Manned and unmanned system cooperative path planning method, program, equipment and storage medium in large-scale non-uniform distribution scene

Abstract

The invention belongs to the technical field of transportation path planning, and particularly relates to a manned and unmanned system collaborative path planning method, program and equipment in a large-scale non-uniform distribution scene, and a storage medium. According to the invention, an improved clustering algorithm is designed to distribute package delivery tasks to each formation and optimize and adjust the distribution result, so that the calculation complexity of the algorithm is reduced, and meanwhile, the workload of the formation is prevented from being unbalanced; based on a task allocation result, designing a low-cost path search algorithm to formulate a low-cost initial routing scheme for each formation; and finally, designing a population reconstruction strategy and a dominant individual supplement strategy in an optimization process to select a Pareto boundary with high-quality diversity and convergence. According to the invention, an order delivery routing scheme with low cost and balanced formation workload can be planned in a large-scale non-uniform distribution scene, and the distribution efficiency is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of transport route planning, and specifically relates to a method, program, equipment and storage medium for collaborative route planning of manned and unmanned systems in large-scale non-uniformly distributed delivery scenarios. Background Art

[0002] With the rapid growth of the e-commerce economy, merchants are increasingly interested in unmanned logistics-assisted delivery systems to improve "last mile" delivery efficiency. Drones, as part of these systems, offer advantages such as limited ground transportation restrictions, low costs, and high speed. However, due to limitations in payload capacity and durability, current drones cannot handle long-distance, high-volume, and extreme weather delivery missions. Furthermore, trucks alone cannot meet customers' diverse logistics service needs. However, researchers have discovered that the combined operation of drones and trucks can overcome these mutual technical limitations, increasing the reach and flexibility of unmanned logistics services. Therefore, collaboration between drones and trucks has become a key solution for improving "last mile" delivery efficiency.

[0003] When applying collaborative delivery solutions involving multiple trucks and drones, most studies focus on factors specific to the trucks and drones, such as the drones' capacity and energy consumption constraints, and the trucks' delivery capabilities and time constraints. Notably, few studies have examined the impact of customer factors on the efficiency of collaborative delivery solutions involving truck-drone platoons (referred to as platoons) from a customer perspective.

[0004] In real life, to achieve low-cost jurisdiction, logistics companies use geographic information to divide urban areas into several sub-regions and assign a team to each sub-region to handle logistics tasks such as delivery and collection. Within urban areas, the distance between each sub-region center and the logistics company varies. Furthermore, the volume and distribution of packages in each sub-region are often large and uneven. Consequently, the sum of the time it takes for each team to arrive at their jurisdiction from the logistics company and the total time they spend serving customers within that jurisdiction—that is, the team's working hours—is inconsistent. Consequently, workloads can be unbalanced across teams, reducing the quality of logistics services.

[0005] The existing unified delivery task allocation method can solve the problem of unbalanced fleet workload, but the uneven distribution of customer locations makes it easy for this method to force trucks and drones to cross multiple sub-areas multiple times to complete delivery tasks, which increases the path cost and management cost of the delivery plan.

[0006] Therefore, in the collaborative routing and delivery problem of trucks and drones, it is necessary to simultaneously consider multiple objectives, such as balancing the fleet's workload and the company's operating costs, to ensure stable and long-term development. Furthermore, the mutual checks and balances between these multiple objectives during the optimization process make it difficult to simultaneously protect the interests of both employees and the company. To this end, this paper designs a multi-objective optimization method based on a hybrid strategy. By combining the advantages of this hybrid strategy, it achieves a collaborative routing and delivery solution that balances the fleet's workload and reduces path costs. Summary of the Invention

[0007] The purpose of the present invention is to provide a method, program, device and storage medium for collaborative path planning of manned and unmanned systems in large-scale unevenly distributed delivery scenarios, to solve the problems of unreasonable task allocation and poor path plan quality in large-scale unevenly distributed scenarios, and to achieve a truck-drone collaborative routing delivery solution with balanced formation workload and low path cost.

[0008] A collaborative path planning method for manned and unmanned systems in a large-scale non-uniformly distributed delivery scenario includes the following steps:

[0009] Obtain the warehouse node location, customer node set, land transport equipment set, and air transport equipment set; construct a graph network of warehouse nodes and all customer nodes;

[0010] Obtain delivery tasks, consider the maximum carrying capacity of air transport equipment, and divide the packages into land transport packages and air transport packages. Then, form a transport formation with one land transport equipment and multiple air transport equipment.

[0011] Construct a land-air collaborative path planning model, including the first and second indicators, and set constraints;

[0012] Considering the distance and time required for land and air transport equipment to pass through each edge in the graph network, and the service time required by each customer node for land and air transport equipment, the difference in task completion time between the transport formations with the longest and shortest working times is used as the first indicator;

[0013] Considering the unit price of land transport equipment, the unit price of air transport equipment, and the starting unit price of the transport fleet to perform the transport mission, the total cost of completing the mission is used as the second indicator;

[0014] The total number of land transport equipment is used as the number of cluster centers to cluster the customer node set. The clustering results are adjusted using the task reallocation algorithm to obtain the initial task allocation plan for each transport formation. The initial task allocation plan for each transport formation is constructed into an initial path matrix using a low-cost path search algorithm.

