Cooperative coevolution with route distance grouping for large-scale capacitated arc routing problems

In this paper, a divide-and-conquer approach is proposed to solve the large-scale capacitated arc routing problem (LSCARP) more effectively. Instead of considering the problem as a whole, the proposed approach adopts the cooperative coevolution (CC) framework to decompose it into smaller ones and solve them separately. An effective decomposition scheme called the route distance grouping (RDG) is developed to decompose the problem. Its merit is twofold. First, it employs the route information of the best-so-far solution, so that the quality of the decomposition is upper bounded by that of the best-so-far solution. Thus, it can keep improving the decomposition by updating the best-so-far solution during the search. Second, it defines a distance between routes, based on which the potentially better decompositions can be identified. Therefore, RDG is able to obtain promising decompositions and focus the search on the promising regions of the vast solution space. Experimental studies verified the efficacy of RDG on the instances with a large number of tasks and tight capacity constraints, where it managed to obtain significantly better results than its counterpart without decomposition in a much shorter time. Furthermore, the best-known solutions of the EGL-G LSCARP instances are much improved.