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Heuristics for the Stochastic Eulerian Tour Problem

Author

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  • Mohan, Srimathy
  • Gendreau, Michel
  • Rousseau, Jean-Marc

Abstract

The Stochastic Eulerian Tour Problem (SETP) seeks the Eulerian tour of minimum expected length on an undirected Eulerian graph, when demand on the arcs that have to be serviced is probabilistic. The SETP is NP-hard and in this paper, we develop three constructive heuristics for this problem. The first two are greedy tour construction heuristics while the third is a sub-tour concatenation heuristic. Our experimental results show that for grid networks, the sub-tour concatenation heuristic performs well when the probability of service of each edge is greater than 0.1. For Euclidean networks, as the number of edges increases, the second heuristic performs the best among the three. Also, the expected length of our overall best solution is lower than the expected length of a random tour by up to 10% on average for grid networks and up to 2% for Euclidean networks.

Suggested Citation

  • Mohan, Srimathy & Gendreau, Michel & Rousseau, Jean-Marc, 2010. "Heuristics for the Stochastic Eulerian Tour Problem," European Journal of Operational Research, Elsevier, vol. 203(1), pages 107-117, May.
    • Handle: RePEc:eee:ejores:v:203:y:2010:i:1:p:107-117
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    References listed on IDEAS

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    1. Alain Hertz & Gilbert Laporte & Pierrette Nanchen Hugo, 1999. "Improvement Procedures for the Undirected Rural Postman Problem," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 53-62, February.
    2. Srimathy Mohan & Michel Gendreau & Jean-Marc Rousseau, 2008. "The Stochastic Eulerian Tour Problem," Transportation Science, INFORMS, vol. 42(2), pages 166-174, May.
    3. Michel Gendreau & Alain Hertz & Gilbert Laporte, 1992. "New Insertion and Postoptimization Procedures for the Traveling Salesman Problem," Operations Research, INFORMS, vol. 40(6), pages 1086-1094, December.
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