Multi-logistics vehicle cooperation method with transportation limitation based on pheromone sharing ant colony system

Abstract

The invention discloses a multi-logistics vehicle cooperation method with transportation limitation based on a pheromone sharing ant colony system, and the method comprises the following steps: firstly, obtaining task and vehicle information, constructing a cost and authority matrix, and building a synchronous optimization model; secondly, setting ant colony parameters, and performing greedy initialization on an information matrix; thirdly, initializing a plurality of ant colonies and distributing a task taboo table; then, the ant colony selects tasks through a state transition equation according to the authority and the taboo table, winning ants are screened according to the cost probability, pheromones are updated, and a preliminary scheme is formed; secondly, optimizing the scheme by using a local search algorithm fused by 2-opt and point migration; then, evaluating an adaptive value, updating a global optimal scheme and global pheromones, and sharing the pheromones to adjacent edges; and finally, iteration is carried out until convergence, and a final cooperation scheme is output. According to the invention, efficient scheduling under transportation limitation is realized, and the cost difference between vehicles is reduced while the total cost is minimized.

Description

Technical Field

[0001] This invention relates to the field of logistics scheduling technology, and in particular to a collaborative method for multiple logistics vehicles with transportation constraints based on a pheromone-sharing ant colony system. Background Technology

[0002] In real-world logistics and distribution, numerous transportation constraints exist. For example, fresh food can often only be delivered by refrigerated trucks, hazardous chemicals by specialized hazardous materials trucks, and medical supplies by specialized medical supply trucks. However, existing logistics vehicle scheduling optimization models generally lack systematic modeling of these transportation constraints, making it difficult to accurately describe the differentiated transportation limitations imposed by logistics tasks on vehicles. This limits the applicability of existing models in practical applications. Due to the introduction of transportation constraints, multi-logistics collaborative optimization not only faces the optimization of logistics task allocation and the subsequent transportation sequence but also the need to satisfy the transportation constraints of the logistics tasks. This leads to existing optimization algorithms encountering problems such as difficulty in constructing feasible transportation paths, low solution efficiency, low accuracy, and susceptibility to local optima.

[0003] Ant Colony Optimization (ACO), a population-based metaheuristic algorithm, is widely used in path planning problems due to its strong global search diversity and low susceptibility to local optima. However, when solving multi-vehicle collaborative scheduling problems with transportation constraints, ACO faces challenges such as difficulty in constructing feasible paths and uneven distribution of logistics tasks. Furthermore, its existing pheromone update rules can lead to excessively rapid accumulation of pheromones on the edges of optimal paths, resulting in loss of diversity and ultimately preventing ACO from finding high-quality optimal solutions. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a collaborative method for multiple logistics vehicles with transportation constraints based on a pheromone-sharing ant colony system, thereby solving the technical problem of insufficient optimization of collaborative multi-logistics vehicles with transportation constraints in existing technologies.

[0005] This invention provides a method for multi-logistics vehicle collaboration with transportation constraints based on a pheromone-sharing ant colony system, comprising the following steps:

[0006] Step 1: Obtain logistics task information and logistics vehicle information, construct a transportation cost matrix and a transportation permission matrix, and establish a multi-logistics vehicle collaborative optimization model with transportation restrictions;

[0007] Step 2: Set the ant colony system parameters and initialize the pheromone matrix using a greedy algorithm;

[0008] Step 3: Initialize multiple ant colonies and assign a logistics task taboo list to each ant colony; each ant colony contains several ants, where the number of ants is the same as the number of logistics vehicles;

[0009] Step 4: Each ant in the ant colony obtains a task set based on the transportation permission matrix and the logistics task taboo table. It selects an intended task through the state transition equation and selects a winning ant from all the ants that have selected an intended task based on the probability selection mechanism based on transportation cost. The intended task selected by the winning ant is added to its transportation path and logistics task taboo table. Other ants abandon the current round of transportation, call the local pheromone update rule, update the pheromone on the edge traversed by the winning ant, and repeat Step 4 until the current task is completed, forming a preliminary collaborative scheme.

[0010] Step 5: Locally optimize the initial cooperative scheme by combining 2-opt and point migration local search algorithms to obtain the optimized cooperative scheme; repeat steps 4 and 5 until all ant colonies have obtained the optimized cooperative scheme.

[0011] Step 6: Evaluate the fitness value of the optimized cooperative scheme for each ant colony, update the globally optimal cooperative scheme, and perform a global pheromone update on the edges in the globally optimal cooperative scheme;

[0012] Step 7: Share the pheromone on each edge in the globally optimal cooperative solution to the adjacent edges;

[0013] Step 8: Repeat steps 3 to 7 until the iteration terminates, and obtain the final globally optimal collaborative solution as the multi-logistics vehicle collaborative solution.

[0014] Furthermore, in step 1, the constructed transportation cost matrix is ​​as follows:

[0015] D=[d ij ] (n+1)×(n+1) ;

[0016] In the formula, d ij n represents the transportation cost from logistics task or warehouse i to logistics task or warehouse j; i and j are the sequence numbers of logistics tasks or warehouses; n is the total number of logistics tasks.

[0017] Furthermore, in step 1, the constructed transportation permission matrix is ​​as follows:

[0018] A=[a ik ] (n+1)×m ;

[0019] In the formula, a ik The transportation authority of logistics vehicle k to logistics task or warehouse i, with a value of 1 or 0; m is the number of logistics vehicles; n is the total number of logistics tasks.

[0020] Furthermore, the multi-logistics vehicle collaborative optimization model is specifically as follows: given several logistics tasks, several logistics vehicles, and a warehouse; the city map is described as a completely undirected graph; each logistics task must be transported and can only be transported once by a logistics vehicle with the required transport permissions; logistics vehicles can only transport logistics tasks with the required transport permissions; logistics vehicles must depart from the warehouse and ultimately return to the warehouse; the optimization objective function is:

[0021] ;

[0022] ;

[0023] In the formula, f is the fitness value; k, k1, and k2 are the serial numbers of the logistics vehicles; m is the number of logistics vehicles; Route k , , Let V represent the transportation routes of logistics vehicles k, k1, and k2, respectively; V is the set of all logistics tasks and warehouses; depot is the logistics warehouse; C(Route) k ) is the transportation route k The transportation cost; i is the sequence number of the logistics task or warehouse; a ik This defines the transportation permissions for logistics vehicle k to logistics tasks or warehouse i.

