AGV path planning method based on construction time cost function improved ant colony algorithm

Abstract

The invention discloses an AGV path planning method based on construction of a time cost function and improvement of an ant colony algorithm, and relates to the technical field of AGV intelligent guide robots, and the method comprises the steps: S1, constructing a grid environment map, and setting initialization parameters; s2, placing a plurality of ants at a starting point of the grating environment map, wherein each ant starts to independently search a path; s3, when all ants walk to the target node, side pheromone updating and pheromone volatilization are carried out according to the time cost of the walking path of each ant, whether the current number of iterations reaches the preset maximum number of iterations is judged, if yes, the next step is carried out, and if not, the S2 is repeated until the preset maximum number of iterations is reached; and S4, selecting the path with the optimal time cost as the final path according to the time cost of the path on which the ant walks in each iteration. According to the invention, the accuracy of path planning is improved, and the total operation time of the AGV is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of AGV intelligent guided robots, and in particular to an AGV path planning method based on improving an ant colony algorithm by constructing a time cost function. Background Art

[0002] AGV (Automated Guided Vehicle) is an automated logistics equipment used to transport and carry goods in factories, warehouses, logistics centers, etc. In recent years, with the development of autonomous navigation, AGV has gradually become the core equipment of intelligent logistics, and has played an increasingly important role in many fields such as workshop processing, instrument production, e-commerce warehousing, etc.

[0003] At present, there are many technologies in the field of AGV path planning, among which Ant Colony Optimization is very common as an AGV path planning method. Traditional ant colony algorithms basically use the shortest path as the basis for pheromone updates. However, for AGV path planning, what should really be considered is the actual time cost of the AGV from the starting point to the destination, rather than the length of the path. The reason is that there is a cost for the turning time of the AGV, and the traditional ant colony algorithm has not been deeply explored in this regard. The path planning is relatively rugged and tortuous. Some scholars have also paid attention to this situation. In the pheromone update of the AGV, a turning factor penalty is introduced separately to constrain the path planning of the AGV, and the number of turns during the AGV driving process is minimized. This method has worked to a certain extent, but the disadvantage is that it is not enough to fit the actual situation, because the final optimization result of the ant colony algorithm is still based on the optimal path for the final evaluation, rather than considering the time cost, which will cause the output result of the debugging algorithm process to be unclear. It is possible that the path has approached the ideal shortest path, but many deviations have occurred. On this basis, if you want to further improve the performance of the algorithm, it is not comprehensive enough to evaluate it only by the path length problem.

[0004] Secondly, for traditional ant colony algorithms, most scholars will use grid maps to mark static obstacles and AGV feasible areas when constructing maps, and the AGV's movement mode in the grid map is either straight up or down, or moving along an irregular trajectory. The former will lose the possibility of finding a shorter path, and the latter will make the ant colony path construction algorithm take a long time and have a high computational complexity due to the planning of irregular trajectories. Summary of the invention

[0005] In order to solve the technical problems existing in the above-mentioned prior art, the present invention proposes an AGV path planning method based on improving the ant colony algorithm by constructing a time cost function. By using the time cost function to update pheromones, the ant colony algorithm can more accurately reflect the actual operation of the AGV.

[0006] To achieve the above object, the present invention provides an AGV path planning method based on constructing a time cost function to improve the ant colony algorithm, comprising:

[0007] S1, construct a grid environment map and set initialization parameters;

[0008] S2, placing a number of ants at the starting point of the grid environment map, and each ant starts to search for a path independently, wherein the ant selects the next moving direction and turning angle according to the pheromone concentration and state transition probability of the current grid;

[0009] S3, when all ants reach the target node, the edge pheromone is updated and the pheromone is volatilized according to the time cost of the path taken by each ant, and it is determined whether the current number of iterations reaches the preset maximum number of iterations. If it reaches it, the next step is performed; if not, S2 is repeated until the preset maximum number of iterations is reached;

[0010] S4. According to the time cost of the paths taken by the ants in each iteration, the path with the best time cost is selected as the final path.

