A computational study of exact knapsack separation for the generalized assignment problem

Computational Optimization and Applications

Volumn 45, Issue 3, 2010, Pages 543-555

  Avella, Pasquale ^a   Boccia, Maurizio ^a   Vasilyev, Igor ^b  

^a UNIVERSITY OF SANNIO   (Italy)

^b MATROSOV INSTITUTE FOR SYSTEM DYNAMICS AND CONTROL THEORY   (Russian Federation)

Author keywords

Cutting plane algorithm; Exact separation; Generalized assignment problem

Indexed keywords

BASIC FORMULATION; BRANCH AND PRICE; CAPACITY CONSTRAINTS; COLUMN GENERATION; COMBINATORIAL OPTIMIZATION PROBLEMS; COMPUTATIONAL STUDIES; CUTTING PLANE ALGORITHM; CUTTING PLANE ALGORITHMS; EFFICIENT IMPLEMENTATION; GENERALIZED ASSIGNMENT PROBLEM; LOWER BOUNDS; NP-HARD; OPTIMALITY; POLYTOPES;

ALGORITHMS; COMBINATORIAL OPTIMIZATION; TOPOLOGY; TRAVELING SALESMAN PROBLEM;

COMPUTATIONAL EFFICIENCY;

EID: 77950520026     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-008-9183-8     Document Type: Article

References (26)

1. Y. Asahiro M. Ishibashi M. Yamashita 2003 Independent and cooperative parallel search methods for the generalized assignment problem Optim. Methods Softw. 18 2 129 141 1070.90066 10.1080/1055678031000107105 1996584
2. J.E. Beasley 1990 Or-library: distributing test problems by electronic mail J. Oper. Res. Soc. 41 11 1069 1072
3. Bonami, M.P.: Étude et mise en oeuvre d'approches polyédriques pour la résolution de programmes en nombres entiers ou mixtes généraux. Ph.D. thesis, L'Université Paris 6 (2003)
4. E.A. Boyd 1993 Generating Fenchel cutting planes for knapsack polyhedra SIAM J. Optim. 3 734 750 0797.90067 10.1137/0803038 1244050
5. Boyd, E.A.: Solving integer programs with cutting planes and preprocessing. In: IPCO 1993, pp. 209-220 (1993)
6. E.A. Boyd 1994 Fenchel cutting planes for integer programming Oper. Res. 42 53 64 0809.90104 10.1287/opre.42.1.53 1261374
7. E.A. Boyd 1995 On the convergence of Fenchel cutting planes in mixed-integer programming SIAM J. Optim. 5 421 435 0834.90095 10.1137/0805021 1330204
8. A. Ceselli G. Righini 2004 A branch and price algorithm for the capacitated p-median problem Networks 45 3 125 142 10.1002/net.20059 2128805
9. P.C. Chu J.E. Beasley 1997 A genetic algorithm for the generalised assignment problem Comput. Oper. Res. 24 17 23 0881.90070 10.1016/S0305-0548(96) 00032-9 1429237 (Pubitemid 127417484)
10. G. Cornuejols C. Lemarechal 2006 A convex-analysis perspective on disjunctive cuts Math. Program. 106 3 567 586 1149.90175 10.1007/s10107-005- 0670-8 2216796 (Pubitemid 43296489)
11. I.R. De Farias G.L. Nemhauser 2001 A family of inequalities for the generalized assignment polytope Oper. Res. Lett. 29 49 51 0981.90050 10.1016/S0167-6377(01)00086-4 1852876 (Pubitemid 32775921)
12. Fukasawa, R., Goycoolea, M.: On the exact separation of mixed integer knapsack cuts. In: Proceedings of the twelfth Integer Programming and Combinatorial Optimization Conference IPCO'07, Ithaca, NY. Lecture Notes in Computer Science, vol. 4513, pp. 225-239 (2007)
13. E.S. Gottlieb M.R. Rao 1990 The generalized assignment problem: Valid inequalities and facets Math. Program. 46 31 52 0694.90071 10.1007/BF01585725 1045569 (Pubitemid 20669520)
14. E.S. Gottlieb M.R. Rao 1990 (1,k)-configuration facets for the generalized assignment problem Math. Program. 46 53 60 0701.90065 10.1007/BF01585726 1045570 (Pubitemid 20669521)
15. Kaparis, K., Letchford, A.N.: Separation algorithms for 0-1 knapsack polytopes. Working paper. Department of Management Science, Lancaster University (2008). Available at http://www.optimization-online.org/DB-HTML/2007/06/1677. html (2007, in preparation)
16. M. Laguna J.P. Kelly J.L. Conzalez-Velarde F.F. Glover 1995 Tabu search for the generalized assignment problem Eur. J. Oper. Res. 82 176 189 0905.90122 10.1016/0377-2217(93)E0174-V
17. R.M. Nauss 2003 Solving the generalized assignment problem: An optimizing and heuristic approach INFORMS J. Comput. 15 3 249 266 10.1287/ijoc.15.3.249. 16075 1996314 (Pubitemid 39042720)
18. I.H. Osman 1995 Heuristics for the generalized assignment problem: Simulated annealing and tabu search approaches OR Spektrum 17 211 225 0841.90098 10.1007/BF01720977
19. M.W. Padberg 1973 On the facial structure of set packing polyhedra Math. Program. 5 199 215 0272.90041 10.1007/BF01580121 368749
20. Pigatti, A., Poggi de Aragao, M., Uchoa, E.: Stabilized branch-and-cut-and-price for the generalized assignment problem. In: 2nd Brazilian Symposium on Graphs, Algorithms and Combinatorics. Electronic Notes in Discrete Mathematics, vol. 19, pp. 389-395. Elsevier, Amsterdam (2005)
21. D. Pisinger 1995 A minimal algorithm for the 0-1 knapsack problem Oper. Res. 46 758 767 1660413 (Pubitemid 127684747)
22. M. Savelsbergh 1997 A branch-and-price algorithm for the generalized assignment problem Oper. Res. 45 6 831 841 0895.90161 10.1287/opre.45.6.831 1605323 (Pubitemid 127684765)
23. L.A. Wolsey 1976 Facets and strong valid inequalities for integer programs Oper. Res. 24 367 372 0339.90036 10.1287/opre.24.2.367 421669
24. M. Yagiura T. Ibaraki F. Glover 2004 An ejection chain approach for the generalized assignment problem INFORMS J. Comput. 16 133 151 10.1287/ijoc.1030.0036 2065994 (Pubitemid 39043199)
25. M. Yagiura T. Ibaraki F. Glover 2006 A path relinking approach with ejection chains for the generalized assignment problem Eur. J. Oper. Res. 169 548 569 1079.90119 10.1016/j.ejor.2004.08.015 2172359 (Pubitemid 41375707)
26. M. Yagiura T. Yamaguchi T. Ibaraki 1998 A variable depth search algorithm with branching search for the generalized assignment problem Optim. Methods Softw. 10 419 441 0947.90070 10.1080/10556789808805722 1754749 (Pubitemid 129619830)