[0015] The Pareto optimization algorithm is used. Each individual in the population represents a set of path matrix solutions. After generating a new solution in the iterative process, the individual fitness is calculated according to the land-air collaborative path planning model. After eliminating inferior individuals, the dominant individual supplementation strategy is used to supplement new individuals to obtain a dominant population. When the maximum number of iterations is reached, the optimal Pareto solution set is output, and the path planning plan for each transport formation is deconstructed according to the individual path matrix.

[0016] Furthermore, the customer node set C = {1, 2, ..., α} and the land transportation equipment set K = {k1, k2, ..., k β}、Air transport equipment set A={a1,a2,...,a γ}; Construct edge set E = {(i, j) | i, j∈V}, V = {0, 1, 2, ..., α}, where the 0th customer node is the warehouse node;

[0017] According to the maximum carrying capacity Q of the air transport equipment D The packages of the customer nodes are divided into land transport packages and air transport packages, and the customer node set C is divided into the land transport package customer set T and the air transport package customer set D, T + D = C;

[0018] A land transport equipment k b With G air transport equipment a c Form a transport formation R b , G ≥ 2 and is less than the maximum number of air transport equipment that can be carried by land transport equipment;

[0019] Get the Manhattan distance required for land transport equipment to pass through edge (i, j) and time The Euclidean distance required for air transport equipment to pass through edge (i, j) and time The unit price of land transport equipment λ1, the unit price of air transport equipment λ2, the starting unit price of the transport fleet to perform the transport task λ3, and the service time required for land transport equipment at each customer node Service time for air freight equipment

[0020] The land-air collaborative path planning model F = {f1, f2} is expressed as:

[0021]

[0022] Among them, f1 is the workload balance index of the formation, which represents the difference in delivery completion time between the formation with the longest working time and the formation with the shortest working time; Indicates land transport equipment Formation The time it takes to return to the warehouse node after completing the task; Indicates land transport equipment The time it takes to return to the warehouse node after completing the task; Indicates air transport equipment a c The time it takes to return to the warehouse node after completing the task; f2 is the path cost of the formation, including land transportation cost, air transportation cost and inherent dispatch cost; if the air transport equipment a c Through the edge (i,j), then x i,j,c =1; otherwise, x i,j,c =0; if land transport equipment k b Through the edge (i,j), then y i,j,b =1; otherwise, y i,j,b =0.

[0023] Furthermore, the constraints include path constraints, time constraints and energy consumption constraints;

[0024] The path constraints are:

[0025] (1) Each customer node can only be transported once by land transport equipment or air transport equipment:

[0026]

[0027] Among them, if the cth air transport equipment a c Serving client node i, then otherwise If the bth land transport equipment k b Serving client node i, then otherwise

[0028] (2) Each land transport device can only serve the customer nodes it passes through:

[0029]

[0030] (3) Each air transport device can only serve the client nodes it passes through and can only return to the land transport device that launched the air transport device:

[0031]

[0032] (4) The traffic flow of each piece of air transport equipment is kept balanced:

[0033]

[0034] The time constraints are:

[0035] (5) If node i∈V is air transport equipment a c Launch node, air transport equipment a cTime to reach customer node j∈C Equal to the time it leaves node i Plus the time required to pass through edge (i,j)

[0036]

[0037] Wherein, M is a sufficiently large positive value;

[0038] (6) Air transport equipment c Time of leaving client node i Equal to the time it takes to reach customer node i Plus the service time required at customer node i

[0039]

[0040] (7) Land transportation equipment b Time of leaving client node i Equal to the air transport equipment it launches a c Returns the time of client node i Plus the service time required at customer node i

[0041]

[0042] (8) Air transport equipment c Returns the time of client node i At the latest for land transport equipment k b The time it takes to return to the client node i after completing the task from the warehouse node

[0043]

[0044] The energy consumption constraint is:

[0045] (9) Air transport equipment c There is enough energy to leave the customer node i and return to node j, and to be transported by land transport equipment k b take over:

[0046]

[0047] Among them, if node j is air transport equipment a c The return node is otherwise, For air transport equipment c The remaining energy when leaving node i; e D is the energy consumption rate of air transport equipment;

[0048] (10) Air transport equipment c From the warehouse node or from the land transport equipment k b Launched at full energy:

[0049]

[0050] Among them, if node j is air transport equipment a c The transmitting node is otherwise, C D is the maximum energy of the air transport equipment;

[0051] (11) Air transport equipment c Weight of the package you carry Not exceeding the maximum carrying capacity Q D :

[0052]

[0053] Furthermore, the initial task allocation plan for each transport formation is obtained, specifically:

[0054] Step 1.1: Take the total number of land transport equipment β as the number of cluster centers, cluster α customer nodes in the customer node set C, and obtain each transport formation R b The cluster center μ b and the client node set C b ;