[0024] Furthermore, in step 2, the pheromone matrix is:

[0025] P=[p ij ] (n+1)×(n+1) ;

[0026] In the formula, p ij The pheromone concentration between logistics task or warehouse i and logistics task or warehouse j; i and j are the sequence numbers of logistics tasks or warehouses; n is the total number of logistics tasks.

[0027] Furthermore, in step 4, the state transition equation is:

[0028] ;

[0029] In the formula, j represents the selected intended logistics task; i represents the current sequence number of the logistics task or warehouse; l represents the sequence number of the candidate logistics task; p il η il Let be the pheromone concentration and heuristic information between the current logistics task or warehouse i and the candidate logistics task l, respectively; α is a parameter controlling the importance of pheromones; β is a parameter controlling the importance of heuristic information; q is a random variable uniformly distributed between [0,1]; q0 is a predefined parameter, and 0≤q0≤1; J is the logistics task selected from the candidate logistics task set by the roulette wheel selection method; Sk This is a set of candidate logistics tasks.

[0030] Furthermore, in step 5, the specific process of the local search algorithm that integrates 2-opt and point migration is as follows:

[0031] Step 51: Optimize each path in the preliminary collaboration scheme using 2-opt. Specifically, select two different task nodes on the path in turn, reverse the path segment between the two nodes, and retain the current reversal result if the path transportation cost is reduced after reversal. Repeat Step 51 until the transportation cost can no longer be reduced.

[0032] Step 52: Optimize routes through point migration. Specifically, select the route with the highest transportation cost, and determine the logistics tasks to be migrated from this route. The specific formula is:

[0033] ;

[0034] In the formula, i is the sequence number of the logistics task; i move For logistics tasks awaiting relocation; Route max The route with the highest transportation cost; For Route max The new transport route after removing task i; C(Route) max ) for Route max Transportation costs; for Transportation costs;

[0035] The optimal ant for receiving the logistics task to be migrated is determined by the following formula:

[0036] ;

[0037] In the formula, k is the ant's index; i move For logistics tasks to be relocated; k target To receive logistics tasks i move The optimal ant; k max For transport routes max The corresponding ant; This corresponds to the value in the transportation permission matrix; Route k The transport path constructed for ant k; C(Route) k ) is the transportation route k Transportation costs; To make task i move Insert into path Route k The route cost after the position that minimizes the increase in transportation costs;

[0038] If the maximum transportation cost of the new collaborative solution after the logistics task migration is less than the maximum transportation cost of the original collaborative solution, then retain the current migration result and repeat step 52 until the maximum transportation cost cannot be reduced.

[0039] Furthermore, in step 6, the specific method for updating the globally optimal cooperative solution is as follows:

[0040] When the fitness value of the current globally optimal collaborative solution is greater than the fitness value of the current optimized collaborative solution, the optimized collaborative solution will be adopted as the updated globally optimal collaborative solution.

[0041] Furthermore, in step 6, the update formula for globally updating the pheromone of the edges in the globally optimal cooperative solution is as follows:

[0042] ;

[0043] In the formula, i and j are the sequence numbers of the logistics task or warehouse; p ij The pheromone concentration between logistics task or warehouse i and logistics task or warehouse j; e ij Let i be the edge between logistics task or warehouse i and logistics task or warehouse j; For pheromone increment, , where f is the fitness function, gbest is the globally optimal cooperative scheme, and γ is the global pheromone evaporation rate.

[0044] Furthermore, in step 7, the sharing formula for pheromone sharing to adjacent edges is:

[0045] ;

[0046] In the formula, i is the logistics task or warehouse number in the globally optimal multi-vehicle collaborative scheme; R is the number of pheromone shared. Let R be the set of R logistics tasks or warehouses that minimize transportation costs originating from logistics task or warehouse i; l is... The logistics task or warehouse sequence number in the data; γ is the global pheromone evaporation rate; p il The pheromone concentration between logistics task or warehouse i and logistics task or warehouse l.

[0047] The beneficial effects of this invention are:

[0048] This method can quickly find the optimal multi-vehicle collaborative scheduling scheme while meeting the transportation constraints of each logistics task. It minimizes the transportation costs of all logistics vehicles while balancing the transportation costs among them, thereby reducing the differences in transportation costs between logistics workshops.

[0049] This invention designs a probabilistic selection mechanism based on transportation costs, which effectively balances the transportation costs among logistics vehicles while minimizing the total transportation cost of all logistics vehicles, reducing the differences in transportation costs between logistics workshops. This invention optimizes the collaborative scheme by integrating a novel local search algorithm combining 2-opt and point migration. It utilizes 2-opt intra-path optimization to eliminate path intersections and reduce single-path costs, and reduces the maximum path transportation cost through point migration inter-path optimization, thereby significantly improving the accuracy of the solution. This invention employs a pheromone sharing mechanism, sharing the pheromone on each edge of the globally optimal collaborative scheme to its adjacent edges. It leverages the spatial correlation between tasks to accelerate algorithm convergence and efficiently constructs feasible paths by combining transportation constraints, thereby rapidly iterating and optimizing to obtain a high-quality globally optimal multi-logistic vehicle collaborative scheme. Attached Figure Description

[0050] The features and advantages of the invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the invention in any way. In the drawings:

[0051] Figure 1 This is a flowchart illustrating a specific embodiment of the present invention;

[0052] Figure 2 This is a schematic diagram illustrating an example of a multi-logistics vehicle collaboration problem with transportation restrictions in a specific embodiment of the present invention;

[0053] Figure 3 This is a schematic diagram of the 2-opt local optimization algorithm in a specific embodiment of the present invention;

[0054] Figure 4 This is a schematic diagram of the point migration local optimization algorithm in a specific embodiment of the present invention;

[0055] Figure 5 This is the path diagram of the globally optimal collaborative scheme obtained in the first iteration in a specific embodiment of the present invention;

[0056] Figure 6 This is a schematic diagram of the pheromone sharing mechanism in a specific embodiment of the present invention;

[0057] Figure 7 This is the path diagram of the globally optimal collaborative scheme obtained after the algorithm finishes optimization in a specific embodiment of the present invention;

[0058] Figure 8 This is a flowchart illustrating an embodiment of a specific example of the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] The present invention will be further illustrated below with reference to specific embodiments. Those skilled in the art should understand that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Modifications to the present invention in various equivalent forms all fall within the scope defined by the appended claims.

