Journal of the Korean Operations Research and Management Science Society (한국경영과학회지)

The Korean Operations Research and Management Science Society (한국경영과학회)
권호 표지
DOI QR코드

DOI QR Code

A Study on the Bi-level Genetic Algorithm for the Fixed Charge Transportation Problem with Non-linear Unit Cost

고정비용과 비선형 단위운송비용을 가지는 수송문제를 위한 이단유전알고리즘에 관한 연구

  • Sung, Kiseok (Industrial and Management Engineering, Gangneung-Wonju National University)
  • 성기석 (강릉원주대학교 산업경영공학과)
  • Received : 2016.08.22
  • Accepted : 2016.11.10
  • Published : 2016.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper proposes a Bi-level Genetic Algorithm for the Fixed Charge Transportation Problem with Non-linear Unit Cost. The problem has the property of mixed integer program with non-linear objective function and linear constraints. The bi-level procedure consists of the upper-GA and the lower-GA. While the upper-GA optimize the connectivity between each supply and demand pair, the lower-GA optimize the amount of transportation between the pairs set to be connected by the upper-GA. In the upper-GA, the feasibility of the connectivity are verified, and if a connectivity is not feasible, it is modified so as to be feasible. In the lower-GA, a simple method is used to obtain a pivot feasible solution under the restriction of the connectivity determined by the upper-GA. The obtained pivot feasible solution is utilized to generate the initial generation of chromosomes. The computational experiment is performed on the selected problems with several non-linear objective functions. The performance of the proposed procedure is analyzed with the result of experiment.

Keywords

References

  1. 성기석, "고정비용과 비선형 단위비용을 가지는 최소비용흐름문제를 위한 유전알고리즘", 한국경영과학회 추계학술대회, 이화여자대학교, 2013.
  2. 성기석, "유전알고리즘에서 선형제약식을 다루는 방법", 한국경영과학회지, 제7권, 제4호(2012), pp.67-72.
  3. Gen, M., A. Kumar, and J.R. Kim, "Recent network design techniques using evolutionary algorithms," Int. J. Production Economics, Vol.98, No.2(2005), pp.251-261. https://doi.org/10.1016/j.ijpe.2004.05.026
  4. Hitchcock, F.L., "The distribution of a product from several sources to numerous localities," Journal of Mathematical Physics, Vol.20, No.1-4(1941), pp.224-230. https://doi.org/10.1002/sapm1941201224
  5. Jo, J.-B., Y. Li, and M. Gen, "Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm," Computers and Industrial Engineering, Vol.53, No.2 (2007), pp.290-298. https://doi.org/10.1016/j.cie.2007.06.022
  6. Munakata, T. and D.J. Hashier, "A Genetic Algorithm Applied to the Maximum Flow Problem," The Fifth International Conference on Genetic Algorithms, Urbana-Champaign, IL, July(1993), pp.488-493.
  7. Nesa, I. and P. Slobodan, "An Evolution Program for Non-Linear Transportation Problems," Journal of Heuristics, Vol.7(2001), pp.145-168. https://doi.org/10.1023/A:1009609820093
  8. Xie, F. and R. Jia, "Nonlinear fixed charge transportation problem by minimum cost flowbased genetic algorithm," Computers and Industrial Engineering, Vol.63, No.4(2012), pp.763-778. https://doi.org/10.1016/j.cie.2012.04.016