CN113237489A - Vehicle path planning method based on improved 2-opt ant colony algorithm - Google Patents

Vehicle path planning method based on improved 2-opt ant colony algorithm Download PDF

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CN113237489A
CN113237489A CN202110550951.6A CN202110550951A CN113237489A CN 113237489 A CN113237489 A CN 113237489A CN 202110550951 A CN202110550951 A CN 202110550951A CN 113237489 A CN113237489 A CN 113237489A
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张润发
邱建龙
郭明
崔慧霞
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Abstract

The invention discloses a vehicle path planning method based on an improved 2-opt ant colony algorithm, which comprises the following steps: compared with the classic 2-opt ant colony algorithm, the method has the following improvements: (1) a 2-opt method used for local updating is improved, and a simpler 2-sopt method is provided; (2) the global update rule set range is set to update the route 15% before the iteration, so that premature convergence is avoided, the algorithm running time (3) is reduced, the range of a global update rule constant (P8) is designed, and the relation between the constant and input data is established, so that the update amount of the pheromone is more reasonable. Through the improvement, the optimization capability of the 2-opt ant colony algorithm can be effectively improved, and the algorithm complexity is reduced.

Description

Vehicle path planning method based on improved 2-opt ant colony algorithm
Technical Field
The invention relates to the field of logistics, in particular to a vehicle path planning method based on an improved 2-opt ant colony algorithm.
Background
The Vehicle Routing Problem (VRP) proposed by Dantzig has been a hot spot problem in the field of logistics. In recent years, with the development of society, the circulation of various industries is increased, logistics becomes more important, and the problem of vehicle routing is receiving more and more attention of scholars. The vehicle path problem is generally described as: from a certain logistics center, a plurality of logistics vehicles carry out goods distribution service on a plurality of customers, and information such as positions and demands of the customers is known. It is asked how to plan the vehicle delivery route under certain constraints (vehicle capacity, time window, delivery time, etc.) in order to minimize the delivery cost (money or time or distance, etc.).
The research on the vehicle path problem focuses mainly on the following two aspects: one is the study of VRP variants: many variations of VRP have been derived based on real-life customer, vehicle, time, etc. constraints. Including CVRP considering the same vehicle transportation, and HFVRP considering multiple vehicle transportation; VRPTW taking into account customer delivery time window characteristics; the VRPPD considers the delivery and receiving requirements of the customers at the same time; MDVRPs considering multiple distribution centers; GVRP problems that minimize harmful gas emissions as optimization targets, and the like, in view of environmental protection issues. Secondly, research on a VRP variant solving algorithm, including accurate algorithms such as image column generation and dynamic programming, ensures that the obtained solution is an optimal solution, but the solution time is too long, so that the method is generally only suitable for solving the problem of small number of clients; the algorithm comprises a two-stage algorithm of a construction type algorithm such as a neighbor algorithm, an insertion algorithm and the like, a clustering first route second algorithm and the like, an improved algorithm such as an inter-route algorithm and the like, and the algorithm is widely applied to various VRP variants by virtue of the specialty thereof; finally, the method also comprises a meta-heuristic algorithm which is generally provided by inspiring of various phenomena and natural laws in nature and comprises a genetic algorithm, a particle swarm algorithm, an ant colony algorithm, a simulated annealing algorithm and the like. The algorithm has short running time and is suitable for solving large-scale problems.
The ant colony algorithm was proposed by Marco Dorigo and 1992, and the inspiration mainly comes from foraging behavior of the ant colony. The ant colony, when looking for food, leaves pheromones on the path traveled. When an ant finds food, it returns to the nest along with the pheromone, and the pheromone is left again. When ants go out again, ants are more likely to select paths with high pheromone concentration (short distance). The above steps are repeated in a circulating way to form positive feedback, more and more ants can search for food along the shortest path, and the shortest path from the food is also found. The traditional 2-opt ant colony algorithm has the advantages of strong robustness, intrinsic parallelism, easy combination with other algorithms and the like. But the method also has the defects of easy premature convergence to the local optimal solution, high time complexity of the algorithm and the like, which is a part of the traditional 2-opt ant colony algorithm which needs to be improved urgently.
Disclosure of Invention
The purpose of the invention is as follows: based on the defects, the invention provides the vehicle path planning method based on the improved 2-opt ant colony algorithm, the improved 2-opt algorithm is introduced to reduce the time complexity of the algorithm, the overall updating rule is improved to update pheromones more reasonably, the overall optimizing capability of the algorithm is enhanced, and the situation that the algorithm falls into local optimization is avoided.