[0061] like Figure 1 As shown, this invention provides a collaborative method for multiple logistics vehicles with transportation constraints based on a pheromone-sharing ant colony system, comprising the following steps:

[0062] Step S1: Read logistics task information and logistics vehicle information. Based on the transportation cost information between logistics tasks and the transportation restrictions on logistics vehicles from the logistics task information, construct the transportation cost matrix between logistics tasks and the transportation permission matrix of logistics vehicles to logistics tasks. Based on the logistics task information and logistics vehicle information, establish a multi-logistics vehicle collaborative optimization model with transportation restrictions.

[0063] The logistics task information includes: the total number of logistics tasks n; the sequence number of the logistics task i; and the coordinates (x, y) of the logistics task. i y i ), where x i and y i The x and y axes represent the coordinates of logistics task i, respectively; the transportation cost d between any two logistics tasks i and j is d. ij Transportation cost d between logistics task i and warehouse depot i,depot and d depot,i The set of transportable logistics vehicles for each logistics task;

[0064] The logistics vehicle information includes: the logistics warehouse depot and its coordinates (x, y). depot y depot ), where x depot and y depot The x and y coordinates represent the logistics warehouse depot, the number of logistics vehicles (m), and the vehicle serial number (k).

[0065] The transportation cost matrix is ​​a two-dimensional matrix of (n+1)×(n+1):

[0066] D=[d ij ] (n+1)×(n+1) ;

[0067] In the formula, d ij The transportation cost from logistics task or warehouse i to logistics task or warehouse j; i and j are the sequence numbers of logistics tasks or warehouses; n is the total number of logistics tasks.

[0068] Logistics task transportation restrictions refer to the transportation permissions of logistics vehicles for logistics tasks; certain logistics tasks can only be transported by logistics vehicles with specific sequence numbers. The transportation permission matrix is ​​a two-dimensional matrix of (n+1)×m:

[0069] A=[a ik ] (n+1)×m ;

[0070] In the formula, i represents the sequence number of the logistics task or warehouse; k represents the sequence number of the logistics vehicle; a ik This represents the transportation authority of logistics vehicle k to logistics task or warehouse i, with a value of 1 or 0. ik A value of 1 indicates that the logistics vehicle k has the right to transport logistics tasks or to warehouse i, a ik A value of 0 indicates that the logistics vehicle k is not authorized to transport logistics tasks or warehouse i; specifically, when i = depot, for any logistics vehicle k, a depot,k =1, meaning all logistics vehicles can depart from and return to the warehouse;

[0071] The multi-logistics vehicle collaborative optimization model with transportation constraints is as follows: given n logistics tasks, m logistics vehicles, and a warehouse; the city map is described as a completely undirected graph.

[0072] G=(V,E);

[0073] In the formula, V={i|1≤i≤n+1} represents the point set consisting of all logistics tasks and warehouses; E={e ij |i,j∈V} represents the set of edges between all points in the point set.

[0074] For the constraints, each logistics task must be transported and can only be transported once by a logistics vehicle with the required transport permissions; the logistics vehicle departs from the warehouse, can only transport logistics tasks with the required transport permissions, is prohibited from transporting logistics tasks without the required transport permissions, and ultimately returns to the warehouse; the optimization objective is to minimize the fitness value, that is, to find m transport paths such that the transport cost of the path with the highest transport cost is minimized. The optimization objective function is defined as:

[0075] ;

[0076] ;

[0077] In the formula, f represents the fitness value, which is the maximum transportation cost among m transportation routes; k, k1, and k2 represent the serial numbers of the logistics vehicles; m represents the number of logistics vehicles; Route k , , Let K represent the transportation routes of logistics vehicles k, k1, and k2, respectively. Each route is a sequence consisting of warehouses and several logistics tasks; V represents the set of all logistics tasks and warehouses; depot represents a logistics warehouse; C(Route) k ) indicates the transportation route. k The transportation cost is calculated by traversing the path and summing the corresponding values ​​in the transportation cost matrix; i represents the sequence number of the logistics task or warehouse; a ik This indicates the transportation permissions of logistics vehicle k to logistics task or warehouse i.

[0078] Step S2: Set the ant colony system parameters, including: ant colony size NP, algorithm iteration number, pheromone importance parameter α, heuristic information importance parameter β, global pheromone evaporation rate γ, development probability q0, local pheromone update intensity λ, and pheromone sharing quantity R; construct a greedy cooperative scheme using a greedy algorithm, assign an initial pheromone value p0 according to this scheme, and initialize the pheromone matrix;

[0079] The greedy collaborative solution does not consider the allocation of logistics tasks or constraints. It obtains a complete transportation path through a greedy algorithm and assigns the initial pheromone value p0 to the reciprocal of the transportation cost of this path. The pheromone matrix is ​​a (n+1)×(n+1) two-dimensional matrix.

[0080] P=[p ij ] (n+1)×(n+1) ;

[0081] In the formula, p ij p represents the pheromone concentration between logistics task or warehouse i and logistics task or warehouse j. At the initial stage of the algorithm, p ij =p0.

