Dual Inequalities for Stabilized Column Generation Revisited

Published Online:https://doi.org/10.1287/ijoc.2015.0670

References

  • Alves C, Valério de Carvalho JM (2008) A stabilized branch-and-price-and-cut algorithm for the multiple length cutting stock problem. Comp. Oper. Res. 35(4):1315–1328.CrossrefGoogle Scholar
  • Alves C, Valério de Carvalho J, Clautiaux F, Rietz J (2014) Multidimensional dual-feasible functions and fast lower bounds for the vector packing problem. Eur. J. Oper. Res. 233(1):43–63.CrossrefGoogle Scholar
  • Balas E, Padberg MW (1976) Set partitioning: A survey. SIAM Rev. 18(4):710–760.CrossrefGoogle Scholar
  • Balas E, Xue J (1991) Minimum weighted coloring of triangulated graphs, with application to maximum weight vertex packing and clique finding in arbitrary graphs. SIAM J. Comput. 20(2):209–221.CrossrefGoogle Scholar
  • Balinski ML (1965) Integer programming: Methods, uses, computation. Management Sci. 12(3):253–313.LinkGoogle Scholar
  • Barnhart C, Johnson EL, Nemhauser GL, Savelsbergh MWP, Vance PH (1998) Branch-and-price: Column generation for solving huge integer programs. Oper. Res. 46(3):316–329.LinkGoogle Scholar
  • Ben Amor H, Desrosiers J, Valério de Carvalho JM (2006) Dual-optimal inequalities for stabilized column generation. Oper. Res. 54(3):454–463.LinkGoogle Scholar
  • Ben Amor H, Valério de Carvalho J (2005) Cutting stock problems. Desaulniers G, Desrosiers J, Solomon M, eds. Column Generation (Springer, New York), 131–161.CrossrefGoogle Scholar
  • Bettinelli A, Cacchiani V, Malaguti E (2014) Bounds and algorithms for the knapsack problem with conflict graph. Technical Report OR-14-16, DEIS—University of Bologna, Bologna, Italy.Google Scholar
  • Bianchessi N, Archetti C, Speranza MG (2014) An exact solution approach for the split commodities mixed routing problem. Presentation, VeRoLog Conference Oslo, Norway.Google Scholar
  • Bode C, Irnich S (2012) Cut-first branch-and-price-second for the capacitated arc-routing problem. Oper. Res. 60(5):1167–1182.LinkGoogle Scholar
  • Caprara A, Toth P (2001) Lower bounds and algorithms for the 2-dimensional vector packing problem. Disc. Appl. Math. 111(3):231–262.CrossrefGoogle Scholar
  • Caprara A, Furini F, Malaguti E (2013) Uncommon Dantzig-Wolfe reformulation for the temporal knapsack problem. INFORMS J. Comput. 25(3):560–571.LinkGoogle Scholar
  • Carraghan R, Pardalos PM (1990) An exact algorithm for the maximum clique problem. Oper. Res. Lett. 9(6):375–382.CrossrefGoogle Scholar
  • Dantzig GB, Wolfe P (1960) Decomposition principle for linear programs. Oper. Res. 8(1):101–111.LinkGoogle Scholar
  • Desaulniers G, Desrosiers J, Ioachim I, Solomon M, Soumis F, Villeneuve D (1998) A unified framework for deterministic time constrained vehicle routing and crew scheduling problems. Crainic T, Laporte G, eds. Fleet Management and Logistics (Kluwer Academic Publisher, Boston), 57–93.CrossrefGoogle Scholar
  • Desrosiers J, Gauthier JB, Lübbecke ME (2014) Row-reduced column generation for degenerate master problems. Eur. J. Oper. Res. 236(2):453–460.CrossrefGoogle Scholar
  • du Merle O, Villeneuve D, Desrosiers J, Hansen P (1999) Stabilized column generation. Disc. Math. 194(1–3):229–237.CrossrefGoogle Scholar
  • Fernandes Muritiba AE, Iori M, Malaguti E, Toth P (2010) Algorithms for the bin packing problem with conflicts. INFORMS J. Comput. 22(3):401–415.LinkGoogle Scholar
  • Fréville A (2004) The multidimensional 0-1 knapsack problem: An overview. Eur. J. Oper. Res. 155(1):1–21.CrossrefGoogle Scholar
  • Garfinkel RS, Nemhauser GL (1969) The set-partitioning problem: Set covering with equality constraints. Oper. Res. 17(5):848–856.LinkGoogle Scholar
  • Gauthier JB, Desrosiers J, Lübbecke ME (2015) Tools for primal degenerate linear programs: IPS, DCA, and PE. EURO J. Transportation Logist., ePub ahead of print March 27, http://dx.doi.org/10.1007/s13676-015-0077-5.Google Scholar
  • Gilmore PC, Gomory RE (1961) A linear programming approach to the cutting-stock problem. Oper. Res. 9(6):849–859.LinkGoogle Scholar
  • Gilmore PC, Gomory RE (1963) A linear programming approach to the cutting stock problem—Part II. Oper. Res. 11(6):863–888.LinkGoogle Scholar
  • Gschwind T, Irnich S (2014) Stabilized column generation for the temporal knapsack problem using dual-optimal inequalities. Technical Report LM-2014-06, Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, Mainz, Germany.Google Scholar
  • Gualandi S, Chiarandini M (2014) Graph coloring benchmarks. Accessed January 25, 2016, https://sites.google.com/site/graphcoloring/home.Google Scholar
