CN111709560A - Method for solving vehicle path problem based on improved ant colony algorithm - Google Patents

Method for solving vehicle path problem based on improved ant colony algorithm Download PDF

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CN111709560A
CN111709560A CN202010474638.4A CN202010474638A CN111709560A CN 111709560 A CN111709560 A CN 111709560A CN 202010474638 A CN202010474638 A CN 202010474638A CN 111709560 A CN111709560 A CN 111709560A
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徐海涛
浦攀
段凤
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Abstract

The invention discloses a method for solving a vehicle path problem based on an improved ant colony algorithm, which is applied to the design and optimization of the vehicle path problem and mainly relates to two fields of logistics vehicle scheduling and swarm intelligence optimization. The optimization process of the method comprises the following steps: the method comprises the steps of firstly partitioning distribution points by using an improved K-means algorithm, then constructing an initial solution for each region by using an ant colony algorithm, then performing global optimization by using an optimal path crossing strategy in a genetic algorithm and performing local optimization by using a classical 2-Opt algorithm, and finally performing pheromone updating operation. The method disclosed by the invention tests the disclosed data set, and proves that the method is real and effective in designing and optimizing the vehicle path problem.

Description

Method for solving vehicle path problem based on improved ant colony algorithm
The technical field is as follows:
the invention belongs to the field of vehicle scheduling and swarm intelligence calculation, and relates to a method for solving a vehicle path problem based on an improved ant colony algorithm.
Background art:
with the continuous development of socioeconomic of China, the logistics expenditure of the whole society is more and more. According to survey reports, the logistics cost of China accounts for about 20% of the proportion of GDP, while the logistics cost of Singapore accounts for about 10.1%, 10.5%, 11.4% and 13.9% of the proportion of GDP in British, American and Japan, which shows that the logistics cost of China is very high and has great improvement space. And reasonable vehicle route planning can greatly reduce logistics cost and promote enterprise operation efficiency.
Algorithms for solving the problem of vehicle paths are mainly divided into an accurate algorithm, a traditional heuristic algorithm and a modern heuristic algorithm. The precise algorithm is divided into: direct tree search algorithm, dynamic programming algorithm and integer linear programming method. The accurate algorithm running time is increased sharply along with the increase of the scale of the client node, so that the method is not suitable for the problems of medium and large scale. The traditional heuristic algorithm comprises: a saving algorithm, a scanning algorithm, a two-stage algorithm, a nearest neighbor algorithm, etc. Modern heuristic algorithms include: neural networks, simulated annealing algorithms, genetic algorithms, ant colony algorithms, tabu searches, and the like. Although the heuristic algorithm cannot solve the accurate solution, the method is very suitable for the design and optimization of the vehicle path problem because the optimal solution can be found quickly and efficiently.
The ant colony Algorithm (ACO) was proposed by MarcoDori in 1992 in his doctor's paper, who observed ants to search for food collectively, and found that ants collaborated with each other by exchanging pheromones with each other to find the best path to reach the food location. In the invention, the ant colony algorithm is used for generating an initial path, then the intersection operation of the genetic algorithm is used for optimizing the initial path, and the local optimization operation of the path is further optimized by using 2-opt.
The invention content is as follows:
the invention provides a vehicle path problem method based on an improved ant colony algorithm. It is intended to improve the efficiency of solving the problem of the vehicle path.
The technical scheme adopted for solving the technical problem comprises the following specific steps:
and (1) carrying out region division on the client nodes by using an improved K-means clustering algorithm.
And (2) initializing basic parameters of the ant colony algorithm, placing the ant colony at the yard and setting the yard as an initial node.
And (3) each ant represents a vehicle and starts from the initial node, the next client node to be visited is selected according to the transition probability, and the client node visited by the ant is added into the taboo list. And after the ants visit all the client nodes, returning to the initial node, and calculating the length of the selected path.
And (4) after all ants complete the search, selecting two paths with the shortest length, and performing optimal path crossing operation to obtain a plurality of optimized paths.
And (5) finding out an optimal path I from the multiple optimal paths, and performing local optimization by using an improved 2-Opt algorithm to obtain and record the optimal path of the iteration.
And (6) after one iteration is completed, updating the pheromone concentration of each path.