[0082] Step S3: Initialize NP ant colonies, assign m ants to each colony and initialize an empty logistics task taboo table T; all ants in each colony start from the warehouse and begin to build a multi-logistics vehicle collaborative solution;

[0083] Step S4: Each ant in the ant colony obtains the set of logistics tasks that the corresponding logistics vehicle can transport based on the transportation permission matrix and the logistics task taboo table. According to the state transition equation, it selects a desired logistics task from the set of tasks to be transported. Then, based on a probability selection mechanism based on transportation cost, a winning ant is selected from all ants that have selected desired logistics tasks. The desired logistics task selected by the winning ant is added to its transportation path and logistics task taboo table. Other ants abandon this round of transportation. The local pheromone update rule is called to update the pheromone along the edges traversed by the winning ant in this round. The specific process is as follows:

[0084] Each ant colony maintains a logistics task taboo table T, which records the logistics tasks that have already been transported and is shared by all ants in the colony. Before ant k selects the next logistics task, it first searches for a set of candidate logistics tasks S based on the transportation permission matrix of the logistics tasks that have not yet been transported. k The formula is shown below:

[0085] ;

[0086] In the formula, S k V represents the set of candidate logistics tasks; V represents the set of all logistics tasks and warehouses; V k Let T represent the set of logistics tasks that logistics vehicle k has the right to transport. This set is obtained by extracting the index of the k-th column of the transportation permission matrix A where the value is equal to 1; T represents the logistics task prohibition table. This represents a set of logistics tasks that have not yet been transported.

[0087] Then, each ant moves from the candidate logistics task set S according to the state transition formula. k Select the intended logistics task j, and the state transition formula is given below:

[0088] ;

[0089] In the formula, j represents the selected intended logistics task; i represents the sequence number of the current logistics task or warehouse; l represents the sequence number of the candidate logistics task; p il η il Let represent the pheromone concentration and heuristic information between the current logistics task or warehouse i and the candidate logistics task l, respectively. Here, the heuristic information is the reciprocal of the transportation cost between logistics tasks, η. il =1 / d il d ilLet α represent the transportation cost from logistics task or warehouse i to logistics task l; α is a parameter controlling the importance of pheromone; β is a parameter controlling the importance of heuristic information; q is a random variable uniformly distributed between [0,1]; q0 is a predefined parameter, 0≤q0≤1, used to control the probability of ant exploration and development, representing that the ant will choose the logistics task with the strongest pheromone concentration and heuristic information with probability q0, and will selectively choose each logistics task with a bias of probability (1-q0); when q>q0, the next logistics task J is selected from the candidate logistics task set S by a roulette wheel selection method. k Select from the options, for each candidate logistics task. The probability of it being selected (Prob) il The calculation is as follows:

[0090] ;

[0091] Where i represents the sequence number of the current logistics task or warehouse; l represents the sequence number of the candidate logistics task; Prob il p represents the probability that logistics task l is selected; il η il Let represent the pheromone concentration and heuristic information between the current logistics task or warehouse i and the candidate logistics task l, respectively; α is a parameter controlling the importance of pheromones; β is a parameter controlling the importance of heuristic information; and the denominator is... The sum of pheromone and heuristic information combinations between all logistics tasks in the candidate set and the current logistics task or warehouse i; o represents the temporary index of the candidate logistics task; p io η io These represent the pheromone concentration and heuristic information between the current logistics task or warehouse i and the logistics task o, respectively.

[0092] For the calculated probability Prob il Generate a random number r uniformly distributed in the interval [0,1], and select from the candidate set in the default index order such that... The first logistics task J is designated as the intended logistics task j; if S k If the set is empty, it means that ant k does not have any logistics task to be transported, and the intended logistics task is set to empty.

[0093] A probabilistic selection mechanism based on transportation costs is used to determine the expected closed-loop transportation cost L for all ants that select their intended logistics tasks. k Calculate the selection weight w k =1 / L k Where k represents the ant's index, and for each ant that selects a desired logistics task, the probability P of being selected as the winning ant is... k The calculation is as follows:

[0094] ;

[0095] In the formula, k represents the ant's index; P k Let denot k represent the probability of ant k being selected; M represents the set of all ants selected for the intended logistics task; n represents the temporary index of an ant in set M; w k w n Let represent the selection weights of ant k and ant n, respectively. The selection weight is the reciprocal of the expected closed-loop transportation cost for that ant. For the calculated probabilities... Generate a random number r uniformly distributed in the interval [0,1], and select from M in the default index order such that... The first ant K is the winning ant and transports its intended logistics task, while the other ants give up the task in this round and wait for the next round of intended logistics task selection.

[0096] Local pheromone updates occur during path construction, each time an ant traverses an edge e. ij All of these will immediately invoke this rule to update the pheromones on that edge. The pheromone update formula is as follows:

[0097] ;

[0098] In the formula, i and j represent the sequence numbers of the logistics task or warehouse; p ij λ represents the pheromone concentration between logistics task or warehouse i and logistics task or warehouse j; λ represents the local pheromone update intensity; p0 represents the initial pheromone value.

[0099] Repeat step S4 until all logistics tasks are transported by ants, and obtain a complete preliminary multi-logistics vehicle collaborative solution.

[0100] Step S5: The novel local search algorithm combining 2-opt and point migration is used to locally optimize the collaborative scheme constructed by the ant colony, thereby obtaining a higher quality multi-logistics vehicle collaborative scheme. The specific process is as follows:

[0101] First, perform 2-opt path optimization on each transportation path in the current collaborative scheme. Specifically, select two different logistics task nodes on the path in turn and try to reverse the path segment between the two nodes. When the transportation cost of the path is reduced after reversal, retain the reversal operation and repeat this process until all interchangeable points in the path can no longer reduce the cost.

[0102] Subsequently, the optimization of migration paths between execution points is performed: first, the route with the highest transportation cost in the current collaboration scheme is selected. max The logistics task i to be migrated is determined from the transportation route according to the following formula. move :

[0103] ;

[0104] In the formula, i represents the sequence number of the logistics task; move Indicates a logistics task to be migrated; Route max This indicates the route with the highest transportation cost in the current collaborative solution; Indicates the route from the transportation path. max The new transport route after removing task i; C(Route) max ) indicates the transportation route. max Transportation costs; Indicates the transportation route The formula aims to select the logistics task whose removal would result in the greatest reduction in transportation costs along the original route.