[0055] Step 1.2: Calculate the R of each transport formation using the WCSS formula b WCSS b ;

[0056]

[0057] Among them, dist(i bρ ,μ b ) is C b Client node i bρ and cluster center μ b the distance between them;

[0058] Step 1.3: Calculate the interval length deta of WCSS; if deta ≥ Y det , then go to step 1.4; otherwise, go to step 1.5;

[0059] deta=max(WCSS b )-min(WCSS b )

[0060] Among them, Y det is the redistribution threshold;

[0061] Step 1.4: Get the corresponding WCSS b The cluster center μ with the largest value bmax and the client node set C bmax , C bmax Medium distance cluster center μ bmax The farthest client node is regarded as an outlier; the outliers and other cluster centers μ are calculated. b After adding the outliers to the client node set corresponding to its nearest cluster center, update the cluster center position of the client node set and return to step 1.2;

[0062] Step 1.5: Output each transport formation R b The customer node set C b , as each transport formation R b Initial task allocation plan.

[0063] Furthermore, according to each transport formation R b Initial task allocation scheme C b , using the low-cost path search algorithm to obtain each transport formation R b The initial path matrix PL b =[Tk b ,DaR b ] T ;

[0064]

[0065] Among them, Tk b is 1×(T b +2) matrix, representing the transport formation R b Inland transportation equipment b The order of the client nodes passed through during the task execution process, the elements of the first and last columns are 0, indicating that it starts from the warehouse node and finally returns to the warehouse node; T b For transport formation R b Inland transportation equipment b The number of client nodes passed through; i bρ For land transport equipment b The index of the ρth client node passed through, i bρ ∈C,ρ=1,2,...,T b ;

[0066] DaR b is 4×(T b +2) matrix, representing the transport formation R b The execution mission process matrix of the air transport equipment of the China G station;

[0067] For transport formation R b The g-th air transport equipment execution mission process matrix, For transport formation R b The index of the g-th air transport equipment, g=1,2,...,G; matrix Each column represents air transport equipment The first line of each column is the starting point of the displacement, the second line is the passing point of the displacement, the third line is the end point of the displacement, and the fourth line is the air transport equipment. 's index; For air transport equipment The index of the σth node passed through, For air transport equipment The number of nodes passed through, and the last node passed through is a warehouse node or a land transport equipment k b Recycled client nodes.

[0068] Furthermore, the Pareto optimization algorithm randomly selects exchange, reversal, and insertion operations to generate new solutions during each iteration, and uses a population reconstruction strategy to eliminate duplicate solutions in the population; calculates individual fitness based on the land-air collaborative path planning model, eliminates inferior individuals, and obtains the number N of individuals to be supplemented, and uses a superior individual supplementation strategy to supplement N new individuals.

[0069] Furthermore, the advantageous individual supplementation strategy specifically includes the following steps:

[0070] Step 2.1: Construct the decision space Ω according to the constraints of the land-air collaborative path planning model and divide the decision space Ω into M sub-areas ω r , r=1,2,...,M; set the maximum number of iterations Y of the dominant individual supplementation strategy, initialize the number of iterations t=0, and initialize the sampling frequency p of each sub-region r (0) = 1 / M;

[0071] Step 2.2: Use the Pareto local search method and calculate the sampling frequency p. r (t) From each sub-region ω r Sampling is performed in each sub-region ω r Construct N×p r (t) group of new solutions as individuals, all individuals constitute the population Z(t);

[0072] Step 2.3: Use the non-dominated sorting algorithm to sort the individuals in the population Z(t) by non-dominated sorting to obtain the number of non-dominated layers φ(t) of the population Z(t) and the dominance level R of each individual in the population Z(t).rn (t) and congestion distance d rn (t);

[0073] Step 2.4: Calculate the Pareto advantage score Sω of each sub-region r (t), update the sampling frequency p of each sub-region r (t+1);

[0074]

[0075]

[0076] Among them, |D m,r | represents the population Z(t) belonging to the mth non-dominated layer and from the subregion ω r The number of individuals in the construct;

[0077] Step 2.5: If t≠0, then integrate the N individuals in the population Z(t) in this iteration with the N individuals retained in the previous iteration, and remove the N individuals in the bottom 50% of the dominance level using the tournament principle, leaving only N individuals;

[0078] Step 2.6: If t < Y, set t = t + 1 and return to step 2.2; otherwise, output the N individuals retained in the current iteration as supplementary dominant individuals.

[0079] A computer device / equipment / system includes a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps of the above-mentioned method for collaborative path planning of manned and unmanned systems in large-scale unevenly distributed delivery scenarios.

[0080] A computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the steps of the above-mentioned method for collaborative path planning of manned and unmanned systems in large-scale non-uniformly distributed delivery scenarios.

[0081] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned method for collaborative path planning of manned and unmanned systems in large-scale non-uniformly distributed delivery scenarios.