The technical scheme is as follows: a vehicle path planning method based on an improved 2-opt ant colony algorithm comprises the following steps.
(1) The algorithm parameters are initialized, the customer information is read and all ants are placed on the distribution centre 1.
(2) Each ant i starts from a distribution center and moves on an unswept node set (all) according to a pseudo-random state transition rulei) An access point is selected, a feasible path R is gradually constructed, and the R is recorded by a path recording table (Route).
(3) And after the ant i constructs the path R, updating all paths passed by the ant i according to the local updating rule.
(4) Number of ants if path construction is completed<Maximum number of ants (max)i) Continuing to execute the step (2); otherwise, executing the step (5).
(5) And (4) optimizing by using a 2-sopt algorithm, and comparing the best result with the optimal path (min (route)) in the iteration, wherein the optimal result is preferably used as min (route).
(6) min (route) and global optimal path set (R)best) (15% of ants), the R is betterbestAnd (5) medium element.
(7) Updating R according to global updating rulebestThe medium path pheromone.
(8) Repeating the steps (2) to (7) until the iteration number reaches the maximum iteration number (iter)max) And obtaining the optimal path after iteration is finished.
Wherein, the 2-sopt method in the step (5) is specifically described as follows:
after each iteration is finished, performing 2-sopt optimization on the optimal route min (route) in the iteration: segmenting the optimal path by taking the distribution center as a boundary; exchanging all node sequences except the distribution center in all road sections, calculating the cost of the road section after each exchange, and finding out the road section with the least cost through comparison; the least expensive path is found by combining the least expensive road segments.
The specific setting method of the global update rule constant range in the step (7) is as follows: first, a constant is set as the number of input customers, 10 runs are performed, and R of the 10 runs is obtainedbestMean (mean), the range of the global update rule constant is: mean/15-mean/18.
The global update policy in step (7) is specifically:
after each iteration is finished, the first 15% of good routes in the iteration are updated according to a global updating formula, wherein the formula is as follows:
Figure DEST_PATH_IMAGE001
wherein τ (I, j) represents the concentration of pheromone in the path from point I to point j, ρ is the volatilization coefficient of pheromone, and cost is the consumption (which can be time, money, distance, etc.) required by the current distance.
Has the advantages that: the invention provides a vehicle path planning method based on an improved 2-opt ant colony algorithm, aiming at the problems that the time complexity is high and the local optimal solution is easy to occur in the traditional 2-opt ant colony algorithm, the improved 2-opt algorithm is introduced to reduce the time complexity of the algorithm, the pheromone can be updated more reasonably by limiting the range of a global updating rule and expanding the applicable route range of the global updating rule, the pseudo-random selection rule of the algorithm is more favorable for selecting a more optimal route, the global optimization searching capability of the algorithm is enhanced, and the algorithm can be prevented from falling into the local optimal.
Description of the drawings.
FIG. 1 is a schematic diagram of a vehicle path planning method of the present invention.
FIG. 2 is a diagram of an example of the operation of the 2-sopt algorithm.
FIG. 3 is a diagram illustrating an example of the operation of the 2-opt algorithm.
FIG. 4 is an example customer information table.
FIG. 5 is an exemplary diagram of an optimal route for the 2-sopt ant colony algorithm.
FIG. 6 is an exemplary graph of the optimal route for the 2-opt ant colony algorithm.
FIG. 7 is an exemplary graph of an optimal path for the bacterial foraging ant colony algorithm.
The specific implementation mode is as follows:
the technical scheme of the invention is further explained by combining the attached drawings.
Fig. 1 shows a vehicle path planning method of the present invention. In the description, matlab simulation software is used for simulation and emulation, as shown in fig. 1, a vehicle path planning method based on an improved 2-opt ant colony algorithm initializes parameters at first, then iterative search is performed, and pheromone is updated by using a local update rule after each ant builds a path through internal circulation; after each iteration of the external loop is completed, R is updatedbestUpdating R with global update rulebestA pheromone. The specific steps are described in detail below.
Step 1, initializing maximum iteration number (Iter)max) Node set not passed (allow)i) Route record table (Route), global optimal path set (R)best) Various parameters such as vehicle information; reading information such as customer position and time requirement; initializing ant colony algorithm basic parameters, such as: the number m of ants, the consumption importance parameter alpha, the heuristic factor beta, all ants are placed in a distribution center, and the like.
Step 2, the ant i starts from the distribution center, if alliIf not, all is done according to the pseudo-random state transition ruleiSelects the next node to be visited and adds this node to its path R and updates the allow if the vehicle meets the requirements (load, gasoline, etc.) of the next visited nodei. If allowiIf the path is empty, representing that the path construction is completed, and adding the path into a path record table Route; if the vehicle condition can not meet the requirement of the next client, the vehicle returnsAnd (4) the distribution center drives a new vehicle to continue distribution.