[0105] Next, under the premise of satisfying the transportation permission matrix A, the optimal target ant k to receive the logistics task is found according to the following formula. target :

[0106] ;

[0107] In the formula, k represents the ant's index; i move Indicates the logistics task to be migrated; k target Indicates receiving logistics task i move The optimal ant; k max Indicates the route max The corresponding ant; This represents the corresponding value in the transportation permission matrix A; Route k C represents the transport path constructed by ant k; k ) indicates the transportation route. k Transportation costs; This indicates that task i move Insert into path Route k The route cost after the position that minimizes the increase in transportation costs;

[0108] If the maximum transportation cost of the new collaborative solution after the migration operation is less than the maximum transportation cost of the original collaborative solution, then retain the migration operation and repeat step S5 until the maximum transportation cost cannot be further reduced.

[0109] Finally, a 2-opt local search is performed on each path in the collaborative scheme for local optimization.

[0110] Step S6: Repeat steps S4 to S5 until all ant colonies have built a multi-logistics vehicle collaborative solution.

[0111] Step S7: Evaluate the fitness value of the optimized cooperative scheme for each ant colony, i.e. the maximum transportation cost in the cooperative scheme, update the globally optimal cooperative scheme based on the fitness value, and perform global pheromone update on the edges in the globally optimal cooperative scheme.

[0112] The specific process of updating the globally optimal collaborative solution gbest is as follows:

[0113] First, the fitness values ​​of the NP ant colonies are calculated using the objective function. Then, the cooperative scheme with the smallest fitness value is marked as best. If f(gbest) > f(best), then gbest is replaced with best; otherwise, gbest remains unchanged. The formula for calculating the fitness value is:

[0114] ;

[0115] ;

[0116] In the formula, f represents the fitness function; k represents the ant index; m represents the number of ants in a single ant colony; h represents the ant colony index; solution h This represents a multi-logistics vehicle collaborative solution built by an ant colony (h). represents the transportation path constructed by ant k in ant colony h; best represents the cooperative solution with the minimum fitness value; NP represents the number of ants in the ant colony; solution represents the cooperative solution of multiple logistics vehicles.

[0117] Global pheromone update refers to the practice where only the ant colony that has constructed the optimal cooperative strategy is allowed to release pheromones after each iteration. The pheromone update formula is as follows:

[0118] ;

[0119] In the formula, i and j represent the sequence numbers of the logistics task or warehouse; p ij This indicates the pheromone concentration between logistics task or warehouse i and logistics task or warehouse j; e ij Represents the edge between logistics task or warehouse i and logistics task or warehouse j; The pheromone increment is the reciprocal of the fitness value of the globally optimal cooperative solution. , where f represents the fitness function, gbest represents the globally optimal cooperative scheme, and γ represents the global pheromone evaporation rate.

[0120] Step S8: Through the pheromone sharing mechanism, the pheromone on each edge in the globally optimal cooperative solution is shared to the adjacent edges;

[0121] The pheromone sharing mechanism shares the pheromone from each edge in the globally optimal multi-logistics vehicle collaborative solution to its corresponding neighboring edges. The pheromone sharing formula is as follows:

[0122] ;

[0123] In the formula, i represents the logistics task or warehouse number in the globally optimal multi-vehicle collaborative solution; R represents the amount of pheromone shared. Let represent the set of R logistics tasks or warehouses that minimize transportation costs starting from logistics task or warehouse i, excluding logistics tasks or warehouses adjacent to logistics task or warehouse i in the globally optimal collaborative solution gbest; l represents The logistics task or warehouse sequence number in the data; γ represents the global pheromone evaporation rate; p il This indicates the pheromone concentration between logistics task or warehouse i and logistics task or warehouse l.

[0124] Repeat steps S3 to S8 until the iteration terminates, and obtain the final globally optimal collaborative solution as the multi-logistics vehicle collaborative solution.

[0125] The present invention will be described in detail below through an embodiment:

[0126] like Figure 2 , 8 As shown, the embodiment includes 50 logistics tasks with different requirements (represented by dots) and a warehouse (represented by an asterisk). The size of the dot is proportional to the number of vehicles authorized to transport that logistics task; that is, the larger the dot, the more logistics vehicles authorized to transport that task. The number in parentheses around the dot represents the sequence number of the logistics vehicle authorized to transport that task. For example, dot 48 (1, 3) means that logistics task number 48 can be transported by logistics vehicle 1 and logistics vehicle 3. The three heterogeneous logistics vehicles need to be rationally scheduled, departing from the warehouse together, completing all logistics tasks, and finally returning to the warehouse.

[0127] Step a: Obtain logistics task information and logistics vehicle information from the data source. Logistics task information includes: the number of logistics tasks to be transported (n=50); the number of logistics vehicles (m=3); the sequence number of the logistics task (i); and the coordinates of the logistics task (x, y, y). i y i The transportation cost d between any two logistics tasks i and j. ij Transportation cost d between logistics task i and warehouse depot i,depot and d depot,i A set of transportable logistics vehicles for each logistics task; the information of the logistics vehicles includes the coordinates (x, y) of the warehouse depot. depot y depot );

[0128] The location information of logistics tasks and warehouses is shown in Table 1 below: Table 1

[0129] The available transport vehicle information for the logistics tasks is shown in Table 2 below: Table 2

[0130] The transportation cost matrix is ​​a 51×51 two-dimensional matrix:

[0131] D=[d ij ] 51×51 ;

[0132] The transportation cost is calculated based on the distance between logistics tasks or between a logistics task and a warehouse, using the distance between logistics tasks or warehouses as the transportation cost.