[0011] Preferably, constructing the grid environment map includes:

[0012] Divide the map into unit grids and represent the map as a two-dimensional grid map. The node set is , the connections between nodes are represented by edge sets It indicates that the ant colony walks in a way that takes the center of each grid of the grid map as the secondary target node, and the size of the grid map is divided according to the size of each AGV;

[0013] Among them, the horizontal and vertical The relationship is:

[0014] ;

[0015] In the formula, Indicates the grid number; Represents the grid length of one unit, Indicates remainder calculation; Indicates rounding up calculation; Respectively indicate the level and vertical The number of raster map rows and columns in the direction.

[0016] Preferably, the state transition probability is the probability that the ant moves from the current grid number node Move to the next grid number node The probability is:

[0017] ;

[0018] In the formula, is the parameter of pheromone importance, is the parameter of the importance of heuristic information, For Ants The set of currently accessible adjacent nodes, For Node To Node The pheromone concentration, For Node To Node Heuristic information, is the state transition probability, and l is the next node selected by the current node i.

[0019] Preferably, in the process of independently searching for paths, the Euclidean distance is used as a heuristic function to guide the search direction of the ants;

[0020] Wherein, the heuristic function is:

[0021] ;

[0022] ;

[0023] In the formula, For Node The Euclidean distance to the target node, For Node To Node Heuristic information, is the horizontal coordinate of the next selected node, is the ordinate of the next selected node, is the horizontal coordinate of the target end point, is the vertical coordinate of the target end point.

[0024] Preferably, the next moving direction and turning angle are selected according to the pheromone concentration and state transition probability of the current grid, including:

[0025] According to the time cost of the path taken by each ant, the pheromone concentration of the corresponding edge in the grid environment map is updated through the pheromone update cost function, and during each movement, the turning angle is determined according to the vector relationship between the current position and the moving direction.

[0026] Preferably, the pheromone update cost function is:

[0027] ;

[0028] ;

[0029] ;

[0030] In the formula, For Ants The total time of the path traveled, is the total cost of straight travel time, is the total cost of the turning time, is the total path length, is the constant speed of AGV, is the turning time per unit angle, is the turning angle, is the total number of turns.

[0031] Preferably, determining the turning angle includes:

[0032] Determine the direction change between adjacent nodes in the path, and determine the turning angle based on the vector relationship between the ant's current position and moving direction. Specifically:

[0033] ;

[0034] In the formula, is the vector dot product, , are the magnitudes of the vectors, is the turning angle.

[0035] Preferably, in S3, at the end of each iteration, after each ant completes the path search, the pheromone increment is updated according to the total path cost:

[0036] ;

[0037] ;

[0038] In the formula, For Ants In the The total path time cost in iterations, M is the total number of ants, Q is the pheromone intensity, is the number of nodes in T iterations The total pheromone increment on the edge formed with node j, For Ants In the In the iteration, the node The size of the pheromone concentration update of the edge formed with node j.

[0039] Compared with the prior art, the present invention has the following advantages and technical effects:

[0040] (1) In view of the fact that the traditional ant colony algorithm only uses the path length of the AGV as the evaluation standard for the planning effect, the present invention proposes to use the actual movement time of the AGV as the evaluation standard, so that the planned path is more in line with the actual needs. According to the movement characteristics of the AGV, the AGV movement is decomposed into straight movement and turning, and the actual straight speed and turning time are set. Finally, a time cost calculation function for straight movement and turning is constructed as the basis for the new ant colony pheromone update, so that the final optimization goal of the ant colony is to find a path strategy with the minimum time cost.

[0041] (2) In response to the problem of movement mode of traditional ant colony algorithm when planning AGV path, the present invention comprehensively considers the straight-line and non-fixed trajectory modes, and proposes to use the center of each grid node in the feasible area of ​​the grid map as the secondary target, so as to ensure that the ant colony has the ability to move diagonally, make the path planning as short as possible while avoiding the algorithm complexity being too high, and also cooperate well with the time cost function to calculate the straight-line and turning time, the two complement each other.