And (7) repeating the steps (2) to (6) until the set iteration times are reached, finding out the optimal path of each iteration, and obtaining the global optimal path.
Preferably, the improved K-means clustering algorithm in step (1) specifically comprises the following steps:
1-1. determining the K value in K-means using equation (1):
Figure BDA0002515440930000021
wherein: f represents a length function, related to the value of k, which is determined when the minimum value of F is determined. m isiMean value representing cluster center, m is mean value of all data points, XiAre some of the column cluster centers.
1-2, dividing the belonged areas of different points by using a formula (2):
Figure BDA0002515440930000022
preferably, the step (4) of selecting two paths with the shortest length to perform the optimal path crossing operation specifically includes:
4-1. in one iterationEnding, selecting the best two paths R1And R2From R1And R2Two points c are respectively randomly selected1And c2Set the initial threshold t to 1 and then generate a random number r ∈ [0,1]. If r is less than or equal to t, selecting the optimal path crossing strategy one: i.e. c, without taking the vehicle load into account1And c2Are respectively inserted into the paths R1And R2Where the objective function can be minimized; if r > t, selecting the optimal path crossing strategy two: i.e. considering the vehicle load, c1And c2Are respectively inserted into the paths R1And R2Where the objective function can be minimized.
And 4-2, running for 10 times, finding out and recording the optimal path in all the running paths.
And 4-3, reducing the initial threshold value t by 10%, continuously running the program for 10 times, finding the optimal path and recording until t is equal to 0.1.
And 4-4, finding out the optimal solution in all the optimal paths as a final optimal path I.
Preferably, the local optimization performed by using the improved 2-Opt algorithm in the step (5) is specifically as follows:
and 5-1, taking out the final optimal path I obtained in the step (4), and dividing the optimal path I according to different vehicles to form an optimal path for each vehicle.
And 5-2, independently using 2-Opt for the optimal path of each vehicle, namely sequentially exchanging positions of the first customer node and other customer nodes, and then sequentially exchanging positions of the second customer node and the subsequent customer nodes until all the customer nodes are completely exchanged, and finding out the optimal path II of each vehicle.
And 5-3, comparing the optimal path II obtained after each vehicle is locally optimized with the original optimal path of the vehicle. And if the optimized optimal path II is better than the original optimal path of the vehicle, using the optimized optimal path II, and otherwise, keeping the original optimal path unchanged.
Preferably, the updating of the pheromone concentration of each path in step (6) is as follows:
Figure BDA0002515440930000031
wherein:
Figure BDA0002515440930000032
is the pheromone concentration between pathways (i, j);
Figure BDA0002515440930000033
is the path (i, j) initial pheromone concentration; ρ is a constant representing the rate of pheromone volatilization; k and K respectively represent the number of vehicles on the path and the total number of vehicles on all paths;
Figure BDA0002515440930000041
is the increase of the path pheromone.
The invention has the following beneficial effects:
the method disclosed by the invention tests the disclosed data set, and proves that the method is real and effective in designing and optimizing the vehicle path problem.
The invention compares the ant colony algorithm which adopts the classical ant colony algorithm and the improved ant colony algorithm of the invention, and fig. 3 and fig. 4 are respectively an optimal solution and an average solution comparison diagram based on different data sets. The result shows that the ant colony algorithm improved by the invention is real and efficient in solving the optimal solution of the vehicle path. Fig. 5 is a convergence diagram of the improved ant colony algorithm, and as can be seen from the convergence curve in the diagram, the algorithm can converge quickly and then tend to stabilize.
Description of the drawings:
FIG. 1 is a flow chart of a vehicle path optimization method implementation provided by the present invention for embodiment 1;
FIG. 2 is a flow chart of the optimal path crossing strategy provided by the present invention for embodiment 1;
FIG. 3 is a comparison of the best results before and after improvement of the algorithm based on different data sets provided by the present invention for example 1;
FIG. 4 is a comparison graph of the average results before and after improvement of the algorithm based on different data sets provided by the present invention for example 1;
FIG. 5 is a graph of improved ant colony algorithm convergence provided by the present invention for example 1;
the specific implementation mode is as follows:
the technical scheme of the invention is further explained by combining the attached drawings.