[0082] The beneficial effects of the present invention are:

[0083] This paper designs an improved clustering algorithm to assign package delivery tasks to individual fleets and optimizes the resulting assignments, reducing the algorithm's computational complexity while avoiding imbalanced fleet workloads. Based on the resulting task assignments, a low-cost path search algorithm is designed to generate a low-cost initial routing plan for each fleet. Finally, during the optimization process, a population reconstruction strategy and a dominant individual supplementation strategy are designed to select a Pareto frontier with high-quality diversity and convergence. This paper can plan low-cost, workload-balanced order delivery routing plans in large-scale, unevenly distributed delivery scenarios, effectively improving delivery efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 It is a flowchart of the overall process of the present invention.

[0085] Figure 2 The Pareto front comparison charts of Random, K-means++ and the present invention in four scale scenarios.

[0086] Figure 3 The figure is a schematic diagram of the task allocation and path planning results of Random, K-means++ and the present invention in a scenario with a customer scale of 80.

[0087] Figure 4 Comparison diagram of the Pareto front of NSGA-II, MOEA / D, the present invention and MOPSO under four scale scenarios. DETAILED DESCRIPTION

[0088] The present invention will be further described below with reference to the accompanying drawings.

[0089] The starting point is the warehouse node, and the customer node set C = {1,2,...,α}, the land transportation equipment set K = {k1,k2,...,k β}、Air transport equipment set A={a1,a2,...,a γ}; Construct edge set E = {(i, j) | i, j∈V}, V = {0, 1, 2, ..., α}, where the 0th customer node is the warehouse node;

[0090] According to the maximum carrying capacity Q of air transport equipment D The packages of the customer nodes are divided into land transport packages and air transport packages, and the customer node set C is divided into the land transport package customer set T and the air transport package customer set D, T + D = C;

[0091] A land transport equipment k b With G air transport equipment a c Form a transport formation R b , G ≥ 2 and is less than the maximum number of air transport equipment that can be carried by land transport equipment;

[0092] Get the Manhattan distance required for land transport equipment to pass through edge (i, j) and time The Euclidean distance required for air transport equipment to pass through edge (i, j) and time The unit price of land transport equipment λ1, the unit price of air transport equipment λ2, the starting unit price of the transport fleet to perform the transport task λ3, and the service time required for land transport equipment at each customer node Service time for air freight equipment

[0093] The land-air collaborative path planning model F = {f1, f2} is expressed as:

[0094]

[0095] Among them, f1 is the workload balance index of the formation, which represents the difference in delivery completion time between the formation with the longest working time and the formation with the shortest working time; Indicates land transport equipment Formation The time it takes to return to the warehouse node after completing the task; Indicates land transport equipment The time it takes to return to the warehouse node after completing the task; Indicates air transport equipment a c The time it takes to return to the warehouse node after completing the task; f2 is the path cost of the formation, including land transportation cost, air transportation cost and inherent dispatch cost; if the air transport equipment a c Through the edge (i,j), then x i,j,c =1; otherwise, x i,j,c =0; if land transport equipment k b Through the edge (i,j), then y i,j,b =1; otherwise, y i,j,b =0;

[0096] Constraints include path constraints, time constraints, and energy consumption constraints;

[0097] The path constraints are:

[0098] (1) Each customer node can only be transported once by land transport equipment or air transport equipment:

[0099]

[0100] Among them, if the cth air transport equipment a c Serving client node i, then otherwise If the bth land transport equipment kb Serving client node i, then otherwise

[0101] (2) Each land transport device can only serve the customer nodes it passes through:

[0102]

[0103] (3) Each air transport device can only serve the client nodes it passes through and can only return to the land transport device that launched the air transport device:

[0104]

[0105] (4) The traffic flow of each piece of air transport equipment is kept balanced:

[0106]

[0107] The time constraints are:

[0108] (5) If node i∈V is air transport equipment a c Launch node, air transport equipment a c Time to reach customer node j∈C Equal to the time it leaves node i Plus the time required to pass through edge (i,j)

[0109]

[0110] Wherein, M is a sufficiently large positive value;

[0111] (6) Air transport equipment c Time of leaving client node i Equal to the time it takes to reach customer node i Plus the service time required at customer node i

[0112]

[0113] (7) Land transportation equipment b Time of leaving client node i Equal to the air transport equipment it launches a c Returns the time of client node i Plus the service time required at customer node i

[0114]

[0115] (8) Air transport equipment c Returns the time of client node i At the latest for land transport equipment k b The time it takes to return to the client node i after completing the task from the warehouse node

[0116]

[0117] The energy consumption constraint is:

[0118] (9) Air transport equipment c There is enough energy to leave the customer node i and return to node j, and to be transported by land transport equipment k b take over:

[0119]

[0120] Among them, if node j is air transport equipment a c The return node is otherwise, For air transport equipment c The remaining energy when leaving node i; e D is the energy consumption rate of air transport equipment;

[0121] (10) Air transport equipment c From the warehouse node or from the land transport equipment k b Launched at full energy:

[0122]

[0123] Among them, if node j is air transport equipment a c The transmitting node is otherwise, C D is the maximum energy of the air transport equipment;