The pseudo-random state transition rule is as follows:
when the random number r<Given a constant a, according to a probability distribution PsIn all by rouletteiSelecting the next node; when the random number r>If = a, the node with the highest probability is directly selected. PsThe formula of (1) is as follows:
Figure DEST_PATH_IMAGE002
。
where s represents the next node, PsThe probability tau (I, s) representing the selection of the next node represents the required cost on the I-s path, eta (I, s) represents the reciprocal of the pheromone content on the I-s path, alpha represents a cost importance parameter, and beta represents a heuristic factor.
Step 3, after the ant i constructs the path R, the pheromone is reduced according to the local updating rule, the optimization range of the ant colony is expanded, the global searching capability of the algorithm is increased, and the specific formula is as follows:
Figure DEST_PATH_IMAGE003
。
step 4, if the number i of the ants is less than the total number (m) of the ants, the traversal operation of all the ants in the generation is not performed, and the execution is continued from the step 2 until the number of the ants reaches the maximum number of the ants; and if all ants have traversed all the steps, executing the step 5.
And 5, optimizing min (route) by using a 2-sopt algorithm, wherein the specific application is as follows: segmenting the optimal path by taking the distribution center as a boundary; exchanging all node sequences except the distribution center in all road sections, calculating the cost of the road section after each exchange, and finding out the road section with the least cost through comparison; the least expensive path is found by combining the least expensive road segments. Examples are: giving a generation of least cost route 1-2-3-4-1-5-6-7-1, wherein the road sections are 1-2-3-4-1, 1-5-6-7-1; sequentially exchanging (2,3), (2,4), (3,4) in the first segment to find the route with the least cost (assumed to be 1-3-2-4-1), and the second segment (assumed to be 1-5-7-6-1); the final shortest consumption path is 1-3-2-4-1-5-7-6-1.
The optimal value after the optimization is compared with min (route), and the optimal value is more preferably min (route).
The 2-opt algorithm is different from the 2-sopt algorithm in that as shown in fig. 2 and fig. 3, the 2-opt algorithm not only needs to interchange positions of two selected points, but also needs to turn over a path between the two points when running; the 2-sopt algorithm only needs to exchange and select the positions of two points during operation, and the path between the two points does not need to be inverted.
Step 6, mixing min (route) and global optimal path set (R)best) All elements in the group are compared, and the element is better remained in the set RbestIn (1).
Step 7, determining the iteration R of the timebestThen, updating R according to the global updating rulebestThe operation of the step is intended to release more pheromones on a better path, increase the probability of selecting the path by the subsequent generation and form a positive feedback effect. The specific formula is as follows:
Figure 324017DEST_PATH_IMAGE001
where ρ is the pheromone evaporation coefficient. P8 is a global update rule constant, RbestcostIs RbestThe cost of each element in the table.
Step 8, repeatedly executing the steps 2-7 until the iteration times reach the maximum iteration times, and outputting min (R) after the iteration is finishedbest)。
The scheme provided by this implementation is illustrated below by way of example:
for example, a fresh delivery vehicle path model is solved, the model takes the minimum delivery cost as an objective function, and the freshness (quality) at the time of customer reception as an influence factor, and the model is as follows:
Figure DEST_PATH_IMAGE004
Figure DEST_PATH_IMAGE005
wherein m1 represents the number of vehicles actually used, P3 represents the cost of cars such as road and bridge fees, and P4 represents the price of fresh goods; q0 is the quality of fresh product at the beginning, K is a coefficient of variation of fresh product with temperature, and is set to be 1, P5 is the time sensitivity coefficient of fresh product, and t isiThe time spent on transporting the fresh products from the starting point to the client i; y isik1 or 0, 1 means that the k-th vehicle serves customer i, and 0 is the opposite; DEiThe order is made for the ith customer, Cap represents vehicle capacity, and P6 is discharge speed (assuming that discharge time is a linear function of discharge quantity).
The objective function (1) represents the objective of minimizing the distribution cost, wherein
Figure DEST_PATH_IMAGE006
Represents the running cost of the cold-chain logistics vehicle,
Figure DEST_PATH_IMAGE007
representing the loss of the cost in the transportation process of the fresh products,
Figure DEST_PATH_IMAGE008
representing the punishment cost of each client soft time window; the constraint function (2) represents that the freshness of the customer i at the time of reception is to satisfy the requirement; the constraint function (3) indicates that the vehicle traffic is less than the vehicle capacity; the constraint function (4) indicates that only 1 vehicle can be served by one client; constraint function (5) indicates that it must be guaranteed that all customers must be delivered; the constraint functions (6) (7) represent the relationship between variables; the constraint function (8) represents a delivery time relationship; the constraint function (9) indicates that every vehicle that departs from the distribution center will return to the distribution center.