[0042] (3) The present invention uses the time cost function to update pheromones, so that the ant colony algorithm can more accurately reflect the actual operation of the AGV; improve the accuracy of path planning, reduce the total operation time of the AGV, enable the AGV to complete the task more efficiently, and improve the overall efficiency of the logistics system. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0044] Figure 1 It is a flow chart of the AGV path planning method based on constructing a time cost function to improve the ant colony algorithm according to an embodiment of the present invention;

[0045] Figure 2 A schematic diagram of a traditional non-fixed trajectory ant colony algorithm according to an embodiment of the present invention;

[0046] Figure 3 Graphs of the original ant colony algorithm path and iteration times of an embodiment of the present invention, wherein (a) is a schematic diagram of the original ant colony algorithm path, and (b) is a graph of the original ant colony algorithm iteration times;

[0047] Figure 4The diagram shows the path and number of iterations of the ant colony algorithm with time cost as the pheromone update function according to an embodiment of the present invention, wherein (a) is a schematic diagram of the path of the ant colony algorithm with time cost as the pheromone update function, and (b) is a diagram of the number of iterations of the ant colony algorithm with time cost as the pheromone update function. DETAILED DESCRIPTION

[0048] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0049] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0050] Basic principles of traditional ant colony algorithm:

[0051] Ant Colony Optimization (ACO) is a heuristic optimization algorithm based on bionics, which imitates the behavior of ants transmitting information through pheromone in the process of searching for food.

[0052] Its main features include:

[0053] Pheromone update mechanism: Ants leave pheromones on the path. The better the path and the more concentrated the pheromone, the more likely subsequent ants are to choose it.

[0054] Heuristic information: Combines the specific characteristics of the problem (such as distance, cost) to guide the ants' search direction.

[0055] Pheromone volatilization: simulate the natural volatilization of pheromones in reality to avoid falling into local optimality.

[0056] Traditional ant colony pheromone update algorithm (ant week form):

[0057] ;

[0058] ;

[0059] ;

[0060] in, The volatile factor that indicates that pheromones gradually oxidize and decompose over time and disappear. Represents a node The total pheromone strength of the edge formed with node j in T+1 iterations, Indicated in In the iteration, stay at the node The total pheromone update concentration at the position of the edge formed by node j, Represents ants exist The next iteration stays at the node The pheromone on the edge formed by node j, Represents ants The path length in this iteration, represents the total amount of pheromone, Represents the total number of ants.

[0061] As can be seen from the above, in the traditional ant colony algorithm, pheromone update is based on path length .

[0062] Based on the above technical background, this embodiment proposes an AGV path planning method based on constructing a time cost function to improve the ant colony algorithm, such as Figure 1 ,include:

[0063] S1, construct a grid environment map and set initialization parameters;

[0064] S2, placing a number of ants at the starting point of the grid environment map, and each ant starts to search for a path independently, wherein the ant selects the next moving direction and turning angle according to the pheromone concentration and state transition probability of the current grid;

[0065] S3, when all ants reach the target node, the edge pheromone is updated and the pheromone is volatilized according to the time cost of the path taken by each ant, and it is determined whether the current number of iterations reaches the preset maximum number of iterations. If it reaches it, the next step is performed; if not, S2 is repeated until the preset maximum number of iterations is reached;

[0066] S4. According to the time cost of the paths taken by the ants in each iteration, the path with the best time cost is selected as the final path.

[0067] Furthermore, a grid environment map is constructed, including:

[0068] Divide the map into unit grids and represent the map as a two-dimensional grid map. The node set is , the connections between nodes are represented by edge sets It is indicated that the ant colony walks in a grid-like map with the center of each grid as the secondary target node, which not only retains the ant colony's ability to move obliquely but also reduces the complexity of the algorithm. The size of the grid-like map is divided according to the size of each AGV.

[0069] like Figure 1 , black is the obstacle area, which cannot be advanced. White is the area that can be advanced. And set the number , the positions of the grid numbers correspond to each other, horizontal and vertical The relationship is:

[0070] ;

[0071] In the formula, Indicates the grid number; Represents the grid length of one unit, Indicates remainder calculation; Indicates rounding up calculation; Respectively indicate the level and vertical The number of raster map rows and columns in the direction.

[0072] Specifically, the operating environment of AGVs includes workshops, textile factories, and other factories. Grid map modeling is performed to connect the simulation environment with reality and make the simulation path fit the reality. Map data is currently generated randomly. The size of each grid on the map is limited by the size of the AGV, and the unit is m. After the map is gridded, the coordinates (x, y) of each grid position can be obtained to facilitate program calculations, such as calculating the heuristic function distance.

