Capacitated Arc Routing Problem Paper

Capacitated Arc Routing Problem (CARP) is a classic combinatorial optimization problem which has a wide range of social applications [1], such as: winter snow removing routes [2], school bus scheduling planning [3], the check of gas pipeline [4] or oil pipelines [5], and the mail delivery planning [6] et al. CARP can be defined as: designing optimization of a path to make a minimum total consumption [7]. Specifically, we make a team start from the garage and serve for the prescribed task sides. Meanwhile, optimize the vehicle route to meet a variety of constraints and determine a scheduling scheme which makes the total consumption of the vehicle minimal. The following are the constraints which need to meet for solving CARP:
1). Each vehicle must proceed from the garage to service the tasks and finally back to the garage;
2). Each task can only be serviced by one vehicle and only be serviced once;
3). The total demand of the tasks which is serviced by each vehicle does not exceed its capacity Q.
In the above three constraints, constraints 1), and 2) are the fundamental constraints that exists in all arc routing problem. However, constraint 3) is

In the graph, each arc (or edge) has a non-negative cost and demand. The demand is the set of tasks that vehicles provide service. Each task has two attributes: demand for service d(r)>0, and service consumption SC(r)>0. Non-mission side does not need to service. In addition, if no service is provided from vi to vj, the consumption of the vehicle is dc(vi,vj) >0. Here the connected graph is symmetric, i.e. dc(vi,vj)=dc(vj,vi) for each edge (vi,vj). CARP can be described as follows: let m vehicles with the capacity of Q start from the garage (dep), then find a minimum cost path to serve all the tasks in the graph under the constraint