[0124] (11) Air transport equipment c Weight of the package you carry Not exceeding the maximum carrying capacity Q D :

[0125]

[0126] The total number of land transport equipment is used as the number of cluster centers to cluster the customer node set. The clustering results are adjusted using the task redistribution algorithm to obtain the initial task allocation plan for each transport formation. The specific steps include:

[0127] Step 1.1: Take the total number of land transport equipment β as the number of cluster centers, cluster α customer nodes in the customer node set C, and obtain each transport formation R b The cluster center μb and the client node set C b ;

[0128] Step 1.2: Calculate the R of each transport formation using the WCSS formula b WCSS b ;

[0129]

[0130] Among them, dist(i bρ ,μ b ) is C b Client node i bρ and cluster center μ b the distance between them;

[0131] Step 1.3: Calculate the interval length deta of WCSS; if deta ≥ Y det , then go to step 1.4; otherwise, go to step 1.5;

[0132] deta=max(WCSS b )-min(WCSS b )

[0133] Among them, Y det is the redistribution threshold;

[0134] Step 1.4: Get the corresponding WCSS b The cluster center μ with the largest value bmax and the client node set C bmax , C bmax Medium distance cluster center μ bmax The farthest client node is regarded as an outlier; the outliers and other cluster centers μ are calculated. b After adding the outliers to the client node set corresponding to its nearest cluster center, update the cluster center position of the client node set and return to step 1.2;

[0135] Step 1.5: Output each transport formation R b The customer node set C b , as each transport formation R b Initial task allocation plan.

[0136] According to each transport formation R b Task allocation scheme C b , using the low-cost path search algorithm to obtain each transport formation R b The initial path matrix PL b =[Tk b ,DaRb ] T ;

[0137]

[0138] Among them, Tk b is 1×(T b +2) matrix, representing the transport formation R b Inland transportation equipment b The order of the client nodes passed through during the task execution process, the elements of the first and last columns are 0, indicating that it starts from the warehouse node and finally returns to the warehouse node; T b For transport formation R b Inland transportation equipment b The number of client nodes passed through; i bρ For land transport equipment b The index of the ρth client node passed through, i bρ ∈C,ρ=1,2,...,T b ;

[0139] DaR b is 4×(T b +2) matrix, representing the transport formation R b The execution mission process matrix of the air transport equipment of the China G station;

[0140] For transport formation R b The g-th air transport equipment execution mission process matrix, For transport formation R b The index of the g-th air transport equipment, g=1,2,...,G; matrix Each column represents air transport equipment The first line of each column is the starting point of the displacement, the second line is the passing point of the displacement, the third line is the end point of the displacement, and the fourth line is the air transport equipment. 's index; For air transport equipment The index of the σth node passed through, For air transport equipment The number of nodes passed through, and the last node passed through is a warehouse node or a land transport equipment k b Recycled client nodes;

[0141] Using the Pareto optimization algorithm, each individual in the population represents a set of path matrix solutions. During each iteration, exchange, reverse, and insertion operations are randomly selected to generate new solutions. The population reconstruction strategy is used to eliminate duplicate solutions in the population. The individual fitness is calculated according to the land-air collaborative path planning model. After eliminating inferior individuals, the dominant individual supplement strategy is used to supplement new individuals to obtain a dominant population. When the maximum number of iterations is reached, the optimal Pareto solution set is output, and the path planning plan for each transport formation is deconstructed according to the individual path matrix.

[0142] The strategy for supplementing dominant individuals specifically includes the following steps:

[0143] Step 2.1: Construct the decision space Ω according to the constraints of the land-air collaborative path planning model and divide the decision space Ω into M sub-areas ω r , r=1,2,...,M; set the maximum number of iterations Y of the dominant individual supplementation strategy, initialize the number of iterations t=0, and initialize the sampling frequency p of each sub-region r (0) = 1 / M;

[0144] Step 2.2: Use the Pareto local search method and calculate the sampling frequency p. r (t) From each sub-region ω r Sampling is performed in each sub-region ω r Construct N×p r (t) group of new solutions as individuals, all individuals constitute the population Z(t);

[0145] Step 2.3: Use the non-dominated sorting algorithm to sort the individuals in the population Z(t) by non-dominated sorting to obtain the number of non-dominated layers φ(t) of the population Z(t) and the dominance level R of each individual in the population Z(t). rn (t) and congestion distance d rn (t);

[0146] Step 2.4: Calculate the Pareto advantage score Sω of each sub-region r (t), update the sampling frequency p of each sub-region r (t+1);

[0147]

[0148] Among them, |D m,r | represents the population Z(t) belonging to the mth non-dominated layer and from the subregion ω r The number of individuals in the construct;

[0149] Step 2.5: If t≠0, then integrate the N individuals in the population Z(t) in this iteration with the N individuals retained in the previous iteration, and remove the N individuals in the bottom 50% of the dominance level using the tournament principle, leaving only N individuals;

[0150] Step 2.6: If t < Y, set t = t + 1 and return to step 2.2; otherwise, output the N individuals retained in the current iteration as supplementary dominant individuals.