[0073] Furthermore, the state transition probability is the ant moving from the current grid number node Move to the next grid number node The probability is:

[0074] ;

[0075] In the formula, is the parameter of pheromone importance, is the parameter of the importance of heuristic information, For Ants The set of currently accessible adjacent nodes, For Node To Node The pheromone concentration, For Node To Node Heuristic information, is the state transition probability, and l is the next node selected by the current node i.

[0076] Specifically, the initialization parameters include the state transition probability , , maximum number of loop iterations, number of ant colonies, target starting point and end point, total pheromone intensity Q, pheromone volatility factor , how many m / s is the uniform speed of AGV, how many seconds is it for AGV to turn 180° on the spot.

[0077] Furthermore, in the process of independent path search, the Euclidean distance is used as a heuristic function to guide the search direction of the ants;

[0078] Wherein, the heuristic function is:

[0079] ;

[0080] ;

[0081] In the formula, For Node The Euclidean distance to the target node, For Node To Node Heuristic information, is the horizontal coordinate of the next selected node, is the ordinate of the next selected node, is the horizontal coordinate of the target end point, is the vertical coordinate of the target end point.

[0082] Furthermore, the next moving direction and turning angle are selected according to the pheromone concentration and state transition probability of the current grid, including:

[0083] According to the time cost of the path taken by each ant, the pheromone concentration of the corresponding edge in the grid environment map is updated through the pheromone update cost function, and during each movement, the turning angle is determined according to the vector relationship between the current position and the moving direction.

[0084] Specifically, the pheromone update cost function is:

[0085] ;

[0086] ;

[0087] ;

[0088] In the formula, For Ants The total time of the path traveled, is the total cost of straight travel time, is the total cost of the turning time, is the total path length, is the constant speed of AGV, is the turning time per unit angle, is the turning angle, is the total number of turns.

[0089] Determine the turning angle, including:

[0090] Determine the direction change between adjacent nodes in the path, and determine the turning angle based on the vector relationship between the ant's current position and moving direction. Specifically:

[0091] ;

[0092] In the formula, is the vector dot product, , are the magnitudes of the vectors respectively.

[0093] Specifically, in this embodiment, it is stipulated that when the ant colony walks diagonally as a whole, it is necessary to consider further optimization of the path, that is, the path with the smallest turning angle and the shortest time. This is reflected in the defined time cost function. The shorter the time taken for the overall path, the stronger the pheromone strength of each edge of this advantageous path will be when the total pheromone strength Q is constant. At the beginning of the next iteration, when the ant colony makes a selection, the edge with high pheromone strength will be given priority, that is, the next node connected to the edge with high pheromone strength will be selected. Two nodes and one edge. , When used to balance the ant colony, it is more important to pay attention to the heuristic function information or the pheromone intensity function. Because the accumulation problem of pheromones may cause the ant colony to fall into the local optimum, there is also pheromone volatilization to further limit pheromone accumulation.

[0094] The mathematical expression of the state transition probability formula is to further retain the random factor, also known as roulette wheel selection. In the above example, the ant colony will spontaneously choose a path with a high pheromone concentration and close to the target end point, but this is ultimately reflected in probability. The state transition probability can be quantified while retaining the ability to jump out of the local optimal point. For example, if the probability of selecting an advantageous node is 80%, the ant colony still has a 20% probability of choosing the suboptimal one, retaining the ability to change.

[0095] Furthermore, in S3, at the end of each iteration, after each ant completes the path search, it updates the pheromone increment according to the total path cost. :

[0096] ;

[0097] ;

[0098] In the formula, For Ants In the The total path time cost in iterations, M is the total number of ants, Q is the pheromone intensity, is the number of nodes in T iterations The total pheromone increment on the edge formed with node j, For Ants In the In the iteration, the node The size of the pheromone concentration update of the edge formed with node j.

