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Multiple Objective Path Optimization for Time Dependent Objective Functions

  • Michael M. Kostreva
  • Laura Lancaster
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 12)

Abstract

The study of time dependent, non-monotone increasing objective functions is interesting for several applications of multiple objective path optimization. In this paper an algorithm which finds the set of non-dominated paths is derived and shown to converge. This algorithm does not reduce to dynamic programming, even for constant cost functions.

Keywords

Cost Function Dynamic Programming Start Node Vector Cost Origin Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. 1.
    R. E. Bellman. Dynamic Programming, Princeton University Press, Princeton, N.J., (1957).Google Scholar
  2. 2.
    T. A. Brown AND R. E. Strauch. “Dynamic Programming in Multiplicative Lattices”, Journal of Mathematical Analysis and Application 12, 364–370, (1965).CrossRefGoogle Scholar
  3. 3.
    R. L. Carraway, T. L. Morn, AND H. Moskowrrz. “Generalized Dynamic Programming for Multicriteria Optimization”, European Journal of Operational Research 44, 95–104, (1990).CrossRefGoogle Scholar
  4. 4.
    K. L. CoonsAND E. Halsey. “The Shortest Route Through a Network with Time-Dependent Internodal Transit Times”, Journal of Mathematical Analysis and Applications 14, 493–498, (1966).CrossRefGoogle Scholar
  5. 5.
    H.W. Corley AND I. D. Moon. “Shortest Paths in Networks with Vector Weights”, Journal of Optimization Theory and Applications 46, 79–86, (1980).CrossRefGoogle Scholar
  6. 6.
    H. G. Daellenbach AND C. A. Dekluyver. “Note on Multiple Objective Ddynamic Programming”, Journal of the Operational Research Society 31, 591–594, (1980).Google Scholar
  7. 7.
    E. W. Dijkstra. “A Note on Two Problems in Connexion with Graphs”, Numerische Mathematik 1, 269–271, (1959).CrossRefGoogle Scholar
  8. 8.
    S. E. Dreyfus. “An Appraisal of Some Shortest-Path Algorithms”, Operations Research 17, 395–412, (1969).CrossRefGoogle Scholar
  9. 9.
    M. Emstermann. Time Dependency in Multiple Objective Dynamic Programming: The General Monotone Increasing Case, Masters Project, Department of Mathematical Sciences, Clemson University, S.C., USA, (1993).Google Scholar
  10. 10.
    T. Getachew. An Algorithm for Multiple-Objective Network Optimization with Time Variant Link-Costs, Ph.D. dissertation, Clemson, S.C., USA, (1992).Google Scholar
  11. 11.
    J. Halpern. “Shortest Route with Time Dependent Length of Edges and Limited Delay Possibilities in Nodes”, Zeitschrift für Operations Research 21, 117–124, (1977).Google Scholar
  12. 12.
    R. Hartley. “Vector Optimal Route by Dynamic Programming”, Mathematics ofMultiobjective Optimization, P. Serafini, Ed., 215–224, (1984).Google Scholar
  13. 13.
    T. Ibaraki. “Enumerative Approaches to Combinatorial Optimization — Part II”, Annals of Operations Research 11, 343–440, (1987).CrossRefGoogle Scholar
  14. 14.
    D. E. Kaufman AND R. L. Smith. “Minimum Travel Time Paths in Dynamic Networks with Application to Intelligent Vehicle-Highway Systems”, University of Michigan, Transportation Research Institute, IVHS Techniccal Report, 90–11, (1990).Google Scholar
  15. 15.
    D. E. Kaufman AND R. L. Smith. “Fastest Paths in Time-Dependent Networks for Intelligent Vehicle-Highway Systems Application”, IVHS Journal 1 (1), 1–11, (1993).Google Scholar
  16. 16.
    M. M. Kostreva AND M. M. Wiecek. “Time Dependency in Multiple Objective Dynamic Programming”, Journal of Mathematical Analysis and Applications 173, 289–307, (1993).CrossRefGoogle Scholar
  17. 17.
    D. Li AND Y. Y. Haimes. “Multiobjective Dynamic Programming: The state of the Art.”, Control Theory and Adv. Tech. 5, No. 4, 471–483, (1989).Google Scholar
  18. 18.
    S. P. Bradley, A. C. Hax, AND T. L. Magnati. Applied Mathematical Programming, Addison-Wesley Publishing Company, Reading, MA, (1977).Google Scholar
  19. 19.
    L. G. Mitten. “Preference Order Dynamic Programming”, Management Science 21, No. 1, 43–46, (1974).CrossRefGoogle Scholar
  20. 20.
    G. L. Nemhauser. Introduction to Dynamic Programming, John Wiley and Sons, Inc. New York, (1966).Google Scholar
  21. 21.
    A. Orda AND R. Rom. “Shortest-Path and Minimum-Delay Algorithms in Networks with Time-Dependent Edge-Length”, Journal of the AMC 37, 607625, (1990).Google Scholar
  22. 22.
    A. B. Phtlpott and A. I. Mees. “Continuous-Time Shortest Path Problems with Stopping And Starting Costs”, Applied Math. Lett. 5, 63–66, (1992).CrossRefGoogle Scholar
  23. 23.
    A. B. Phnpott AND A. I. Mees. “A Finite-Time Algorithm for Shortest Path Problems with Time-Varying Costs”, Applied Math. Lett. 6, 91–94, (1993).Google Scholar
  24. 24.
    H. J. Sebastian. “Dynamic Programming for Problems with Time-Dependent Parameters”, Differential Equations 14, 242–249, (1978).Google Scholar
  25. 25.
    E. S. Lff “Dynamic Programming and Principles of Optimality”, Journal of Mathematical Analysis and Applications 65, 586–606, (1978).CrossRefGoogle Scholar
  26. 26.
    B. Villareal and M. H. Karwan. “Multicriteria Integer Programming A (Hybrid) Dynamic Programming Recursive Approach”, Mathematical Programming 21, 204–223, (1981).CrossRefGoogle Scholar
  27. 27.
    M. Wilson. A Time Dependent Vector Dynamic Programming Algorithm for the Path Planning Problems, Masters Project, Department of Mathematical Sciences, Clemson University, Clemson, USA, (1992).Google Scholar
  28. 28.
    J. Whrre. Dynamic Programming, Holden-Day, San Francisko, CA, (1969).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Michael M. Kostreva
    • 1
  • Laura Lancaster
    • 1
  1. 1.Department of Mathematical SciencesClemson UniversityClemsonUSA

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