[0151] Example 1:

[0152] The global optimal Pareto solution of the truck-drone formation path planning scheme rout i To decode:

[0153]

[0154] The routing plan for the truck in the first formation is <0,1,2,5,0>. The truck departs from warehouse node 0, serves customers at nodes 1, 2, and 5, and then returns to the warehouse node. The routing plan for drone #1 in the formation is <0,3,4,6,2>. Drone #1 is launched from warehouse node 0 and serves customers at nodes 3, 4, and 6, before being recovered by the truck at customer node 2. The routing plan for drone #2 in the formation is <1,7,8,5>. Drone #2 is launched from customer node 1 and serves customers at nodes 7 and 8, before being recovered by the truck at customer node 5.

[0155] In order to verify the effectiveness of the algorithm, this embodiment designs the following experiment. Since there are few algorithms that directly solve the problem of truck-drone collaborative path planning in large-scale non-uniformly distributed delivery scenarios, this invention uses three popular multi-objective optimization algorithms, MOEA / D, NSGA-II, and MOPSO, as baseline algorithms. The algorithm parameters are set as follows. The number of individuals N and the number of iterations Iter of the algorithm are set to 100 and 200 respectively. In MOEA / D, the number of weight vectors w = 100. In NSGA-II, P c =0.9, P m = 0.1. In MOPSO, the inertia weight is ω = 0.5, and the acceleration parameter is c1 = c2 = 2. In the present invention, the crossover rate q c and mutation rate q m 0.6 and 0.4 respectively, WCSS k The tolerable length of the difference is α=50.

[0156] The test cases are as follows. Since there is no dedicated test set for the problem proposed in this invention, this invention is based on the famous traveling salesman problem test set Dumas'TSPTW benchmark, and proposes 20, 40, 60, and 80 groups of examples for experiments. This invention utilizes the customer point number, customer point coordinates, and customer point time window information in the original test set. Assume that the speed of the drone and the truck is the same, but the transportation cost of the truck is 25 times that of the drone. Assume that each formation contains 1 truck and 2 drones, and the weight of 75% of the customers' packages meets the drone load requirements. In order to set the maximum range of the drone, this invention assumes that 50% of the flight paths can meet the maximum range constraint of the drone.

[0157] like Figure 2 As shown, in the four-scale examples, the Pareto front quality of the allocation algorithm of the present invention is significantly better than that of the other two allocation algorithms. Specifically, K-means++ and Random algorithms are higher than the present invention in terms of formation workload balance f1 and path cost f2. At the same time, the f1 value of K-means++ is similar to that of the present invention, but its performance in f2 is worse than that of the present invention and the Random algorithm. In contrast, the f2 value of Random is similar to that of the present invention, but its performance in f1 is worse than that of the present invention and the Random algorithm. Therefore, the present invention takes into account the advantages of the other two algorithms.

[0158] like Figure 3 In (a), (b), and (c), in the example with 80 customers, the Random algorithm allocates 4 teams with 22, 22, 20, and 16 tasks, respectively. However, the teams perform delivery tasks across multiple regions. The K-means++ algorithm allocates 4 teams with 34, 20, 10, and 16 tasks, respectively, and the teams only perform tasks in independent regions. The present invention allocates 4 teams with 22, 20, 20, and 18 tasks, respectively, and the teams only perform delivery tasks across multiple regions four times. Therefore, the present invention achieves a more optimal delivery solution.

[0159] like Figure 4 As shown in the figure, in the four scale examples, compared with NSGA-II, MOEA / D and MOPSO algorithms, the proposed method performs better on the Pareto front of f1 and f2, that is, it has better overall convergence and diversity, which proves the effectiveness of the proposed algorithm. Figure 4 The quality of the Pareto solution set in (b) is the best, and it is obvious that the Pareto front of the present invention is closer to the true solution. Figure 4 The quality of the Pareto solution set in (d) is inferior to that of the solution sets of the other three sizes, but more than 60% of the Pareto solution sets are still optimal.

[0160] In summary, the present invention considers a multi-objective collaborative routing problem of multiple trucks and drones, including the scale and location distribution of packages, where customer nodes can be served by trucks or drones. The present invention optimizes the balanced workload of formation and routing cost by developing a multi-objective optimization method based on a hybrid strategy. The algorithm includes initial task reallocation and path search methods, genetic operations and population solution reconstruction strategies, and dominant individual supplementation strategies including PLS. At the same time, the technical advantages of the hybrid strategy are utilized to improve the diversity and convergence of the population. Simulation results show that the present invention can generate path planning solutions with high-quality Pareto fronts on test cases at four scales, and outperforms existing algorithms in both workload balance and routing costs.

