Heuristics for the Stochastic Eulerian Tour Problem

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. In an earlier paper, we have shown that the SETP is NP-hard and derived several properties of the optimal tour. In this paper, we develop three constructive heuristics for the SETP. The first two are greedy tour construction heuristics while the third is a sub-tour concatenation heuristic. We tested the performance of the three heuristics and a post-optimization procedure on grid networks and on Euclidean graphs. Our results indicate that the sub-tour construction heuristic performs well when the probability of occurrence of each edge in the graph, p > 0.1 for the grid networks. For the Euclidean networks, as the number of edges increases, the second heuristic performs the best among the three, though the margin of improvement is small.