FIG. 1 is a vehicle path optimization flow diagram of the present invention. In the present invention, a simulation experiment was performed using Matlab language. As shown in fig. 1, firstly, a client node area is reasonably divided by using an improved K-means algorithm, then basic parameter variables are initialized, an initial path is generated, then an optimal path crossing strategy is selected for optimization, and finally 2-opt local optimization is used. And (4) after each iteration is finished, counting the optimal path, updating the pheromone, and then performing the next iteration until the preset times are reached.
The following detailed steps are carried out:
(1) and carrying out region division on the client nodes by using an improved K-means clustering algorithm.
The K value in K-means is determined using the following formula:
Figure BDA0002515440930000051
wherein: f represents a length function, related to the value of k, which is determined when the minimum value of F is determined. m isiMean value of cluster centers, m is mean value of all data points, XiAre some of the column cluster centers.
The areas of the different points are divided using the following formula:
Figure BDA0002515440930000052
(2) initializing basic parameters of the ant colony algorithm, placing the ant colony at the train yard and setting the train yard as an initial node. Manually setting parameters such as: ant number, heuristic factor, iteration times and initial node.
(3) Each ant represents a vehicle and starts from the initial node, the next client point to be visited is selected according to the transition probability, and the client nodes visited by the ants are added into the taboo list. The next accessed client node is selected by the following formula.
Figure BDA0002515440930000053
Wherein p isij(k) Denotes the probability of selecting client j as the next access point for client i, τ(i,j)And η(i,j)Pheromone concentration and route visibility representing routes between customers i and j, respectively, α and β represent the importance of pheromone concentration and route visibility.
(4) After all ants complete the search, two paths with the shortest length are selected for optimal path crossing operation, and fig. 2 is a flow chart of an optimal path crossing strategy.
At the end of an iteration, the best two paths R are selected1And R2From R1And R2Two points c are respectively randomly selected1And c2Set the initial threshold t to 1 and then generate a random number r ∈ [0,1]. If r < ═ t, then the optimal path intersection strategy one is selected, i.e. c will be chosen without considering the vehicle load1And c2Are respectively inserted into the paths R1And R2Where the objective function can be minimized. If r > t, then the optimal path intersection strategy two is selected, i.e. c is taken into account for the vehicle load1And c2Are respectively inserted into the paths R1And R2Where the objective function can be minimized.
And (5) running the program for 10 times, finding out and recording the optimal path in all the running paths. Then, the value of t is reduced by 10%, and the program continues to run 10 times, finds the optimal path and records until t is 0.1. And finding out the optimal solution in the optimized path as the optimal path.
(5) And finding out the optimal path from all paths, and performing local optimization by using an improved 2-Opt algorithm to obtain and record the optimal path of the iteration. The method comprises the following specific steps:
firstly, the optimal path obtained in the step (4) is taken out, and the optimal path is divided according to different vehicles to form a single path for one vehicle.
Then, the 2-Opt is independently used for the path of each vehicle, namely, the first customer node sequentially exchanges positions with other customer nodes, and then the second node sequentially exchanges positions with the following nodes until all the nodes are exchanged, so that the optimal path is found out.
And finally, comparing the optimal path obtained after each vehicle is locally optimized with the original path. If the optimized path is better than the original path, the optimized path is used, otherwise, the original path is kept unchanged.
(6) After one iteration is completed, the pheromone concentration of each path is updated.
The pheromone is updated using the following formula:
Figure BDA0002515440930000061
wherein:
Figure BDA0002515440930000062
is the pheromone concentration between pathways (i, j);
Figure BDA0002515440930000063
is the path (i, j) initial pheromone concentration; ρ is a constant representing the rate of pheromone volatilization; k and K respectively represent the number of vehicles on the path and the total number of vehicles on all paths;
Figure BDA0002515440930000064
is the increase of the path pheromone.
(7) And (5) repeating the step (2) to the step (6) until the set iteration times are reached, and finding out the optimal path of each iteration to obtain the global optimal path.
Through simulation experiments, the ant colony algorithm improved by the classical ant colony algorithm and the invention is compared, and fig. 3 and 4 are respectively an optimal solution and an average solution contrast diagram based on different data sets. The result shows that the ant colony algorithm improved by the invention is real and efficient in solving the optimal solution of the vehicle path. Fig. 5 is a convergence diagram of the improved ant colony algorithm, and as can be seen from the convergence curve in the diagram, the algorithm can converge quickly and then tend to stabilize.

