Estimation of the Distribution Algorithm With a Stochastic Local Search for Uncertain Capacitated Arc Routing Problems

The uncertain capacitated arc routing problem is a challenging problem in which the demands of tasks, the costs of edges, and the presence of tasks and edges are uncertain. The objective of this problem is to find a robust optimal solution for a finite set of possible scenarios. In this paper, we propose a novel robust optimization approach, called an estimation of distribution algorithm (EDA) with stochastic local search (SLS), to tackle this problem. The proposed method integrates an EDA with a novel two phase SLS procedure to minimize the maximal total cost over a set of different scenarios. The SLS procedure avoids excessive fitness evaluations of unpromising moves in local search. Our experimental results on two sets of benchmark problems (a total of 55 problem instances) showed that the proposed approach outperformed existing state-of-the-art algorithms.