Solving Stochastic Path Problem: Particle Swarm Optimization Approach

  • Saeedeh Momtazi
  • Somayeh Kafi
  • Hamid Beigy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5027)


An stochastic version of the classical shortest path problem whereby for each node of a graph, a probability distribution over the set of successor nodes must be chosen so as to reach a certain destination node with minimum expected cost. In this paper, we propose a new algorithm based on Particle Swarm Optimization (PSO) for solving Stochastic Shortest Path Problem (SSPP). The comparison of our algorithm with other algorithms indicates that its performance is suitable even by the less number of iterations.


Particle Swarm Optimization Stochastic Shortest Path Problem Swarm Intelligence 


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  1. 1.
    Deo, N., Pang, C.: Shortest Path Algorithms: Taxonomy and Annotation. Networks 14, 275–323 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Frank, H.: Shortest paths in probabilistic graphs. Operations Research 17, 583–599 (1969)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Loui, R.P.: Optimal paths in graphs with stochastic or multidimensional weights. Communications of the ACM 26, 670–676 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Murthy, I., Sarkar, S.: A relaxation based pruning technique for a class of stochastic shortest path problems. Transportation Science 30, 220–236 (1996)zbMATHGoogle Scholar
  5. 5.
    Murthy, I., Sarkar, S.: Stochastic shortest path problems with piecewise linear concave utility functions. Management Science 44, 125–136 (1998)CrossRefGoogle Scholar
  6. 6.
    Rasteiro, D.M., Anjo, A.B.: Metaheuristics for stochastic shortest path problem. In: Proceedings of 4th MetaHeuristics International Conference (MIC), Porto, Portugal (2001)Google Scholar
  7. 7.
    Meybodi, M.R., Beigy, H.: Solving Stochastic Shortest Path Problem Using Distributed Learning Automata. In: Proceedings of 6th Annual International Computer Society of Iran Computer Conference CSICC, Isfehan, Iran, February 2001, pp. 70–86 (2001)Google Scholar
  8. 8.
    Beigy, H., Meybodi, M.R.: A. New Distributed Learning Automata Based Algorithm For Solving Stochastic Shortest Path Problem. In: Proceeding of Joint Conference on Information Sciences (JCIS), North Carolina, USA, pp. 339–343 (2002)Google Scholar
  9. 9.
    Fukuyama, Y.: Fundamentals of particle swarm optimization techniques. In: IEEE PES Tutorial on Modern Heuristic Optimization Techniques with Application to Power Systems, ch. 5 (January 2002)Google Scholar
  10. 10.
    Colorni, A., Dorigo, M., Maniezzo, V.: Distributed Optimization by Ant Colonies. In: Proceeding of First European Conference on Artificial Life, pp. 134–142. MIT Press, Cambridge (1991)Google Scholar
  11. 11.
    Kennedy, J., Eberhart, R.: Particle Swarm Optimization. In: Proceedings of IEEE International Conference on Neural Networks (ICNN), vol. IV, Perth, Australia, pp. 1942–1948 (1995)Google Scholar
  12. 12.
    Eberhart, R.C., Kennedy, J.: A New Optimizer using Particle Swarm Theory. In: Proceeding of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, pp. 39–43 (1995)Google Scholar
  13. 13.
    Dijkstra, E.W.: A note on two problems in connection with graphs. Numerische Mathematics, pp. 269–271 (1959)Google Scholar
  14. 14.
    Beigy, H., Meybodi, M.R.: Utilizing Distributed Learning Automata to Solve Stochastic Shortest Path Problems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 14, 591–615 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Alexopoulos, C.: State Space Partitioning Methods for Stochastic Shortest Path Problems. Networks 30, 9–21 (1997)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Saeedeh Momtazi
    • 1
  • Somayeh Kafi
    • 1
  • Hamid Beigy
    • 1
    • 2
  1. 1.Computer Engineering DepartmentSharif University of TechnologyTehranIran
  2. 2.Institutes for Studies in Theoretical Physics and Mathematics (IPM)School of Computer ScienceTehranIran

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