The Application of The Improved Hybrid Ant Colony Algorithm in Vehicle Routing Optimization Problem International Conference on Future Computer and Communication, Vol. 1, p.p , May 2010

Outline Abstract INTRODUCTION VEHICLE ROUTING OPTIMIZATION PROBLEM THE BASIC IDEA OF THE ALGORITHM AND THE IMPROVED HYBRID ANT COLONY ALGORITHM STEPS OF ALGORITHM EXPERIMENTAL RESULTS CONCLUSION

Abstract Vehicle Routing Problem (VRP) is one of critical problems in modern logistics service. Due to small batch and dynamic changes of VRP, an effective and fast algorithm solution of VRP is greatly needed. But in traditional Ant Colony Algorithm, the searching speed is slow, and it is easy to fall into the local optimization when solve this problem.

In order to overcome these disadvantages, basing on the new hybrid algorithm of Ant Colony Algorithm and Artificial Fish School Algorithm, this paper further improves the Aswarm Degree in the Artificial Fish School Algorithm and proposes the Insertion Point Algorithm to solve the problem rapidly. The simulation results show that the improved algorithm has a better searching ability of global optimization. The improved algorithm is an effective algorithm of solving the VRP optimization problem.

INTRODUCTION Recently, many scholars have applied ACO algorithm to solve VRP and have gotten some achievements. But it is found that the traditional ant colony algorithm’s searching speed is slow and is easy to fall into the local optimization. Therefore, many scholars further propose the idea of Hybrid Ant Colony Algorithm. Not only has Hybrid Algorithm have some advantages of several algorithms, to some extent, it also can compensate for the defects in single algorithm.

Basing on the traditional Ant Colony Algorithm for solving VRP, we introduce the new hybrid algorithm of Ant Colony Algorithm and Artificial Fish School Algorithm, and further propose the Insertion Point Algorithm. This new algorithm takes fully advantage of the capabilities of Artificial Fish School Algorithm and Insertion Point Algorithms, which can overcome the local optimization, and obtain a convenient and efficient global optimization of the problem.

VEHICLE ROUTING OPTIMIZATION PROBLEM A. Vehicle Routing Optimization Problem B. Ant Colony Algorithm in the Application of Vehicle Routing Problem (VRP)

A. Vehicle Routing Optimization Problem The Vehicle Routing Problem (VRP) requires the determination of a optimal set of routes for a set of vehicles to serve a set of customers. The problem as it appears on real life may have several classes of additional constraints, as limit on the capacity of the vehicles, time windows for the customer to be served, limits on the time a driver can work, limits on the lengths of the routes, etc.

We want to define routes for the vehicles starting and ending at the distribution center that satisfy the clients demand at a minimum total cost. Meanwhile, it must meet the following conditions and assumptions:

–Every customer is visited exactly once by exactly one vehicle. – All vehicle routes begin and end at the distribution center. –For every vehicle route, total demand does not exceed vehicle capacity Q. –For every vehicle route, total route length does not exceed a given bound L.

B. Ant Colony Algorithm in the Application of Vehicle Routing Problem (VRP) Basing on Ant Colony Algorithm, we used the vehicles to replace the ants, and let each vehicle start from the distribution center to serve each customer. When its capacity is able to meet the next customer’s requirement, the vehicle will serve him. Otherwise, the vehicle will return to the distribution center for re-loading goods and start from the distribution center again according to the principle that total demand does not exceed its capacity to serve the remained customers.

We seems when each customer has been served by the vehicle as an ant completed this traversal. Then the ant will wait for other ants to complete a traversal. When all ants have completed their traversal, we can save the current shortest path and its length, and update the pheromone on each path, then come into the next iteration.

THE BASIC IDEA OF THE ALGORITHM AND THE IMPROVED HYBRID ANT COLONY ALGORITHM

STEPS OF ALGORITHM

EXPERIMENTAL RESULTS This paper introduces the following issues as the basic test data. Assuming: there is a distribution center 0, which has eight vehicles and the largest payload is 250 (unit: ton), and has nine distribution nodes (including distribution center 0), the coordinate (x, y) of each node is randomly distributed in the region of 20 × 20 km2, the demand q is expressed in table.

In this case, the respective value of each parameter is as follow:

It can be seen from Table that the average length is km after 10 times of calculation in the traditional Ant Colony Algorithm, however, the optimal solution is km, which is correspond to specific routes as: The result of distribution routes is shown in Fig.1.

Next, we used the improved Hybrid Ant Colony Algorithm to solve the above problem. It can be seen that after 10 times of calculation, the average length is km, and the optimal solution is km, which is better than the previous solution. We can correspond it to specific routes as: The result of distribution routes is shown in Fig.2.

From the results and figures, we can see that, compared with the traditional Ant Colony Algorithm, The improved Hybrid Ant Colony Algorithm is slower in locating the optimal solution, but we can see that the obtained result is better than the previous solution. In general, it enhances the global search ability, which is help to find the global optimal solution, and avoids falling into the local optimization.

CONCLUSION In this paper, we improved Hybrid Ant Colony Algorithm, which enhancing the algorithm ability of global optimization, and avoiding stagnation and falling into a local optimization. According to the characteristics of The Vehicle Routing Problem, this paper proposes the Insertion Point Algorithm to further obtain feasible solution of VRP based on solution of the TSP. In addition, we have obtained a better solution and further improved the performance of Ant Colony Algorithm.

The disadvantage of the algorithm is that when we want to improve the ability of finding out the global optimization, we also wake the convergence of the global optimization.