RoCaSH2: An Effective Route Clustering and Search Heuristic for Large-Scale Multi-Depot Capacitated Arc Routing Problem

The Multi-Depot Capacitated Arc Routing Problem (MDCARP) is an important combinatorial optimization problem with wide applications in logistics. Large Scale MDCARP (LSMDCARP) often occurs in the real world, as the problem size (e.g., number of edges/tasks) is usually very large in practice. It is challenging to solve LSMDCARP due to the large search space and complex interactions among the depots and the tasks. Divide-and-conquer strategies have shown success in solving large-scale problems by decomposing the problem into smaller sub-problems to be solved separately. However, it is challenging to find accurate decomposition for LSMDCARP. To address this issue and alleviate the negative effect of inaccurate problem decomposition, this article proposes a new divide-and-conquer strategy for solving LSMDCARP, which introduces a new restricted global optimization stage within the typical dynamic decomposition procedure. Based on the new divide-and-conquer strategy, this article develops a problem-specific Task Moving among Sub-problems (TMaS) process for the global optimization stage and incorporates it into the state-of-the-art RoCaSH algorithm for LSMDCARP. The resultant algorithm, namely, RoCaSH2, was compared with the state-of-the-art algorithms on a wide range of LSMDCARP instances, and the results showed that RoCaSH2 can achieve significantly better results than the state-of-the-art algorithms within a much shorter time.