A primer in column generation

Column Generation

Volumn , Issue , 2005, Pages 1-32

  Desrosiers, Jacques ^a   Lübbecke, Marco E ^b  

^a GERAD   (Canada)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84889960231     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/0-387-25486-2_1     Document Type: Chapter

References (35)

1. Ahuja, R.K., Magnanti, T.L., and Orlin, J.B. (1993). Network Flows: Theory, Algorithms and Applications. Prentice-Hall, Inc., Englewood Cliffs, New Jersey.
2. Barnhart, C, Johnson, E.L., Nemhauser, G.L., Savelsbergh, M.W.P., and Vance, P.H. (1998). Branch-and-price: Column generation for solving huge integer programs. Operations Research, 46(3):316-329.
3. Ben Amor, H. and Desrosiers, J. (2003). A proximal trust region algorithm for column generation stabilization. Les Cahiers du GERAD G-2003-43, HEC, Montreal, Canada. Forthcoming in: Computers & Operations Research.
4. Ben Amor, H., Desrosiers, J., and Valério de Carvalho, J.M. (2003). Dual-optimal inequalities for stabilized column generation. Les 30
5. Ben Amor, H. and Valério de Carvalho, J.M. (2004). Cutting stock problems. In this book.
6. Dantzig, G.B. and Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8:101-111.
7. Desaulniers, G., Desrosiers, J., Ioachim, I., Solomon, M.M., Soumis, F., and Villeneuve, D. (1998). A unified framework for deterministic time constrained vehicle routing and crew scheduling problems. In: Fleet Management and Logistics (T.G. Crainic and G. Laporte, eds.), pp. 57-93, Kluwer, Norwell, MA.
8. Desaulniers, G., Desrosiers, J., and Solomon, M.M. (2001). Accelerating strategies in column generation methods for vehicle routing and crew scheduling problems. In: Essays and Surveys in Metaheuristics (C.C. Ribeiro and P. Hansen, eds.), pp. 309-324, Kluwer, Boston.
9. du Merle, O., Villeneuve, D., Desrosiers, J., and Hansen, P. (1999). Stabilized column generation. Discrete Mathematics, 194:229-237.
10. Elhallaoui, L, Villeneuve, D., Soumis, F., and Desaulniers, G. (2003). Dynamic aggregation of set partitioning constraints in column generation. Les Cahiers du GERAD G-2003-45, HEC, Montréal, Canada. Forthcoming in: Operations Research.
11. Ford, L.R. and Fulkerson, D.R. (1958). A suggested computation for maximal multicommodity network flows. Management Science, 5:97-101.
12. Geoffrion, A.M. (1974). Lagrangean relaxation for integer programming. Mathematical Programming Study (Series), 2:82-114.
13. Gilmore, P.C. and Gomory, R.E. (1961). A linear programming approach to the cutting-stock problem. Operations Research, 9:849-859.
14. Gilmore, P.C. and Gomory, R.E. (1963). A linear programming approach to the cutting stock problem. Part II. Operations Research, 11:863-888.
15. Goffin, J.-L. and Vial, J,-Ph. (1999). Convex nondifferentiable optimization: A survey focused on the analytic center cutting' plane method. Technical Report 99.02, Logilab, Université de Genève. Forthcoming in: Optimization Methods & Software.
16. Guignard, M. (2004). Lagrangean relaxation. In: Handbook of Applied Optimization (M. Resende and P. Pardalos, eds.), Oxford University Press.
17. Hiriart-Urruty, J.-B. and Lemaréchal, C. (1993). Convex Analysis and Minimization Algorithms, Part 2: Advanced Theory and Bundle Methods, volume 306, Grundlehren der mathematischen Wissenschaften, Springer, Berlin.
18. Kantorovich, L. (1960). Mathematical methods of organising and planning production. Management Science, 6:366-422.
19. Kelley Jr., J.E. (1961). The cutting-plane method for solving convex programs. Journal of the Society for Industrial and Applied Mathematics, 8(4):703-712.
20. Lasdon, L.S. (1970). Optimization Theory for Large Systems. Macmillan, London.
21. Lübbecke, M.E. and Desrosiers, J. (2002). Selected topics in column generation. Les Cahiers du GERAD G-2002-64, HEC, Montréal, Canada. Forthcoming in: Operations Research.
22. Nemhauser, G.L. and Wolsey, L.A. (1988). Integer and Combinatorial Optimization. John Wiley & Sons, Chichester.
23. Mamer, J.W. and McBride, R.D. (2000). A decomposition-based pricing procedure for large-scale linear programs-An application to the linear multicommodity flow problem. Management Science, 46(5):693-709.
24. Marsten, R.E. (1975). The use of the boxstep method in discrete optimization. Mathematical Programming Study, 3:127-144.
25. Marsten, R.E., Hogan, W.W., and Blankenship, J.W. (1975). The BOXSTEP method for large-scale optimization. Operations Research, 23:389-405.
26. Poggi de Aragâo, M. and Uchoa, E. (2003). Integer program reformulation for robust branch-and-cut-and-price algorithms. In: Proceedings of the Conference Mathematical Program in Rio: A Conference in Honor of Nelson Maculan, pp. 56-61.
27. Schrijver, A. (1986). Theory of Linear and Integer Programming. John Wiley & Sons, Chichester.
28. Valério de Carvalho, J.M. (1999). Exact solution of bin-packing problems using column generation and branch-and-bound. Annals of Operations Research, 86:629-659.
29. Valério de Carvalho, J.M. (2002). LP models for bin-packing and cutting stock problems. European Journal of Operational Research, 141(2):253-273.
30. Valério de Carvalho, J.M. (2003). Using extra dual cuts to accelerate convergence in column generation. Forthcoming in: INFORMS Journal of Computing.
31. Vanderbeck, F. (2000). On Dantzig-Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm. Operations Research, 48(1):111-128.
32. Vanderbeck, F. (2004). Implementing mixed integer column generation. In this book.
33. Vanderbeck, F. and Wolsey, L.A. (1996). An exact algorithm for IP column generation. Operations Research Letters, 19:151-159.
34. Villeneuve, D., Desrosiers, J., Lübbecke, M.E., and Soumis, F. (2003). On compact formulations for integer programs solved by column generation. Les Cahiers du GERAD G-2003-06, HEC, Montréal, Canada. Forthcoming in: Annals of Operations Research.
35. Walker, W.E. (1969). A method for obtaining the optimal dual solution to a linear program using the Dantzig-Wolfe decomposition. Operations Research, 17:368-370.