Divide-and-Conquer Large Scale Capacitated Arc Routing Problems with Route Cutting Off Decomposition

TL;DR

This paper introduces a novel route cutting off operator for large scale capacitated arc routing problems, enhancing divide-and-conquer methods by better handling task interactions, leading to improved solutions especially in very large instances with limited computation time.

Contribution

The paper proposes a new route cutting off operator that improves problem decomposition in divide-and-conquer algorithms for large scale arc routing problems.

Findings

The route cutting off operator improves decomposition effectiveness.

Enhanced algorithms outperform original methods on benchmark instances.

Significant improvements observed in very large problems with tight time constraints.

Abstract

The capacitated arc routing problem is a very important problem with many practical applications. This paper focuses on the large scale capacitated arc routing problem. Traditional solution optimization approaches usually fail because of their poor scalability. The divide-and-conquer strategy has achieved great success in solving large scale optimization problems by decomposing the original large problem into smaller sub-problems and solving them separately. For arc routing, a commonly used divide-and-conquer strategy is to divide the tasks into subsets, and then solve the sub-problems induced by the task subsets separately. However, the success of a divide-and-conquer strategy relies on a proper task division, which is non-trivial due to the complex interactions between the tasks. This paper proposes a novel problem decomposition operator, named the route cutting off operator, which considers the interactions between the tasks in a sophisticated way. To examine the effectiveness of the route cutting off operator, we integrate it with two state-of-the-art divide-and-conquer algorithms, and compared with the original counterparts on a wide range of benchmark instances. The results show that the route cutting off operator can improve the effectiveness of the decomposition, and lead to significantly better results especially when the problem size is very large and the time budget is very tight.