[0133] The transportation permission matrix is ​​generated based on the transportable vehicle information for logistics tasks, and is a 51×3 two-dimensional matrix:

[0134] A=[a ik ] 51×3 ;

[0135] Step b: Set the ant colony system parameters: Ant colony size NP=10, Algorithm iterations=300, Pheromone importance parameter α=1.0, Heuristic information importance parameter β=2.0, Global pheromone evaporation rate γ=0.1, Development probability q0=0.9, Local pheromone update intensity λ=0.1, Pheromone sharing quantity R=16;

[0136] Construct a greedy cooperative scheme using a greedy algorithm, with the initial pheromone value p0 = 3.80 × 10⁻⁶. -5 The pheromone matrix is ​​a 51×51 two-dimensional matrix:

[0137] P=[p ij ] 51×51 ;

[0138] At the beginning of the algorithm, p ij =p0.

[0139] Step c: Initialize 10 ant colonies, assign 3 ants to each colony, and initialize an empty logistics task taboo table T; each ant colony is responsible for constructing a collaborative solution, represented as:

[0140] solution={Route1,Route2,Route3};

[0141] In the formula, Route k=[],1≤k≤3.

[0142] All the ants in the ant colony start from the warehouse and begin to build a multi-logistics vehicle collaborative solution. At this time, solution={

[46] ,

[46] ,

[46] }.

[0143] Step d: The three ants choose intentional logistics tasks 12, 51, and 12 respectively. According to the probability selection mechanism based on transportation costs, ant 2 is selected as the winning ant and transports logistics task 51. Ants 1 and ant 3 give up this round of transportation and wait for the next round of intentional logistics task selection.

[0144] Based on the parameter settings in step b, λ = 0.1, p0 = 3.80 × 10⁻⁶. -5 Ant 2 has been moved from warehouse 46 to logistics task 51, requiring an update to edge e. 46,51 The pheromones on the surface, while updating p 46,51 .

[0145] Repeat the above steps until all logistics tasks have been transported by the logistics vehicles. At this point, you will obtain the first complete multi-logistics vehicle collaborative solution:

[0146] solution={[46,49,9,16,30,5,12,17,37,15,41,13,25,1,46],[46,51,27,32,22,8,26,31,3,20,35,36 ,23,43,14,18,44,42,45,33,46],[46,38,11,2,29,21,34,50,10,39,48,7,24,6,47,4,19,40,28,46]}.

[0147] Step e: as Figure 3 As shown, taking the transportation path constructed by ant 2 in the first multi-vehicle collaborative scheme as an example, the transportation path, after optimization by the 2-opt algorithm, eliminates the intersections existing in the original transportation path and reduces transportation costs; after performing local optimization of the three transportation paths using 2-opt, the optimized multi-vehicle collaborative scheme is obtained:

[0148] solution={[46,25,13,41,17,15,37,12,5,49,30,9,16,1,46],[46,51,27,32,22,20,35,36,3,31,8,26 ,43,23,14,18,42,44,45,33,46],[46,47,4,19,40,6,24,7,48,28,29,21,50,34,39,10,38,2,11,46]};

[0149] At this point, the transportation costs for the three routes are 170.83, 247.06, and 272.57, respectively, with cost reductions of 23.49, 33.88, and 50.49, respectively.

[0150] like Figure 4 As shown, after performing local optimization of point migration on the first collaborative solution, the optimized multi-logistics vehicle collaborative solution is obtained:

[0151] solution={[46,48,24,25,13,40,41,42,17,15,37,12,5,49,30,9,16,1,46],[46,51,27,32,22,20,35, 36,3,31,8,26,43,23,14,18,44,45,33,46],[46,47,4,19,6,7,28,29,21,50,34,39,10,38,2,11,46]};

[0152] At this point, the transportation costs for the three routes are 225.54, 235.62, and 234.56, respectively.

[0153] By performing local optimization on each path in the collaborative solution, the collaborative solution is obtained:

[0154] solution={[46,16,9,30,49,5,12,17,37,15,42,40,41,13,25,24,48,1,46],[46,51,27,32,22,20,35, 36,3,31,8,26,43,23,14,18,44,45,33,46],[46,47,4,19,6,7,28,29,21,50,34,39,10,38,2,11,46]};

[0155] At this point, the transportation costs for the three routes are 211.17, 235.62, and 234.56, respectively.

[0156] Step f: Repeat steps d to e until all ant colonies have built multi-vehicle collaborative solutions. At this point, 10 multi-vehicle collaborative solutions are obtained, as shown below:

[0157] solution1={[46,16,9,30,49,5,12,17,37,15,42,40,41,13,25,24,48,1,46],[46,51,27,32,22,20,35,36,3,31,8,26,43,23,14,18,44,45,33,46],[46,47,4,19,6,7,28,29,21,50,34,39,10,38,2,11,46]};

[0158] solution2={[46,11,1,36,20,16,50,34,30,10,49,9,5,17,41,40,13,25,12,46],[46,51,27,18,14,24,43,23,26,8,32,22,3,35,21,33,45,46],[46,6,48,7,31,28,2,29,38,39,15,44,42,19,4,37,47,46]};

[0159] solution3={[46,12,5,49,9,50,16,21,34,30,10,15,17,4,41,40,13,25,24,23,48,1,46],[46,51,27,32,11,20,35,36,3,22,8,26,43,18,45,33,46],[46,47,37,44,42,19,14,6,7,31,28,2,29,39,38,46]};

[0160] solution4={[46,12,5,49,9,50,16,21,34,30,10,15,17,4,41,40,13,25,24,1,46],[46,51,27,32,11,20,35,36,3,22,8,26,43,23,18,45,33,46],[46,47,37,44,42,19,14,6,48,7,31,28,2,29,39,38,46]};

[0161] solution5={[46,12,5,49,9,50,16,21,34,30,10,37,17,41,13,25,14,24,31,1,46],[46,51,27,32,11,20,35,36,3,22,8,26,43,23,18,45,33,46],[46,6,48,7,28,2,29,39,15,44,42,40,19,4,47,38,46]};

[0162] solution6={[46,12,5,49,9,50,16,21,34,30,10,17,41,40,13,25,14,24,8,1,46],[46,51,33,45,18,43,26,31,3,36,35,20,22,27,32,11,46],[46,6,48,23,7,28,2,29,38,39,15,44,42,19,4,37,47,46]};