Consideration of ET by soft time window penalty functioni(customer earliest allowed arrival time of goods), ETi d(customer expected earliest arrival time of goods), LTi d(customer expected latest arrival time of goods))，LTi(customer latest allowed goods arrival time) and the goods arrival time is ti. The formula is as follows:
Figure DEST_PATH_IMAGE009
。
the cold chain vehicle is provided with a refrigerator, so the fuel oil use cost is not only considered for the distance cost but also considered for the refrigeration cost. In addition, in order to better preserve the fresh products in the transportation process, a driver usually precools the fresh products before loading the fresh products, and the precooling time is generally 45 min. And the refrigerator is only served in the customer distribution process, and the refrigerator does not work when returning to the distribution center. According to the recent diesel oil price, the fixed diesel oil price is 5.4 yuan/L. The fuel cost is as follows:
Figure DEST_PATH_IMAGE010
。
p1 represents the fuel utilization efficiency of the refrigerator, and the unit is L/h; 1 represents a distribution center, (n-1) is the number of customers, and m represents the maximum number of vehicles; i, j represents a customer number, k represents a vehicle number; xi,j,kIs 1 or 0, 1 represents the kth vehicle passing the route (i, j), and 0 is the opposite; di,jRepresents the distance between customer i and customer j; v represents an average speed during the vehicle shifting travel; p2 represents the fuel consumption per kilometer of the engine in units of dollars/km.
The customer data is shown in figure 4.
The simulation data is set as follows: a fresh logistics distribution company has several refrigerated vehicles with Cap =15t load, and provides distribution service for 23 distribution customers, and coordinates, demand and soft time window of the distribution center and the customers are shown in fig. 4. The number of the distribution center is 1, and the numbers of the customers are 2-24 respectively. The using cost of each cold-chain logistics vehicle is 100 yuan, the average speed V =35km/h of the variable-speed running of the vehicle, the oil consumption efficiency P1=2.45L/h of the refrigerating machine, the oil consumption of an engine per kilometer is 0.22L, P2=1.2 yuan/km, the cost coefficient P3=0.7 yuan/km of the vehicle such as road and bridge cost, the price P4=6 yuan/kg of fresh products, the time sensitivity coefficient P5=1/310 of the fresh products, the maximum time penalty cost M3=200 yuan, the maximum penalty cost M4=500 yuan, and the unloading speed P6=0.25 t/h. The work hours of the distribution center are 6:30 in the morning.
The algorithm parameters are set as follows: the 2-opt ant colony algorithm has the same data settings as the 2-sopt ant colony algorithm, and comprises the following steps: the coefficients α =1, β =3, the number of loop generations is 300, the number of ants is 24, the pseudo-random constant P7=0.5, the global update rule constant P8 is set to 60 as in the above rule, and the pheromone evaporation coefficient ρ =0.85 in the pseudo-random state transition rule. The parameters of the bacterial foraging ant colony algorithm are set as alpha =1, beta =5, the number of cycle generations is 300, the number of ants is 24, and the pheromone evaporation coefficient rho = 0.5.
In 21 experiments on my notebook computer (8gRAM, CPU i7-5500U), the data obtained by comparing the three algorithms with the minimum cost, average running time and standard deviation of cost are shown in the following table (the obtained data only retain one decimal fraction):
Figure DEST_PATH_IMAGE011
。
as can be seen from the above table, the comprehensive cost optimum, the average value and the average running time obtained by solving the bacterial foraging ant colony algorithm are far inferior to the 2-sopt ant colony algorithm and the 2-opt ant colony algorithm in value standard deviation; the minimum cost, average cost, and minimum runtime of the 2-sopt ant colony algorithm are better than the 2-opt ant colony algorithm, but the value standard deviation is worse than the 2-opt ant colony algorithm. This shows that the 2-sopt ant colony algorithm is superior to the 2-opt ant colony algorithm in the aspects of optimizing capability, optimizing effect and time consumption, but is inferior to the 2-opt ant colony algorithm in the aspect of stability.
