The basic step in solving the optimization problem applying ant colony algorithm is: the ant walk paths are delegated with feasible solutions of optimization problem, the entire ant group staying on all paths constitutes the solution space of optimization problems. Released pheromone amounts in short path is more than others, with the passage of time, the accumulation of pheromone concentration on the shorter path is increasing gradually, more and more ants will choose these paths. Ultimately, the ants will focus on the best path under the action of the positive feedback.

Ant colony algorithm has played an important role in solving the traveling salesman problem [14] , the shortest path search [15] [16] , scheduling problem [17] , etc.

Without loss of generality, supposing that the number for a whole ants group are m, network topology for the road node numbers are n, the distance between the road node i and j is , at the t moment, the pheromone concentration between the node i and j is, each pheromone concentration in every road node is set with in the initial time.

The ant decides the next choice node according to the various sections of the pheromone concentration, supposing shows the probability that is the ant moves from node i to node j in the t moment, calculating formula is that:

: pheromone concentration between the node i to node j, the value will gradually decay with the passage of time;

: expectations of the node i to node j, it represents a kind of local heuristic information, some local experience can guide a better path, it stands the reciprocal of distance to the node i and j in the paper;

: This value can be adjust through experiments, represents for importance degree of;

: It represents importance degree of that can be adjust through experiments；

: sets of the next node when ants from one node to another node. This value is dynamically changing. At the time n, the next equation is the updating pheromone concentration formula when ants completing a path searching from the start to the end:

In the formula, is the path pheromone concentration variation, indicated as:

represents the k ant releases the pheromone concentration from the node i to the node j.

A suboptimal routing road can be planned with the Dijkstra algorithm on the MAKLINK graph, is free link line that is corresponding to node. On the assumption that and are two endpoints of, the other nodes can be shown with following formula:

Of which, is scale parameter, d is the number of nodes in link divide.

The Formula (4) shows that Dijkstra algorithm will get the initial path through the link line, as long as a new set of parameters is given, you can get a new path from start to finish, ant colony algorithm is aimed to choose the best parameters in.

It is required to disperse work space before using ant colony algorithm. Due to the initialization of the freedom of choice link line length is differ, the method of the link line division is named fixed distance classification method. Setting the length is, division number at link L is:

If the is odd number, midpoint is also a path point, will be added one. In consideration of the link line is divided by, so the link line arriving at the link line has roads to choose .

Ant colony algorithm is used to obtain the path parameter set, which is aimed at find the shortest path in the discretizable spaces. Let us suppose that there is m ants from start S to finish T. Circular path is. represents that the path point is located in position j at the link line d. With the moving of the every ant, ant will choose the node j from link line to link line through following formula:

i is the whole points in link lines, q is a random number between [0,1], is a adjustable parameter in [0,1], is heuristic value, is pheromone.

As for the calculation method of j, firstly calculating the select probability from the link line node to the next j, then using roulette selection to elect the next node j according to the probability, design formula of is:

Pheromone update includes real-time pheromone update and path pheromone update. Over here real-time pheromone update demands each ant must update the node pheromone after selecting a node, namely:

is initial value of pheromones, is a adjustable parameter ranging of [0,1].

It is completed the iterative search when all the ants move from the initial point to the finish line. In order to select a shortest path length when all the ants move to the end, pheromone on each road should be updated, the formula is:

, is the length of the shortest path, is a adjustable parameter in [0,1].

When an ant is searching for the node to the next node, the traditional algorithm is calculating the probability of the next node which is one of all optional nodes that is based on pheromone and distance calculation and then choose the, assuming that optional sections of node are. Each node selection is to reduce the total length from the current node to the end, so if you select the angle line node to that comparing the angle of starting and ending angle they are consistent or similar, the node is to give priority to the node. As shown in Figure 1. In this paper, we will use this method to finding the next node.

To explore the ant number influence on the optimal path, we had analyzed six different sets of ant species, the Figure 2 shows that when the number of ants are selected 5, 10 or15 respectively, as the number of ants increasing, the shortest path planning will reduce on the contrary, the Figure 3 shows that when m is 30 or 50, with the increasing of the ant species, the shortest path distance is also gradually increased with the increase of number of ant species. When m is 15, it can play a optimal path planning.

The Figure 4 shows that when the pheromone of importance factor is 1 and pheromone importance factor is 2, difference in path planning is not obvious, however when the a = 1, the convergence speed of path planning is faster than a = 2, so in this paper, a = 1 finally is elected to important parameter for the pheromone factor.

The Figure 5 shows that when importance factor of the heuristic function is b = 1, the path planning results are volatile, to the contrary, when the parameter is b = 2, the result is stabilized. Therefore in this paper, we choose b = 2 as the importance factor of heuristic function which could deservebetter path planning than other factors.

The Figure 6 shows that choosing r = 0.1, as the addition number of iterations, the shortest path is gradually converged, when r = 0.2 or 0.3, the results of path planning is fluctuating with the increase of iterations. Therefore in this paper we select r = 0.1 which can play a more ideal path planning.

The optimum calculation parameters can be chosen in this paper, as a whole, the number of ants is 15, pheromone importance factor is a = 1, importance factor inspired by the function is 2, pheromone volatilization factor is 0.1, the number of iterations is 500. Figure 7 and Figure 8 show the convergence speed of two algorithms and optimal path plans. The Figure 7 shows that improved algorithm has a certainly better effect comparing with the original algorithm. Before improvement, the optimal distance of two-dimension path planning is 175.5889 kilometers, after improvement, the optimal distance of two-dimension path planning is 164.5734 kilometers. Figure 8 shows the improved ant colony algorithm and the original planning are together planning the path. The red figure shows that is programming optimal path by improved ant colony algorithm, blue figure is using the original algorithm. Obviously, improved ant colony algorithm can plan out a better path than the original algorithm.