[0163] solution7={[46,25,13,41,40,42,17,37,15,5,49,10,30,34,21,50,9,16,11,1,46],[46,33,45,44,18,24,43,23,8,22,3,36,35,20,32,27,51,46],[46,38,39,29,2,28,31,26,7,48,6,14,19,4,47,12,46]};

[0164] solution8={[46,11,5,49,16,20,36,22,1,48,23,25,13,41,40,42,44,37,17,12,46],[46,9,50,34,30,10,33,45,18,14,24,43,26,31,3,35,32,27,51,46],[46,6,7,8,28,29,21,39,15,19,4,47,38,2,46]};

[0165] solution9={[46,12,5,49,9,50,16,21,34,30,10,17,41,40,13,25,1,11,46],[46,33,45,18,14,24,43,23,26,8,31,3,36,35,20,22,32,27,51,46],[46,47,4,19,42,44,37,15,39,38,29,2,28,7,48,6,46]};

[0166] solution 10={[46,12,24,25,13,41,40,42,4,17,37,44,15,10,49,5,16,1,46],[46,51,27,32,11,9,30,34,50,21,20,35,3,23,43,18,47,45,33,46],[46,38,39,29,2,22,36,28,31,8,26,7,48,6,14,19,46]}.

[0167] Step g: Obtain the fitness values ​​of the 10 collaborative solutions as follows: 235.62, 246.81, 230.93, 234.74, 244.13, 236.64, 224.43, 239.38, 235.76, and 260.71. Among them, solution 7 has the smallest fitness value, so it is marked as best.

[0168] Since the current algorithm is in its first iteration, best is the globally optimal cooperative solution, i.e.:

[0169] gbest={[46,25,13,41,40,42,17,37,15,5,49,10,30,34,21,50,9,16,11,1,46],[46,33,45,44,18,2 4,43,23,8,22,3,36,35,20,32,27,51,46],[46,38,39,29,2,28,31,26,7,48,6,14,19,4,47,12,46]};

[0170] Its path diagram is as follows Figure 5 As shown, the collaborative scheme meets the optimization objectives and transportation constraints.

[0171] Step h: At this point, This process updates the pheromones on the three paths in gbest sequentially.

[0172] Step i: In this example, the pheromone sharing quantity R=16, and the first edge e in the path constructed by ant 1 in the globally optimal cooperative scheme gbest is... 46,25 For example, the shared target edge corresponding to this edge is as follows: Figure 6 As shown. By definition, the pheromone of the shared target edges corresponding to all edges in the optimal cooperative solution gbest is updated.

[0173] Step j: Repeat steps c to i. After 300 iterations, the final globally optimal cooperative solution is obtained.

[0174] gbest={[46,12,17,37,15,44,42,40,41,13,25,14,23,48,1,11,16,50,9,49,5,46],[46,51,27,32,2 0,35,36,3,8,43,24,18,45,33,46],[46,47,4,19,6,7,26,31,28,22,2,29,21,34,30,39,10,38,46]};

[0175] The transportation costs for the three routes are 200.37, 217.79, and 215.03 respectively, with an optimal value of 217.79. The route diagram is shown below. Figure 7 As shown, the multi-logistics vehicle collaborative solutions obtained by this method are all feasible path solutions that satisfy the constraints. Thanks to the probabilistic selection mechanism based on transportation costs, the transportation costs among multiple logistics vehicles are relatively balanced.

[0176] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A multi-vehicle coordination method based on pheromone sharing ant colony system with transport restrictions, characterized in that, The method comprises the following steps: Step 1: obtaining logistics task information and logistics vehicle information, constructing a transportation cost matrix and a transportation permission matrix, and establishing a multi-logistics vehicle collaborative optimization model with transportation restrictions; Step 2: setting ant colony system parameters and initializing the pheromone matrix through a greedy algorithm; Step 3: initializing multiple ant colonies and assigning each ant colony a logistics task taboo list; each ant colony includes a plurality of ants, wherein the number of ants is the same as the number of logistics vehicles; Step 4: each ant in the ant colony obtains a task set according to the transportation permission matrix and the logistics task taboo list, selects an intended task through a state transition equation, and selects a winning ant from all ants that have selected an intended task according to a probability selection mechanism based on transportation cost, adds the intended task selected by the winning ant to its transportation path and logistics task taboo list, and other ants abandon the current transportation, update the pheromone on the edges passed by the winning ant through a local pheromone update rule, and repeat step 4 until the current task is completed, forming a preliminary collaborative scheme; Step 5: performing local optimization on the preliminary collaborative scheme through a local search algorithm that combines 2-opt and point migration to obtain an optimized collaborative scheme; repeating steps 4 and 5 until all ant colonies obtain optimized collaborative schemes; Step 6: evaluating the fitness of the optimized collaborative scheme of each ant colony, updating the global optimal collaborative scheme, and updating the global pheromone on the edges in the global optimal collaborative scheme; Step 7: sharing the pheromone on each edge in the global optimal collaborative scheme to adjacent edges; Step 8: repeating steps 3 to 7 until iteration terminates, and obtaining the final global optimal collaborative scheme as the multi-logistics vehicle collaborative scheme.

2. The pheromone-based shared-ant colony system band transportation limited multi-vehicle coordination method according to claim 1, wherein, In step 1, the transportation cost matrix constructed is: D=[d ij ] (n+1)×(n+1) ; In the formula, d ij is the transportation cost from logistics task or warehouse i to logistics task or warehouse j; i, j are the serial numbers of logistics task or warehouse; n is the total number of logistics tasks.

3. The pheromone-based shared-ant colony system band transportation limited multi-vehicle coordination method according to claim 1, wherein, In step 1, the transportation permission matrix constructed is: A=[a ik ] (n+1)×m ; In the formula, a ik is the transport permission of the logistics vehicle k to the logistics task or warehouse i, and takes the value of 1 or 0; m is the number of logistics vehicles; and n is the total number of logistics tasks.

