한국컴퓨터정보학회논문지 (Journal of the Korea Society of Computer and Information)

  • 제20권9호
  • /
  • Pages.21-29
  • /
  • 2015
  • /
  • 1598-849X(pISSN)
  • /
  • 2383-9945(eISSN)
한국컴퓨터정보학회 (Korean Society of Computer Information)
권호 표지
DOI QR코드

DOI QR Code

An Integer Programming-based Local Search for the Set Partitioning Problem

  • Hwang, Junha (Dept. of Computer Engineering, Kumoh National Institute of Technology)
  • 투고 : 2015.07.14
  • 심사 : 2015.08.26
  • 발행 : 2015.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

  1. R.E. Marsten, "An Algorithm for Large Set Partitioning Problem," Management Science, Vol. 20, No. 5, pp.774-787, Jan. 1974. https://doi.org/10.1287/mnsc.20.5.774
  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. https://doi.org/10.1287/mnsc.39.6.657
  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. https://doi.org/10.1023/A:1008668508685
  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. https://doi.org/10.7903/ijecs.1138
  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. https://doi.org/10.9708/jksci.2012.17.6.013
  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. https://doi.org/10.9708/jksci.2014.19.10.013
  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. https://doi.org/10.1287/trsc.1120.0441
  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. https://doi.org/10.1057/jors.1990.166