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GENIIS, a New Hybrid Algorithm for Solving the Mixed Chinese Postman Problem

  • Published : 2008.09.30

Abstract

Mixed Chinese Postman Problem (MCPP) is a practical generalization of the classical Chinese Postman Problem (CPP) and it could be applied in many real world. Although MCPP is useful in terms of reality, MCPP has been proved to be a NP-complete problem. To find optimal solutions efficiently in MCPP, we can reduce searching space to be small effective searching space containing optimal solutions. We propose GENIIS methodology, which is a kind of hybrid algorithm combines the approximate algorithms and genetic algorithm. To get good solutions in the effective searching space, GENIIS uses approximate algorithm and genetic algorithm. This paper validates the usefulness of the proposed approach in a simulation. The results of our paper could be utilized to increase the efficiencies of network and transportation in business.

Keywords

References

  1. 조희연, "유전자 알고리즘을 이용한 주식투자 수익률 향상에 관한 연구", 정보시스템연구, 제12권, 제2호, 2003, pp. 10-28.
  2. 박송미, 채영신, "프로젝트 위험요인 인식에 관한 비교 연구", 정보시스템연구, 제16권, 제4호, 2007, pp. 243-268.
  3. Ahuja, R. K., Magnanti, T. L., and Orlin, J. B., Network Flows, Theory, Algorithms, and Applications, Prentice Hall, 1993.
  4. Ahr, D. and Reinelt, G., "A Tabu Search Algorithm for the Min Max k-Chinese Postman Problem," Computers & Operations Research, Vol. 3, No. 12, 2006, pp. 3403-3422.
  5. Ahr, D. and Reinelt, G., "New Heuristics and Lower Bounds for the Min Max k-Chinese Postman Problem," Lecture Notes in Computer Science, Vol. 2461, 2002, pp. 64-74.
  6. Benavent, E., A., Corberan, A., Sanchis, J. M., and Vigo, D., "Lower Bounds and Heuristics for the Windy Rural Postman Problem," European Journal of Operational Research, Vol. 176, No. 2, 2007, pp. 855-869. https://doi.org/10.1016/j.ejor.2005.09.021
  7. Christofides, N., Benavent, E., Campos, V., Corberan, A., and Mota, E., "An Optimal Method for the Mixed Postman Problem, System Modelling and Optimization," Lecture Notes in Control and Information Sciences, Vol. 59, 1984, pp. 641-649. https://doi.org/10.1007/BFb0008937
  8. Corberan, A., Plana, I., Reinelt, G., and Sanchis, J. M., "New Results on the Windy Postman Problem," 21st European Conference on Operational Research Technical Reports, 2007.
  9. Corberan, A., and Sanchis, J. M., "A GRASP for the Mixed Chinese Postman Problem," Technical Report, University of Valencia, 2000.
  10. Edmonds, J., "The Chinese's Postman Problem," Operation Research. Vol. 13:B-73, S.1, 1965. https://doi.org/10.1287/opre.13.1.1
  11. Edmonds, J., and Johnson, E. L., "Matching, Euler Tours and the Chinese Postman," Mathematical Programming, Vol. 5, 1973, pp. 88-124. https://doi.org/10.1007/BF01580113
  12. Frederickson, G. N., "Approximation Algorithms for Some Postman Problems," Journal of the ACM, Vol. 26, No. 3, 1979, pp. 538-554. https://doi.org/10.1145/322139.322150
  13. Ghiani, G., and Laporte, G., "A Branch and Cut Algorithm for the Undirected Rural Postman Problem," Mathematical Programming, Vol. 87, No. 3, 2000, pp. 467-481. https://doi.org/10.1007/s101070050007
  14. Guan, M., "Graphic Programming Using Odd and Even Points," Chinese Mathematics, Vol. 1, 1962, pp. 273-277.
  15. Grotschel, M., and Win, Z., "A Cutting Plane Algorithm for the Windy Postman Problem," Mathematical Programming, Vol. 55, No. 3, 1992, pp. 339-358. https://doi.org/10.1007/BF01581206
  16. Jun, ByungHyun and Han, ChiGeun, "Solving the Chinese Postman Problem on Mixed Networks Using an Efficient Genetic Algorithm," Proceeding of the 1st Korea-Japan Joint Conference on Industrial Engineering and Management, 1998, pp. 121-124.
  17. Laporte, G., "Modelling and Solving Several Classes of Arc Routing Problems As Travelling Salesman Problems," Computers & Operations Research, Vol. 24, No. 11, 1997, pp. 1057-1061. https://doi.org/10.1016/S0305-0548(97)00013-0
  18. Papadimitriou, C. H., "On the Complexity of Edge Traversing," Journal of the ACM, Vol. 23, No. 3, 1976, pp. 544-554. https://doi.org/10.1145/321958.321974
  19. Raghavachary, B., and Veerasamy, J., "Approximation Algorithms for the Mixed Chinese Postman Problem," Lecture Notes in Computer Science, Vol. 1414, 1998, pp. 169-179.
  20. Schrijver, A., A Course in Combinatorial Optimization Lecture, 2007.
  21. Zaragoza, F. J., Postman Problems on Mixed Graphs, Thesis, 2003.