Claims (5)

1. A method for solving a vehicle path problem based on an improved ant colony algorithm is characterized by comprising the following specific steps:
step (1) using an improved K-means clustering algorithm to divide the client nodes into regions;
initializing basic parameters of an ant colony algorithm, placing the ant colony at a train yard and setting the train yard as an initial node;
step (3), each ant represents a vehicle and starts from an initial node, a next client node to be visited is selected according to the transition probability, and the client node visited by the ant is added into a taboo list; after the ants finish visiting all the client nodes, returning to the initial node, and calculating the length of the selected path;
after all ants finish searching, selecting two paths with the shortest length, and performing optimal path crossing operation to obtain a plurality of optimized paths;
step 5, finding out an optimal path I from the multiple optimal paths, and performing local optimization by using an improved 2-Opt algorithm to obtain and record an optimal path of the iteration;
after one iteration is completed, updating the pheromone concentration of each path;
and (7) repeating the steps (2) to (6) until the set iteration times are reached, finding out the optimal path of each iteration, and obtaining the global optimal path.
2. The method for solving the vehicle path problem based on the improved ant colony algorithm as claimed in claim 1, wherein the improved K-means clustering algorithm in the step (1) comprises the following specific steps:
1-1. determining the K value in K-means using equation (1):
Figure FDA0002515440920000011
wherein: f represents a length function, and is related to a k value, and when the minimum value of F is determined, the k value is also determined; m isiMean value representing cluster center, m is mean value of all data points, XiAre some of the column cluster centers;
1-2, dividing the belonged areas of different points by using a formula (2):
Figure FDA0002515440920000012
3. the method for solving the vehicle path problem based on the improved ant colony algorithm according to claim 2, wherein the step (4) of selecting the two paths with the shortest length to perform the optimal path crossing operation specifically comprises the following steps:
4-1. at the end of an iteration, the best two paths R are selected1And R2From R1And R2Two points c are respectively randomly selected1And c2Deleting, setting initial threshold t to 1, and generating random number r ∈ [0,1](ii) a If r is less than or equal to t, selecting the optimal path crossing strategy one: i.e. c, without taking the vehicle load into account1And c2Are respectively inserted into the paths R1And R2Where the objective function can be minimized; if r > t, selecting the optimal path crossing strategy two: i.e. considering the vehicle load, c1And c2Are respectively inserted into the paths R1And R2Where the objective function can be minimized;
4-2, running for 10 times, finding out and recording the optimal path in all the running obtained paths;
4-3, reducing the initial threshold value t by 10%, continuously running the program for 10 times, finding out the optimal path and recording until t is 0.1;
and 4-4, finding out the optimal solution in all the optimal paths as a final optimal path I.
4. The method for solving the vehicle path problem based on the improved ant colony algorithm as claimed in claim 3, wherein the local optimization using the improved 2-Opt algorithm in the step (5) is specifically:
5-1, taking out the final optimal path I obtained in the step (4), and dividing the optimal path I according to different vehicles to form a vehicle with an optimal path;
5-2, independently using 2-Opt for the optimal path of each vehicle, namely sequentially exchanging positions of a first customer node and other customer nodes, and then sequentially exchanging positions of a second customer node and a subsequent node until all the customer nodes are exchanged, and finding out the optimal path II of each vehicle;
5-3, comparing the optimal path II obtained after each vehicle is locally optimized with the original optimal path of the vehicle; and if the optimized optimal path II is better than the original optimal path of the vehicle, using the optimized optimal path II, and otherwise, keeping the original optimal path unchanged.
5. The method for solving the vehicle path problem based on the improved ant colony algorithm according to claim 4, wherein the pheromone concentration of each path is updated in the step (6) as follows:
Figure FDA0002515440920000031
wherein:
Figure FDA0002515440920000032
is the pheromone concentration between pathways (i, j);
Figure FDA0002515440920000033
is the path (i, j) initial pheromone concentration; ρ is a constant representing the rate of pheromone volatilization; k and K respectively represent the number of vehicles on the path and the total number of vehicles on all paths;
Figure FDA0002515440920000034
is the increase of the path pheromone.
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