Heuristics for the stochastic Eulerian tour problem
Given an undirected Eulerian graph, a subset of its edges that require a probabilistic service, a designated depot, and a distance between every pair of nodes, the stochastic Eulerian tour problem (SETP) seeks a tour of minimum expected length [\textit{S. Mohan, M. Gendreau} and \textit{J.-M. Rousseau}, ``The stochastic Eulerian tour problem'', Transp. Sci. 42, 166--174 (2008)]. From the authors' summary: ``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.''
scientific article; zbMATH DE number 5643704