An exact approach for the 0-1 knapsack problem with setups

Abstract We consider the 0–1 Knapsack Problem with Setups. We propose an exact approach which handles the structure of the ILP formulation of the problem. It relies on partitioning the variables set into two levels and exploiting this partitioning. The proposed approach favorably compares to the algorithms in literature and to solver CPLEX 12.5 applied to the ILP formulation. It turns out to be very effective and capable of solving to optimality, within limited CPU time, all instances with up to 100, 000 variables.

[1]  Hans Kellerer,et al.  Knapsack problems , 2004 .

[2]  Kurt M. Bretthauer,et al.  Exact and heuristic solution approaches for the mixed integer setup knapsack problem , 2008, Eur. J. Oper. Res..

[3]  Robert M. Nauss,et al.  An Efficient Algorithm for the 0-1 Knapsack Problem , 1976 .

[4]  Emmanuel D. Chajakis,et al.  Exact Algorithms For The Setup Knapsack Problem , 1994 .

[5]  Edward Y. H. Lin,et al.  A Bibliographical Survey On Some Well-Known Non-Standard Knapsack Problems , 1998 .

[6]  Fabio Guido Mario Salassa,et al.  Improved LP-based algorithms for the closest string problem , 2012, Comput. Oper. Res..

[7]  Umit Akinc.  Approximate and exact algorithms for the fixed-charge knapsack problem , 2006, Eur. J. Oper. Res..

[8]  Nancy Perrot,et al.  Knapsack problems with setups , 2009, Eur. J. Oper. Res..

[9]  J. Carlier.  The one-machine sequencing problem , 1982 .

[10]  Sheldon H. Jacobson,et al.  Algorithms for the bounded set-up knapsack problem , 2007, Discret. Optim..

[11]  Andrea Grosso,et al.  Simplex Algorithms for Linear Programming , 2013 .

[12]  Egon Balas,et al.  The Shifting Bottleneck Procedure for Job Shop Scheduling , 1988 .

[13]  Ellis Horowitz,et al.  Computing Partitions with Applications to the Knapsack Problem , 1974, JACM.

[14]  Marco Caserta,et al.  A cross entropy algorithm for the Knapsack problem with setups , 2008, Comput. Oper. Res..

[15]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[16]  Robert L. Bulfin,et al.  An exact algorithm for the Knapsack Problem with Setup , 2009 .

[17]  Paolo Toth,et al.  New trends in exact algorithms for the 0-1 knapsack problem , 2000, Eur. J. Oper. Res..

[18]  Mahdi Khemakhem,et al.  A dynamic programming algorithm for the Knapsack Problem with Setup , 2015, Comput. Oper. Res..