الگوریتم ترکیبی بهینه‌سازی کلونی مورچه برای مسئله مسیریابی دوسطحی وسایل نقلیه

A hybrid heuristic ant colony algorithm is proposed and applied to solving the two echelon vehicle routing problem, which combines three heuristic or meta-heuristics. The problem is divided into m+1 CVRP by a separation strategy (distance-based cluster). Then better feasible solutions are built by an improve ant colony optimization with multiple neighborhood descent (IACO_MND), which is taken as the initial solution of the threshold-based local search procedure, two different neighborhood structures, i.e., threshold-based insert and threshold-based swap are successively used. Computational results on the 22 benchmark problems with the size ranging from 20 to 50 show that the proposed hybrid algorithm can find the best known solution for some problems in short time, which indicates that the proposed method outperforms other algorithm in literature.

Proposed by Dantzig and Ramser [1] in 1959, VRP has made a lot of research achievement in decades. But the researches about the problem more concentrated in single-level scheduling system, and the researches about the multi-level system, such as ME-VRP, are very small. Crainic et al. [2] apply the multi-level system to the practice first time for a City Logistics instance in 2004. Feliu et al. [3,4] integrated the multi-level system into the VRP first time and build the mathematical model for it, they call it Multi-Echelon Vehicle Routing Problem (ME-VRP). With the model and complexity of logistics increase, more and more researchers began to study and discuss the issue. Since VRP is a NP hard problem, so ME-VRP is NP hard, and more complex than the basic VRP. Therefore, the method for solving such problem mainly focused in heuristic and meta-heuristic which can fine the better solution in a relatively short time. And it has achieved some results. Such as Feliu et al. [3,4] use Base-Math heuristic algorithm for solving a number of public instance about 2E-VRP. Crainic et al. [5] proposed aClustering-based Heuristic algorithm. Then they simple improved their algorithm, and proposed Multi-Start Heuristic Algorithm [6], it asked that the local search will continue until the object value is not be improved. Crainic et al. [7] analyzed the relationship of the distribution of customers, the system layout and the cost, and compared the multi-level system with the traditional single-level VRP in performance and efficiency, which can shows the feasibility and effectiveness of the Multi-Echelon VRP. Perboli et al. [8,9] derived new families of valid inequalities for the two-echelon vehicle routing problem, in order to more efficiently obtain better strength feasible solution. Therefore, this paper proposed a hybrid ant colony optimization algorithm for 2E-VRP.

It is a hot research field that combination of the advantages of different heuristic and meta-heuristic to design more effective hybrid heuristic algorithm for combinatorial optimization problems. Combination of greedy algorithm, ant colony optimization and local search algorithm, this paperproposed a hybrid ant colony optimization algorithm to solve the 2E-VRP. Make use of the rapid of the traditional heuristic, the search diversity of ant colony optimization and the strong local search ability of local search to improve the quality of the solution and speed up the convergence of the algorithm. In the experiment, we run our method in 22 different scale benchmark data. The result illustrates that our algorithm can obtain optimal or better feasible solution in a short time. Furthermore, we compared our algorithm with other 2 literatures, and our method increased 1.59%, 5.56% than they are. It shows that our algorithm is superior to existing algorithm.