용량이 변화하는 (0, 1)-배낭문제에 대한 절단평면 생성방안

A Cut Generation Method for the (0, 1)-Knapsack Problem with a Variable Capacity

  • 이경식 (한국전자통신연구원 우정기술연구부) ;
  • 박성수 (한국과학기술원 산업공학과)
  • 발행 : 2000.09.01

초록

In this paper, we propose a practical cut generation method based on the Chvatal-Gomory procedure for the (0, 1)-Knapsack problem with a variable capacity. For a given set N of n items each of which has a positive integral weight and a facility of positive integral capacity, a feasible solution of the problem is defined as a subset S of N along with the number of facilities that can satisfy the sum of weights of all the items in S. We first derive a class of valid inequalities for the problem using Chvatal-Gomory procedure, then analyze the associated separation problem. Based on the results, we develop an affective cut generation method. We then analyze the theoretical strength of the inequalities which can be generated by the proposed cut generation method. Preliminary computational results are also presented which show the effectiveness of the proposed cut generation method.

키워드

참고문헌

  1. Mathematical Programming v.8 Facets of Knapsack Polytope Balas, E.
  2. SIAN Journal of Applied Mathematics v.34 Facets of the Knapsack Polytope from Minimal Covers Balas, E.;E. Zemel
  3. Using CPLEX callable Library Bixby, R. E.;E. Boyd
  4. CORE Discussion paper Designing Private Line Network0Poly-hedral Analysis and Computation Brockmuller, B.;O. Gunluk;L. A. Wolsey
  5. Mathematical Programming v.81 Cutting Planes for Integer Programs with General Integer Variables Ceria, S.;C. Cordier;H. Marchand;L. A. Wolsey
  6. Network and Discrete Location: Models, Algorithms, and Applications Daskin, M. S.
  7. Computers and Intractibility Garey, M. R.;D. S. Johnson
  8. Integer programming Garfinkel, R. S.;G. L. Nemhauser
  9. Computational Optimization and Applications v.8 Generating Cuts from Surrogate Constraint Analysis for Zero-One and Multiple Choice Programming Glover, F.;H. D. Sherali;Y. Lee
  10. Bulletin of American Mathematical Society v.64 Outline of an algorithm for integer solutions to linear programs Gomory, R. E.
  11. Combinatorial Analysis Solving linear programming problems in integers Gomory, R. E.;R. E. Bellman(ed.);M. Hall, Jr.(ed.)
  12. Recent Advances in Mathematical Programming An Algorithm for Integer Solutions to Linear Programs Gomory, R. E.
  13. Routing and Capacity Assignment Models and Algorithms for the Design of Telecommunication Networks Lee, K.
  14. US West Advanced Technologies Working paper A technology selection problem in designing multimedia broadband telecommunication networks under uncertainty Lee, Y.;H-. S. Oh
  15. Integer and Combinatorial Optimization Nemhauser, G. L.;L. A. Wolsey