Browse > Article
http://dx.doi.org/10.7232/JKIIE.2012.38.2.074

Separation Heuristic for the Rank-1 Chvatal-Gomory Inequalities for the Binary Knapsack Problem  

Lee, Kyung-Sik (Department of Industrial and Management Engineering, Hankuk University of Foreign Studies)
Publication Information
Journal of Korean Institute of Industrial Engineers / v.38, no.2, 2012 , pp. 74-79 More about this Journal
Abstract
An efficient separation heuristic for the rank-1 Chvatal-Gomory cuts for the binary knapsack problem is proposed. The proposed heuristic is based on the decomposition property of the separation problem for the fixedcharge 0-1 knapsack problem characterized by Park and Lee [14]. Computational tests on the benchmark instances of the generalized assignment problem show that the proposed heuristic procedure can generate strong rank-1 C-G cuts more efficiently than the exact rank-1 C-G cut separation and the exact knapsack facet generation.
Keywords
Chvatal-Gomory cut; Knapsack problem; Separation heuristic;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 CPLEX 9.1, http://www.ibm.com, 2007.
2 Achterberg, T., Koch, T., and Martin, A. (2003), MIPLIB 2003, Operations Research Letters, 34, 361-372.
3 Avella, P., Boccia, M., and Vailyev, I. (2010), A computational study of exact knapsack separation for the generalized assignment problem, Computational Optimization and Applications, 45, 543-555.   DOI   ScienceOn
4 Balas, E. (1975), Facets of the knapsack polytope, Mathematical Programming, 8, 146-164.   DOI   ScienceOn
5 Balas, E. and Zemel, E. (1978), Facets of the knapsack polytope from minimal covers, SIAM Journal on Applied Mathematics, 34, 119-148.   DOI   ScienceOn
6 Beasley, J. E. (1990), OR-Library : Distributing test problems by electronic mail, Journal of the Operational Research Society, 41, 1069-1072.   DOI
7 Crowder, H., Johnson, E., and Padberg, M. (1983), Solving largescale 0-1 linear programming problems, Operations Research, 31, 803-834   DOI   ScienceOn
8 Eisenbrand, F. (1999), On the Membership Problem for the Elementary Closure of a Polyhedron, Combinatorica, 19, 297-300.   DOI   ScienceOn
9 Glover, F., Sherali, H. D., and Lee, Y. (1997), Generating Cuts from Surrogate Constraint Analysis for Zero-One and Multiple Choice Programming, Computational Optimization and Application, 8, 151-172.   DOI   ScienceOn
10 Kaparis, K. and Letchford, A. N. (2010), Separation algorithms for 0-1 knapsack polytopes, Mathematical Programming, 124, 69-91.   DOI   ScienceOn
11 Klabjan, D., Nemhauser, G. L., and Tovey, C. (1998), The complexity of cover inequality separation, Operations Research Letters, 23, 35-40.   DOI   ScienceOn
12 Lee, K. and Park, S. (2000), A Cut Generation Method for the (0, 1)-Knapsack Problem with a Variable Capacity, Journal of the Korean OR/MS Society, 25(3), 1-15.   과학기술학회마을
13 Nemhauser, G. L. and Wolsey, L. A. (1988), Integer and Combinatorial Optimization, Wiley.
14 Park, K. and Lee, K. (2011), On the separation of the rank-1 Chvatal-Gomory Inequalities for the fixed-charge 0-1 knapsack problem, Journal of the Korean OR/MS Society, 36(2), 43-50.   과학기술학회마을
15 Xpress Optimizer 17.10.04, http://www.fico.com, 2007.