Heuristics for the Stochastic Eulerian Tour Problem

Srimathy Mohan, Michel Gendreau, Jean Marc Rousseau

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)107-117
Number of pages11
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - May 16 2010


  • Arc routing
  • Eulerian Tour Problem
  • Heuristics
  • Routing
  • Stochastic demand

ASJC Scopus subject areas

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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