A novel heuristic method to solve the capacitated arc routing problem

The capacitated arc routing problem is one of the most important routing problems with many applications in real world situations such as snow removing, winter gritting, refuse collection, etc. Since this problem is NP-hard, many of researchers have been developed numerous heuristics and metaheuristics to solve it. In this paper, we propose a new constructive and improvement heuristic in which forming a vehicle’s tour is based on choosing an unserved edge randomly as current partial tour and then extending this partial tour from its both of end nodes base on four effective proposed criteria. When the vehicle load is near its capacity, it should come back to the depot immediately. Finally, the constructed tours are merged into more efficient and cheaper tours. The quality of this new approach was tested on three standard benchmark instances and the results were compared with some known existing heuristics and metaheuristics in the literature. The computational results show an excellent performance of our new method.