  • Gualandi S, Malucelli F (2012) Exact solution of graph coloring problems via constraint programming and column generation. INFORMS J. Comput. 24(1):81–100.LinkGoogle Scholar
  • Held S, Cook W, Sewell EC (2012) Maximum-weight stable sets and safe lower bounds for graph coloring. Math. Programming Comput. 4(4):363–381.CrossrefGoogle Scholar
  • Hifi M, Michrafy M (2007) Reduction strategies and exact algorithms for the disjunctively constrained knapsack problem. Comp. Oper. Res. 34(9):2657–2673.CrossrefGoogle Scholar
  • Hiriart-Urruty J-B, Lemaréchal C (1993) Convex Analysis and Minimization Algorithms, Part 2: Advanced Theory and Bundle Methods, Grundlehren der Mathematischen Wissenschaften, Vol. 306 (Springer, Berlin).Google Scholar
  • Irnich S, Desaulniers G (2005) Shortest path problems with resource constraints. Desaulniers G, Desrosiers J, Solomon M, eds. Column Generation (Springer, New York), 33–65.CrossrefGoogle Scholar
  • Kellerer H, Pferschy U, Pisinger D (2004) Knapsack Problems (Springer, Berlin).CrossrefGoogle Scholar
  • Lee C, Park S (2011) Chebyshev center based column generation. Disc. Appl. Math. 159(18):2251–2265.CrossrefGoogle Scholar
  • Lübbecke ME, Desrosiers J (2005) Selected topics in column generation. Oper. Res. 53(6):1007–1023.LinkGoogle Scholar
  • Malaguti E, Monaci M, Toth P (2011) An exact approach for the vertex coloring problem. Disc. Opt. 8(2):174–190.CrossrefGoogle Scholar
  • Marsten RE, Hogan WW, Blankenship JW (1975) The Boxstep method for large-scale optimization. Oper. Res. 23(3):389–405.LinkGoogle Scholar
  • Martello S, Toth P (1990) Knapsack Problems: Algorithms and Computer Implementations, Wiley Intersience Series in Discrete Mathematics and Optimization (Wiley, New York).Google Scholar
  • Mehrotra A, Trick MA (1996) A column generation approach for graph coloring. INFORMS J. Comput. 8(4):344–354.LinkGoogle Scholar
  • Méndez-Díaz I, Zabala P (2006) A branch-and-cut algorithm for graph coloring. Disc. Appl. Math. 154(5):826–847.CrossrefGoogle Scholar
  • Östergård PRJ (2002) A fast algorithm for the maximum clique problem. Disc. Appl. Math. 120(1–3):197–207.CrossrefGoogle Scholar
  • Ozden M (1988) A solution procedure for general knapsack problems with a few constraints. Comp. Oper. Res. 15(2):145–155.CrossrefGoogle Scholar
  • Pattillo J, Youssef N, Butenko S (2013) On clique relaxation models in network analysis. Eur. J. Oper. Res. 226(1):9–18.CrossrefGoogle Scholar
  • Pferschy U, Schauer J (2009) The knapsack problem with conflict graphs. J. Graph Algorithms Appl. 13(2):233–249.CrossrefGoogle Scholar
  • Rousseau L-M, Gendreau M, Feillet D (2007) Interior point stabilization for column generation. Oper. Res. Lett. 35(5):660–668.CrossrefGoogle Scholar
  • Sadykov R, Vanderbeck F (2013) Bin packing with conflicts: A generic branch-and-price algorithm. INFORMS J. Comput. 25(2):244–255.LinkGoogle Scholar
  • Scholl A, Klein R, Jürgens C (1997) Bison: A fast hybrid procedure for exactly solving the one-dimensional bin packing problem. Comp. Oper. Res. 24(7):627–645.CrossrefGoogle Scholar
  • Sim K, Hart E (2013) Generating single and multiple cooperative heuristics for the one dimensional bin packing problem using a single node genetic programming island model. Proc. 15th Ann. Conf. Genetic Evolutionary Comput. (ACM, New York),1549–1556.CrossrefGoogle Scholar
  • Valério de Carvalho JM (1998) Exact solution of cutting stock problems using column generation and branch-and-bound. Internat. Trans. Oper. Res. 5(1):35–44.CrossrefGoogle Scholar
  • Valério de Carvalho JM (1999) Exact solution of bin-packing problems using column generation and branch-and-bound. Ann. Oper. Res. 86:629–659.CrossrefGoogle Scholar
  • Valério de Carvalho JM (2005) Using extra dual cuts to accelerate column generation. INFORMS J. Comput. 17(2):175–182.LinkGoogle Scholar
  • Vance P, Barnhart C, Johnson E, Nemhauser G (1994) Solving binary cutting stock problems by column generation and branch-and-bound. Comput. Optim. Appl. 3(2):111–130.CrossrefGoogle Scholar
  • Vanderbeck F (1999) Computational study of a column generation algorithm for bin packing and cutting stock problems. Math. Programming 86(3):565–594.CrossrefGoogle Scholar
  • Vanderbeck F (2000) On Dantzig-Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm. Oper. Res. 48(1):111–128.LinkGoogle Scholar
  • Vanderbeck F (2005) Implementing mixed integer column generation. Desaulniers G, Desrosiers J, Solomon M, eds. Column Generation (Springer, New York), 331–358.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.