4. The pheromone-based shared-ant colony system band transportation limited multi-vehicle coordination method according to claim 1, wherein, The multi-logistics vehicle collaborative optimization model is specifically: a plurality of logistics tasks, a plurality of logistics vehicles and a warehouse are given; a city map is described as a complete undirected graph; each logistics task must be transported and can only be transported by one logistics vehicle that meets the transportation permission once; a logistics vehicle can only transport logistics tasks that meet the transportation permission; a logistics vehicle must start from the warehouse and finally return to the warehouse; and the optimization objective function is: ； ； In the formula, f is an adaptive value; k, k1, k2 are all serial numbers of the logistics vehicles; m is the number of the logistics vehicles; Route k , , are respectively the transportation paths of the logistics vehicles k, k1, k2; V is a set composed of all logistics tasks and warehouses; depot is a logistics warehouse; C(Route k ) is the transportation cost of the transportation path Route k ; i is a serial number of a logistics task or a warehouse; a ik is the transportation authority of the logistics vehicle k to the logistics task or the warehouse i.

5. The pheromone-based shared-ant colony system band transportation limited multi-vehicle coordination method according to claim 1, wherein, In step 2, the pheromone matrix is: P=[p ij ] (n+1)×(n+1) ; In the formula, p ij is the pheromone concentration between the logistics task or warehouse i and the logistics task or warehouse j; i, j are the serial numbers of the logistics task or warehouse; n is the total number of logistics tasks.

6. The pheromone-based shared-ant colony system band transportation limited multi-vehicle coordination method according to claim 1, wherein, In step 4, the state transition equation is: ； where j is the selected logistics task of intention; i is the serial number of the current logistics task or warehouse; l is the serial number of the candidate logistics task; p il , η il are the pheromone concentration and heuristic information between the current logistics task or warehouse i and the candidate logistics task l, respectively; and a is a parameter for controlling the importance of pheromone. β is a parameter that controls the importance of the heuristic information; q is a random variable uniformly distributed in the interval [0, 1]; q0 is a predefined parameter and 0 < q0 < 1; J is a logistic task selected by roulette wheel selection from the set of candidate logistic tasks; S k is the set of candidate logistic tasks.

7. The pheromone-based shared-ant colony system band transportation limited multi-vehicle coordination method according to claim 1, wherein, In step 5, the specific process of the local search algorithm that combines 2-opt and point migration is as follows: Step 51: performing intra-path optimization on each path in the preliminary collaborative scheme through 2-opt, specifically: selecting two different task nodes on the path in turn, reversing the path segment between the two nodes, and retaining the current reversal result when the transportation cost is reduced after reversal; and repeating step 51 until the transportation cost cannot be reduced any more; Step 52: performing inter-path optimization through point migration, specifically: selecting the path with the largest transportation cost, determining a logistics task to be migrated from the largest path, and the specific formula is: ； wherein i is the serial number of the logistics task; i move is the logistics task to be migrated; Route max max is the path with the largest transportation cost; is the new transportation path after removing task i from Route max ; C(Route max ) is the transportation cost of Route max ; is the transportation cost of ; obtaining an optimal ant that can receive the logistics task to be migrated, and the specific formula is: ； wherein k is the serial number of the ant; i move is the logistics task to be migrated; k target is the optimal ant receiving the logistics task i move ; k max is the transport path Route max corresponding to the ant; is the corresponding value in the transport permission matrix; Route k is the transport path constructed by the ant k; C(Route k ) is the transport cost of the transport path Route k ; is the path cost after inserting the task i move into the path Route k in the position with the minimum increase in transport cost; When the maximum transportation cost of the new collaborative scheme after the logistics task migration is less than the maximum transportation cost of the original collaborative scheme, the current migration result is retained, and step 52 is repeated until the maximum transportation cost cannot be reduced.

8. The pheromone-based shared-ant colony system band transportation limited multi-vehicle coordination method according to claim 1, wherein, In step 6, the specific method for updating the global optimal collaborative scheme is as follows: When the fitness value of the current global optimal collaborative scheme is greater than the fitness value of the optimized collaborative scheme, the optimized collaborative scheme is updated as the global optimal collaborative scheme.

9. The pheromone-based shared-ant colony system's band transportation limited multi-vehicle coordination method according to claim 8, wherein, In step 6, the update formula for updating the global information of the edges in the global optimal collaborative scheme is as follows: ； where i, j are the serial numbers of the logistics tasks or warehouses; p ij is the pheromone concentration between logistics task or warehouse i and logistics task or warehouse j; e ij is the edge between logistics task or warehouse i and logistics task or warehouse j; is the pheromone increment, where f is the fitness function, gbest is the global optimal collaborative scheme, and γ is the global pheromone evaporation rate.

10. The pheromone-based shared-ant colony system band transportation limited multi-vehicle coordination method according to claim 1, wherein, In step 7, the sharing formula for sharing the information to the adjacent edges is as follows: In step 7, the sharing formula for sharing the information to the adjacent edges is as follows: ； In the formula, i is the logistics task or warehouse serial number in the global optimal multi-vehicle coordination scheme; R is the number of pheromone sharing; is the set of R logistics tasks or warehouses with the minimum transportation cost from the logistics task or warehouse i; l is the logistics task or warehouse serial number in the set of R logistics tasks or warehouses with the minimum transportation cost from the logistics task or warehouse i; γ is the global pheromone evaporation rate; p is the pheromone concentration between the logistics task or warehouse i and the logistics task or warehouse l. is the set of R logistics tasks or warehouses with the minimum transportation cost from the logistics task or warehouse i; l is the logistics task or warehouse serial number in the set of R logistics tasks or warehouses with the minimum transportation cost from the logistics task or warehouse i; γ is the global pheromone evaporation rate; p il is the set of R logistics tasks or warehouses with the minimum transportation cost from the logistics task or warehouse i; l is the logistics task or warehouse serial number in the set of R logistics tasks or warehouses with the minimum transportation cost from the logistics task or warehouse i

Images