Divide-and-conquer initialization and mutation operators for the large-scale mixed Capacitated Arc Routing Problem

As cities continue to grow, thus will the size of the routing problems necessary to the functioning of all cities. Applications such as waste collection, road maintenance, or winter gritting span over an entire city, therefore algorithms must be designed to solve large-scale problems. The Capacitated Arc Routing Problem (CARP) is an important combinatorial optimization problem that is typically used to model these applications. Classical algorithms for CARP struggle to find quality solutions for large-scale instances with thousands of services within a reasonable computational budget. To address the issue of scalability, several divide-and-conquer heuristics have recently been proposed. In this paper, we propose to integrate divide-and-conquer heuristics into a memetic algorithm by adapting these as an initialization method and as a mutation operator. The resulting algorithm, which we call Memetic Algorithm with Divide-and-Conquer Mutation (MADCoM), outperforms state-of-the-art algorithms on large-scale instances and new best solutions are found for 17 instances of MCARP, 2 of which are optimal solutions, and for 23 large-scale CARP instances. These results demonstrate the potential of the integration of divide-and-conquer heuristics into metaheuristics as a strategy to efficiently solve large-scale problems.