[0161] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A collaborative path planning method for manned and unmanned systems in large-scale, unevenly distributed delivery scenarios, characterized by: Obtain the warehouse node location, customer node set, land transport equipment set, and air transport equipment set; construct a graph network of warehouse nodes and all customer nodes; Obtain delivery tasks, consider the maximum carrying capacity of air transport equipment, and divide the packages into land transport packages and air transport packages. Then, form a transport formation with one land transport equipment and multiple air transport equipment. Construct a land-air collaborative path planning model, including the first and second indicators, and set constraints; Considering the distance and time required for land and air transport equipment to pass through each edge in the graph network, and the service time required by each customer node for land and air transport equipment, the difference in task completion time between the transport formations with the longest and shortest working times is used as the first indicator; Considering the unit price of land transport equipment, the unit price of air transport equipment, and the starting unit price of the transport fleet to perform the transport mission, the total cost of completing the mission is used as the second indicator; The total number of land transport equipment is used as the number of cluster centers to cluster the customer node set. The clustering results are adjusted using the task reallocation algorithm to obtain the initial task allocation plan for each transport formation. The initial task allocation plan for each transport formation is constructed into an initial path matrix using a low-cost path search algorithm. The Pareto optimization algorithm is used. Each individual in the population represents a set of path matrix solutions. After generating a new solution in the iterative process, the individual fitness is calculated according to the land-air collaborative path planning model. After eliminating inferior individuals, the dominant individual supplementation strategy is used to supplement new individuals to obtain a dominant population. When the maximum number of iterations is reached, the optimal Pareto solution set is output, and the path planning plan for each transport formation is deconstructed according to the individual path matrix.

2. The method for collaborative path planning for manned and unmanned systems in large-scale non-uniformly distributed delivery scenarios according to claim 1, characterized in that: Get the customer node set C = {1,2,...,α}, the land transportation equipment set K = {k1,k2,...,k β }、Air transport equipment set A={a1,a2,...,a γ }; Construct edge set E = {(i, j) | i, j∈V}, V = {0, 1, 2, ..., α}, where the 0th customer node is the warehouse node; According to the maximum carrying capacity Q of the air transport equipment D The packages of the customer nodes are divided into land transport packages and air transport packages, and the customer node set C is divided into the land transport package customer set T and the air transport package customer set D, T + D = C; A land transport equipment k b With G air transport equipment a c Form a transport formation R b , G ≥ 2 and is less than the maximum number of air transport equipment that can be carried by land transport equipment; Get the Manhattan distance required for land transport equipment to pass through edge (i, j) and time The Euclidean distance required for air transport equipment to pass through edge (i, j) and time The unit price of land transport equipment λ1, the unit price of air transport equipment λ2, the starting unit price of the transport fleet to perform the transport task λ3, and the service time required for land transport equipment at each customer node Service time for air freight equipment The land-air collaborative path planning model F = {f1, f2} is expressed as: Among them, f1 is the workload balance index of the formation, which represents the difference in delivery completion time between the formation with the longest working time and the formation with the shortest working time; Indicates land transport equipment Formation The time it takes to return to the warehouse node after completing the task; Indicates land transport equipment The time it takes to return to the warehouse node after completing the task; Indicates air transport equipment a c The time it takes to return to the warehouse node after completing the task; f2 is the path cost of the formation, including land transportation cost, air transportation cost and inherent dispatch cost; if the air transport equipment a c Through the edge (i,j), then x i,j,c =1; otherwise, x i,j,c =0; if land transport equipment k b Through the edge (i,j), then y i,j,b =1; otherwise, y i,j,b =0.

3. The method for collaborative path planning for manned and unmanned systems in large-scale, unevenly distributed delivery scenarios according to claim 2, characterized in that: The constraints include path constraints, time constraints and energy consumption constraints; The path constraints are: (1) Each customer node can only be transported once by land transport equipment or air transport equipment: Among them, if the cth air transport equipment a c Serving client node i, then otherwise If the bth land transport equipment k b Serving client node i, then otherwise (2) Each land transport device can only serve the customer nodes it passes through: (3) Each air transport device can only serve the client nodes it passes through and can only return to the land transport device that launched the air transport device: (4) The traffic flow of each piece of air transport equipment is kept balanced: The time constraints are: (5) If node i∈V is air transport equipment a c Launch node, air transport equipment a c Time to reach customer node j∈C Equal to the time it leaves node i Plus the time required to pass through edge (i,j) Wherein, M is a sufficiently large positive value; (6) Air transport equipment c Time of leaving client node i Equal to the time it takes to reach customer node i Plus the service time required at customer node i (7) Land transportation equipment b Time of leaving client node i Equal to the air transport equipment it launches a c Returns the time of client node i Plus the service time required at customer node i (8) Air transport equipment c Returns the time of client node i At the latest for land transport equipment k b The time it takes to return to the client node i after completing the task from the warehouse node The energy consumption constraint is: (9) Air transport equipment c There is enough energy to leave the customer node i and return to node j, and to be transported by land transport equipment k b take over: Among them, if node j is air transport equipment a c The return node is otherwise, For air transport equipment c The remaining energy when leaving node i; e D is the energy consumption rate of air transport equipment; (10) Air transport equipment c From the warehouse node or from the land transport equipment k b Launched at full energy: Among them, if node j is air transport equipment a c The transmitting node is otherwise, C D is the maximum energy of the air transport equipment; (11) Air transport equipment c Weight of the package you carry Not exceeding the maximum carrying capacity Q D :

