems. Management Science. 27(1):1981;1-18.
50. Greenberg H.J., Pierskalla W.P. Surrogate mathematical programming. Operations Research. 18:1970;924-939.
51. Glover F. Surrogate constraint duality in mathematical programming. Operations Research. 23(3):1975;434-451.
52. Glover F. Tutorial on surrogate constraint approaches for optimization in graphs. Journal of Heuristics. 9(3):2003;175-227.
53. Glover F. Surrogate constraints: tutorial notes. October 1998.
54. Zhang GQ, Glover F, Kochenberger G. Critical event tabu search method for multi-diminution knapsack problem. Presented at the Spring INFORMS National Meeting in Salt Lake City, UT, May 2000.
55. Li VC, Curry GL. Tight oscillations in critical event tabu search for multidimensional knapsack problems with GUB sets. 2003, submitted for publication.