[0099] The method for updating the overall pheromone is:

[0100] ;

[0101] In the formula, The volatile factor that indicates that pheromones gradually oxidize and decompose over time and disappear. Indicated in In the iteration, stay at the node The total pheromone update concentration on the edge formed by node j, Represents a node The edge formed with node j is The total pheromone strength in the iteration, Represents a node The edge formed with node j is The total pheromone strength in iterations.

[0102] The newly generated pheromone update formula of T iterations and the overall pheromone update process together constitute the total pheromone intensity component of T+1 iterations. The update of pheromones more directly reflects the time cost of the actual operation of AGV, and the goal of ant colony planning is also based on this.

[0103] Specifically, after initializing the parameters, the ant colony algorithm will start. At the beginning, the pheromone intensity of each node is the same, so the ant colony will choose according to the heuristic function, point out a general direction for the ant colony, and then the ant colony will start to walk. For example, 50 ants will walk 50 roads, and eventually leave different pheromone intensities on each edge. This is the first round of cycles. When the next cycle starts, the 50 ants will continue to start from the starting point. At this time, they will no longer only consider the heuristic function when selecting the next node, but will also make a choice based on the pheromone intensity, and then continue to iterate. The final criterion for judging the optimal path is the path with the minimum time cost. At the end of each iteration, screening will be performed to select the optimal path.

[0104] In this embodiment, since the ant colony is more than one ant, The pheromone superposition of the edge formed with node j has more than one ant providing pheromone. It is to calculate whether there are ants passing through the node If there is an edge with node j, assign pheromone to node j. The edge formed by node j, and this judgment should be made for all ants. For example, out of 50 ants, 25 choose a path that passes through node and node j, then there will be 25 ants with nodes The pheromone of the edge formed by ant and node j is contributed, while the other 25 ants do not have it. Then the pheromone updated by these 25 ants is accumulated to get the pheromone of node The pheromone on the edge formed by node j in T iterations is updated, and then the next iteration is decided to use node What should be the pheromone concentration of the edge formed with node j? This includes the total pheromone intensity at T iterations. The remaining amount after volatilization plus the new pheromone intensity updated during T iterations .

[0105] like Figure 1 After defining the map and initializing the parameters, the ant colony algorithm will start. At the beginning, the pheromone intensity of each node is the same. The ant colony will choose according to the heuristic function. The role of the heuristic function is to let the ant colony know the approximate direction of the target location when it sets out, and point out a general direction for the ant colony. Then the ant colony starts to walk. 50 ants will walk 50 roads, and eventually leave different pheromone intensities on each edge, which is the first round of the cycle. At the beginning of the next cycle, the 50 ants will continue to start from the starting point. At this time, the ants will no longer only consider the heuristic function when selecting the next node, but will also make a choice based on the pheromone intensity, and then continue to iterate. The final criterion for judging the optimal path is the path with the minimum time cost. At the end of each iteration, screening will be performed to select the optimal path.

[0106] The traditional ant colony algorithm quantifies the path length when updating pheromones, while the method proposed in this embodiment makes judgments based on time, which is more in line with the actual AGV task completion time requirement and takes the actual performance of the AGV, such as turning performance, into consideration to avoid excessive deflections and turns in the path.

[0107] In order to more clearly express the technical solution of the present invention, the following is explained through experimental simulation results:

[0108] Figure 2 This is a schematic diagram of the traditional non-fixed trajectory ant colony algorithm. Figure 2 It can be seen that even with the existence of heuristic function information, the original ant colony algorithm is still not detailed enough in selecting the bends in the path, and cannot quantify the cost of turning well. Figure 3 is the original ant colony algorithm path and iteration number graph, Figure 3 (a) is a schematic diagram of the original ant colony algorithm path. Figure 3 (b) is the original ant colony algorithm iteration number diagram; Figure 4 The graph of the path and number of iterations of the ant colony algorithm with time cost as the pheromone update function is shown below. Figure 4 (a) is a schematic diagram of the ant colony algorithm path with time cost as the pheromone update function. Figure 4 (b) is the number of iterations of the ant colony algorithm with time cost as the pheromone update function, which is given by Figure 4 It can be seen that the improved ant colony algorithm can use time cost as the final evaluation system. According to the actual AGV turning cost time, the ant colony can automatically consider the turning time when planning the path, so that the output path is in line with the AGV task completion time indicator, rather than just the length of the path, and the consideration level is more detailed.