4. The method for collaborative path planning for manned and unmanned systems in large-scale, unevenly distributed delivery scenarios according to claim 3, characterized in that: Get the initial task allocation plan for each transport formation, specifically: Step 1.1: Take the total number of land transport equipment β as the number of cluster centers, cluster α customer nodes in the customer node set C, and obtain each transport formation R b The cluster center μ b and the client node set C b ; Step 1.2: Calculate the R of each transport formation using the WCSS formula b WCSS b ; Among them, dist(i bρ ,μ b ) is C b Client node i bρ and cluster center μ b the distance between them; Step 1.3: Calculate the interval length deta of WCSS; if deta ≥ Y det , then go to step 1.4; otherwise, go to step 1.5; deta=max(WCSS b )-min(WCSS b ) Among them, Y det is the redistribution threshold; Step 1.4: Get the corresponding WCSS b The cluster center μ with the largest value bmax and the client node set C bmax , C bmax Medium distance cluster center μ bmax The farthest client node is regarded as an outlier; the outliers and other cluster centers μ are calculated. b After adding the outliers to the client node set corresponding to its nearest cluster center, update the cluster center position of the client node set and return to step 1.2; Step 1.5: Output each transport formation R b The customer node set C b , as each transport formation R b Initial task allocation plan.

5. The method for collaborative path planning for manned and unmanned systems in large-scale non-uniformly distributed delivery scenarios according to claim 4 is characterized by: According to each transport formation R b Initial task allocation scheme C b , using the low-cost path search algorithm to obtain each transport formation R b The initial path matrix PL b =[Tk b ,DaR b ] T ; Among them, Tk b is 1×(T b +2) matrix, representing the transport formation R b Inland transportation equipment b The order of the client nodes passed through during the task execution process, the elements of the first and last columns are 0, indicating that it starts from the warehouse node and finally returns to the warehouse node; T b For transport formation R b Inland transportation equipment b The number of client nodes passed through; i bρ For land transport equipment b The index of the ρth client node passed through, i bρ ∈C,ρ=1,2,...,T b ; DaR b is 4×(T b +2) matrix, representing the transport formation R b The execution mission process matrix of the air transport equipment of the China G station; For transport formation R b The g-th air transport equipment execution mission process matrix, For transport formation R b The index of the g-th air transport equipment, g=1,2,...,G; matrix Each column represents air transport equipment The first line of each column is the starting point of the displacement, the second line is the passing point of the displacement, the third line is the end point of the displacement, and the fourth line is the air transport equipment. 's index; For air transport equipment The index of the σth node passed through, For air transport equipment The number of nodes passed through, and the last node passed through is a warehouse node or a land transport equipment k b Recycled client nodes.

6. The method for collaborative path planning for manned and unmanned systems in large-scale non-uniformly distributed delivery scenarios according to claim 5, characterized in that: The Pareto optimization algorithm randomly selects exchange, reversal, and insertion operations to generate new solutions during each iteration, and uses a population reconstruction strategy to eliminate duplicate solutions in the population; calculates individual fitness based on the land-air collaborative path planning model, eliminates inferior individuals, and obtains the number N of individuals to be supplemented, and uses a superior individual supplementation strategy to supplement N new individuals.

7. The method for collaborative path planning for manned and unmanned systems in large-scale non-uniformly distributed delivery scenarios according to claim 6, characterized in that: The advantageous individual supplementation strategy specifically comprises the following steps: Step 2.1: Construct the decision space Ω according to the constraints of the land-air collaborative path planning model and divide the decision space Ω into M sub-areas ω r , r=1,2,...,M; set the maximum number of iterations Y of the dominant individual supplementation strategy, initialize the number of iterations t=0, and initialize the sampling frequency p of each sub-region r (0) = 1 / M; Step 2.2: Use the Pareto local search method and calculate the sampling frequency p. r (t) From each sub-region ω r Sampling is performed in each sub-region ω r Construct N×p r (t) group of new solutions as individuals, all individuals constitute the population Z(t); Step 2.3: Use the non-dominated sorting algorithm to sort the individuals in the population Z(t) by non-dominated sorting to obtain the number of non-dominated layers φ(t) of the population Z(t) and the dominance level R of each individual in the population Z(t). rn (t) and congestion distance d rn (t); Step 2.4: Calculate the Pareto advantage score Sω of each sub-region r (t), update the sampling frequency p of each sub-region r (t+1); Among them, |D m,r | represents the population Z(t) belonging to the mth non-dominated layer and from the subregion ω r The number of individuals in the construct; Step 2.5: If t≠0, then integrate the N individuals in the population Z(t) in this iteration with the N individuals retained in the previous iteration, and remove the N individuals in the bottom 50% of the dominance level using the tournament principle, leaving only N individuals; Step 2.6: If t < Y, set t = t + 1 and return to step 2.2; otherwise, output the N individuals retained in the current iteration as supplementary dominant individuals.

8. A computer device / apparatus / system comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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