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An Integer Programming-based Local Search for the Set Partitioning Problem
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 Title & Authors
An Integer Programming-based Local Search for the Set Partitioning Problem
Hwang, Junha;
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 Abstract
The set partitioning problem is a well-known NP-hard combinatorial optimization problem, and it is formulated as an integer programming model. This paper proposes an Integer Programming-based Local Search for solving the set partitioning problem. The key point is to solve the set partitioning problem as the set covering problem. First, an initial solution is generated by a simple heuristic for the set covering problem, and then the solution is set as the current solution. Next, the following process is repeated. The original set covering problem is reduced based on the current solution, and the reduced problem is solved by Integer Programming which includes a specific element in the objective function to derive the solution for the set partitioning problem. Experimental results on a set of OR-Library instances show that the proposed algorithm outperforms pure integer programming as well as the existing heuristic algorithms both in solution quality and time.
 Keywords
Set partitioning problem;Set covering problem;Integer programming-based local search;
 Language
Korean
 Cited by
 References
1.
R.E. Marsten, "An Algorithm for Large Set Partitioning Problem," Management Science, Vol. 20, No. 5, pp.774-787, Jan. 1974. crossref(new window)

2.
K.L. Hoffman, and M. Padberg, "Solving Airline Crew Scheduling Problems by Branch-and-cut," Management Science, Vol. 39, No. 6, pp.657-682, June 1993. crossref(new window)

3.
D. Bredstrom, K. Jornsten, M. Ronnqvist, and M. Bouchard, "Searching for Optimal Integer Solutions to Set Partitioning Problems using Column Generation," International Transactions in Operational Research, Vol. 21, No. 2, pp.117-197, March 2014.

4.
P.C. Chu, and J.E. Beasley, "Constraint Handling in Genetic Algorithms: The Set Partitioning Problem," Journal of Heuristics, Vol. 4, No. 4, pp.323-357, Dec. 1998. crossref(new window)

5.
B. Crawford, R. Soto, E. Monfroy, et al., "A Hybrid Soft Computing Approach for Subset Problems," Mathematical Problems in Engineering, Vol. 2013, Article ID 716069, 12 pages, June 2013.

6.
C.A. Lin, "Generational Model Genetic Algorithm for Real World Set Partitioning Problems," International Journal of Electronic Commerce Studies, Vol. 4, No. 1, pp.33-46, June 2013. crossref(new window)

7.
J. Hwang, "Integer Programming-based Local Search Techniques for the Multidimensional Knapsack Problem", Journal of The Korea Society of Computer and Information, Vol. 17, No. 6, pp. 13-27, June 2012.

8.
J. Hwang, "An Integer Programming-based Local Search for the Set Covering Problem", Journal of The Korea Society of Computer and Information, Vol. 19, No. 10, pp. 13-21, Oct. 2014. crossref(new window)

9.
A. Erera, M. Hewitt, M. Savelsbergh, and Y. Zhang, "Improved Load Plan Design Through Integer Programming Based Local Search," Transportation Science, Vol. 47, No. 3, pp.412-427, Nov. 2012.

10.
K. Genova, and V. Guliashki, "Linear Integer Programming Methods and Approaches-A Survey," Cybernetics And Information Technologies, Vol. 11, No. 1, pp.3-25, 2011.

11.
J. E. Beasley, "OR-Library: Distributing Test Problems by Electronic Mail," The Journal of the Operational Research Society, Vol. 41, No. 11, pp. 1069-1072, 1990. crossref(new window)