[0109] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. The AGV path planning method based on the improved ant colony algorithm based on the construction of time cost function is characterized by: include: S1, construct a grid environment map and set initialization parameters; S2, placing a number of ants at the starting point of the grid environment map, and each ant starts to search for a path independently, wherein the ant selects the next moving direction and turning angle according to the pheromone concentration and state transition probability of the current grid; S3, when all ants reach the target node, the edge pheromone is updated and the pheromone is volatilized according to the time cost of the path taken by each ant, and it is determined whether the current number of iterations reaches the preset maximum number of iterations. If it reaches it, the next step is performed; if not, S2 is repeated until the preset maximum number of iterations is reached; S4. According to the time cost of the paths taken by the ants in each iteration, the path with the best time cost is selected as the final path.

2. The AGV path planning method based on improving the ant colony algorithm by constructing a time cost function according to claim 1 is characterized in that: Constructing the grid environment map includes: Divide the map into unit grids and represent the map as a two-dimensional grid map. The node set is , the connections between nodes are represented by edge sets It indicates that the ant colony walks in a way that takes the center of each grid of the grid map as the secondary target node, and the size of the grid map is divided according to the size of each AGV; Among them, the horizontal and vertical The relationship is: ； In the formula, Indicates the grid number; Represents the grid length of one unit, Indicates remainder calculation; Indicates rounding up calculation; Respectively indicate the level and vertical The number of rows and columns of the raster map in the direction.

3. The AGV path planning method based on improving the ant colony algorithm by constructing a time cost function according to claim 1 is characterized in that: The state transition probability is the probability that the ant moves from the current grid node Move to the next grid number node The probability is: ； In the formula, is the parameter of pheromone importance, is the parameter of the importance of heuristic information, For Ants The set of currently accessible adjacent nodes, For Node To Node The pheromone concentration, For Node To Node Heuristic information, is the state transition probability, and l is the next node selected by the current node i.

4. The AGV path planning method based on improving the ant colony algorithm by constructing a time cost function according to claim 1, characterized in that: In the process of the independent path search, the Euclidean distance is used as a heuristic function to guide the search direction of the ants; Wherein, the heuristic function is: ； ； In the formula, For Node The Euclidean distance to the target node, For Node To Node Heuristic information, is the horizontal coordinate of the next selected node, is the ordinate of the next selected node, is the horizontal coordinate of the target end point, is the vertical coordinate of the target end point.

5. The AGV path planning method based on improving the ant colony algorithm by constructing a time cost function according to claim 1, characterized in that: The next moving direction and turning angle are selected according to the pheromone concentration and state transition probability of the current grid, including: According to the time cost of the path taken by each ant, the pheromone concentration of the corresponding edge in the grid environment map is updated through the pheromone update cost function, and during each movement, the turning angle is determined according to the vector relationship between the current position and the moving direction.

6. The AGV path planning method based on improving the ant colony algorithm by constructing a time cost function according to claim 5 is characterized in that: The pheromone update cost function is: ； ； ； In the formula, For Ants The total time of the path traveled, is the total cost of straight travel time, is the total cost of the turning time, is the total path length, is the constant speed of AGV, is the turning time per unit angle, is the turning angle, is the total number of turns.

7. The AGV path planning method based on improving the ant colony algorithm by constructing a time cost function according to claim 5, characterized in that: Determining the turning angle includes: Determine the direction change between adjacent nodes in the path, and determine the turning angle based on the vector relationship between the ant's current position and moving direction. Specifically: ； In the formula, is the vector dot product, , are the magnitudes of the vectors, is the turning angle.

8. The AGV path planning method based on improving the ant colony algorithm by constructing a time cost function according to claim 1 is characterized in that: In S3, at the end of each iteration, after each ant completes the path search, the pheromone increment is updated according to the total path cost: ； ； In the formula, For Ants In the The total path time cost in iterations, M is the total number of ants, Q is the pheromone intensity, is the number of nodes in T iterations The total pheromone increment on the edge formed with node j, For Ants In the In the iteration, the node The size of the pheromone concentration update of the edge formed with node j.

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