As can be seen from fig. 5, the number of vehicles used and the optimal distribution route obtained by the 2-sopt ant colony algorithm are as follows:
delivery vehicle: 4 vehicles
Distribution route 1: 1-4-3-16-19-15-20-23-1
Distribution route 2: 1-5-12-2-9-6-1
Distribution route 3: 1-11-10-22-14-17-1
The distribution route 4: 1-7-21-13-8-18-24-1.
As can be seen from fig. 6, the number of vehicles used and the optimal distribution route obtained by the 2-opt ant colony algorithm are:
delivery vehicle: 4 vehicles
Distribution route 1: 1-4-14-12-15-19-18-24-1
Distribution route 2: 1-7-23-13-20-2-8-1
Distribution route 3: 1-3-9-5-21-22-1
The distribution route 4: 1-10-11-16-6-17-1.
As can be seen from fig. 7, the number of vehicles used and the optimal distribution route obtained by the bacterial foraging ant colony algorithm are as follows:
delivery vehicle: 4 vehicles
Distribution route 1: 1-24-13-4-10-9-16-1
Distribution route 2: 1-14-3-6-18-17-1
Distribution route 3: 1-7-5-21-20-19-8-15-1
The distribution route 4: 1-22-11-23-12-2-1.
The experimental result shows that compared with the 2-opt ant colony algorithm, the 2-sopt ant colony algorithm makes certain progress in the aspects of the minimum distribution cost, the average distribution cost and the average running time, and the optimization capability and the search capability of the simpler 2-sopt algorithm are better than those of the traditional 2-opt algorithm. As can be seen from Table 2, the 2-sopt ant colony algorithm is better than the 2-opt ant colony algorithm in the aspects of optimizing ability and algorithm time complexity. Of course, the optimization capability, time complexity and stability of the 2-sopt ant colony algorithm are far superior to those of the bacterial foraging ant colony algorithm.

Claims (4)

1. A vehicle path planning method based on an improved 2-opt ant colony algorithm is characterized by comprising the following steps:
(1) initializing algorithm parameters, reading customer information, and placing all ants on a distribution center 1;
(2) each ant i starts from a distribution center and moves on an unswept node set (all) according to a pseudo-random state transition rulei) Selecting the next access point, gradually constructing a feasible path R, and recording the path with a path record table (R)outer) record R;
(3) after the ants i construct the path R, updating all paths passed by the ants i according to the local updating rule;
(4) number of ants if path construction is completed<Maximum number of ants (max)i) Continuing to execute the step (2); otherwise, executing the step (5);
(5) optimizing by using a 2-sopt algorithm, and comparing the best result with the optimal path (min (route)) in the iteration, wherein the optimal result is used as min (route);
(6) min (route) and global optimal path set (R)best) (15% of ants), the R is betterbestMiddle element;
(7) updating R according to global updating rulebestA medium path pheromone;
repeating the steps (2) to (7) until the iteration number reaches the maximum iteration number (iter)max) And obtaining the optimal path after iteration is finished.
2. The vehicle path planning method based on the improved 2-opt ant colony algorithm as claimed in claim 1, wherein the 2-sopt method in the step (5) is specifically:
after each iteration is finished, performing 2-sopt optimization on the optimal route min (route) in the iteration: segmenting the optimal path by taking the distribution center as a boundary; exchanging all node sequences except the distribution center in all road sections, calculating the cost of the road section after each exchange, and finding out the road section with the least cost through comparison; the least expensive path is found by combining the least expensive road segments.
3. The vehicle path planning method based on the improved 2-opt ant colony algorithm as claimed in claim 1, wherein the specific setting method of the global update rule constant range in the step (7) is as follows: first, a constant is set as the number of input customers, 10 runs are performed, and R of the 10 runs is obtainedbestMean value (mean) of, the range of the global update rule constant P8 is: mean/15-mean/18.
4. The method for planning the vehicle path based on the improved 2-opt ant colony algorithm as claimed in claim 1, wherein the global update strategy in the step (7) is specifically as follows:
after each iteration is finished, the first 15% of good routes in the iteration are updated according to a global updating formula, wherein the formula is as follows:
τ(I,j) = ρτ(I,j) + P8 / Rbestcost
wherein tau (I, j) represents the concentration of path pheromone between point I and point j, rho is pheromone volatilization coefficient, P8 is global updating constant, RbestcostThe consumption (which can be time, money, distance, etc.) required for the current distance.
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CN116843262B (en) * 2023-06-16 2024-02-06 山东大舜医药物流有限公司 Intelligent medicine logistics distribution path planning method based on big data
CN118332766A (en) * 2024-03-15 2024-07-12 南京信息工程大学 Access constraint multi-logistics vehicle scheduling method based on adjacent edge diffusion ant colony algorithm

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