DOI QR코드

DOI QR Code

Uncertain Programming Model for Chinese Postman Problem with Uncertain Weights

  • Zhang, Bo ;
  • Peng, Jin
  • Received : 2011.12.02
  • Accepted : 2012.02.17
  • Published : 2012.03.01

Abstract

IChinese postman problem is one of the classical combinatorial optimization problems with many applications. However, in application, some uncertain factors are frequently encountered. This paper employs uncertain programming to deal with Chinese postman problem with uncertain weight Within the framework of uncertainty theory, the concepts of expected shortest route, ${\alpha}$-shortest route, and distribution shortest route are proposed. After that, expected shortest model, and ${\alpha}$-shortest model are constructed. Taking advantage of properties of uncertainty theory, these models can be transf-ormed into their corresponding deterministic forms, which can be solved by classical algorithm..

Keywords

Chinese Postman Problem;Uncertainty Theory;Uncertain Programming

References

  1. Bhattacharyya, R., Chatterjee, A., and Kar, S. (2010), Uncertainty theory based novel multi-objective optimization technique using embedding theorem with application to R&D project portfolio selection, Applied Mathematics, 1, 189-199. https://doi.org/10.4236/am.2010.13023
  2. Chen, X. and Liu, B. (2010), Existence and uniqueness theorem for uncertain differential equations, Fuzzy Optimization and Decision Making, 9, 69-81. https://doi.org/10.1007/s10700-010-9073-2
  3. Edmonds, J. and Johnson, E. L. (1973), Matching, Euler tours and the Chinese postman, Mathematical Programming, 5, 88-124. https://doi.org/10.1007/BF01580113
  4. Gao, X., Gao, Y., and Ralescu, D. A. (2010), On Liu's inference rule for uncertain systems, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 18, 1-11. https://doi.org/10.1142/S0218488510006349
  5. Gao, Y. (2011), Shortest path problem with uncertain arc lengths, Computers and Mathematics with Applications, 62, 2591-2600. https://doi.org/10.1016/j.camwa.2011.07.058
  6. Huang, X. X. (2011), Mean-risk model for uncertain portfolio selection, Fuzzy Optimization and Decision Making, 10, 71-89. https://doi.org/10.1007/s10700-010-9094-x
  7. Kuan, M. K. (1962), Graphic programming using odd or even points, Chinese Mathematics, 1, 273-277.
  8. Lin, Y. X. and Zhao, Y. C. (1988), A new algorithm for the directed Chinese postman problem, Computers and Operations Research, 15, 577-584. https://doi.org/10.1016/0305-0548(88)90053-6
  9. Liu, B. (2007), Uncertainty Theory, 2nd ed., Springer-Verlag, Berlin.
  10. Liu, B. (2008), Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems, 2, 3-16.
  11. Liu, B. (2009a), Some research problems in uncertainty theory, Journal of Uncertain Systems, 3, 3-10.
  12. Liu, B. (2009b), Theory and Practice of Uncertain Programming, 2nd ed., Springer-Verlag, Berlin.
  13. Liu, B. (2010a), Uncertain set theory and uncertain inference rule with application to uncertain control, Journal of Uncertain Systems, 4, 83-98.
  14. Liu, B. (2010b), Uncertain risk analysis and uncertain reliability analysis, Journal of Uncertain Systems, 4, 163-170.
  15. Liu, B. (2010c), Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Berlin.
  16. Liu, B. (2012), Why is there a need for uncertainty theory? Journal of Uncertain Systems, 6, 3-10.
  17. Liu, Y. H. and Ha, M. H. (2010), Expected value of function of uncertain variables, Journal of Uncertain Systems 4,181-186.
  18. Minieka, E. (1979), The Chinese postman problem for mixed networks, Management Science, 25, 643-648. https://doi.org/10.1287/mnsc.25.7.643
  19. Nobert, Y. and Picard, J. C. (1996), An optimal algorithm for the mixed Chinese postman problem, Networks, 27, 95-108.
  20. Pearn, W. L. and Chou, J. B. (1999), Improved solutions for the Chinese postman problem on mixed networks, Computers and Operations Research, 26, 819-827. https://doi.org/10.1016/S0305-0548(98)00092-6
  21. Peng, J. and Yao, K. (2011), A new option pricing model for stocks in uncertainty markets, International Journal of Operations Research, 8, 18-26.
  22. Rong, L. X. (2011), Two new uncertainty programming models of inventory with uncertain costs, Journal of Information and Computational Science, 8, 280-288.
  23. Zhu, Y. (2010), Uncertain optimal control with application to a portfolio selection model, Cybernetics and Systems, 41, 535-547. https://doi.org/10.1080/01969722.2010.511552

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