Urban low-altitude logistics route network design optimization method based on adaptive evolution

Abstract

The invention relates to the technical field of low-altitude airline network design, in particular to an urban low-altitude logistics airline network design optimization method based on self-adaptive evolution, which comprises the following steps of: performing grid division on a low-altitude logistics planning area, and determining a low-altitude logistics network model to be optimized; a network total cost function established based on the transportation demand cost and the cost of the construction hub and the hub route, and a third-party security risk function established based on the population density of the transportation area; determining constraint conditions for optimizing the low-altitude logistics network model, wherein the constraint conditions comprise a network topology constraint, a flow distribution constraint and a voyage limitation constraint; optimizing the to-be-optimized low-altitude logistics network based on the objective function and the constraint condition by adopting an adaptive evolutionary algorithm to obtain a Pareto frontier optimization result of the low-altitude logistics network; according to the invention, economic cost and safety factors can be considered and balanced in logistics route network optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of low-altitude route network design, and in particular to an urban low-altitude logistics route network design optimization method based on adaptive evolution. Background Art

[0002] Urban low-altitude logistics is a new concept in the field of urban air transportation, which involves the application of advanced aircraft, such as drones, to transport goods within urban areas. Compared with traditional ground transportation logistics modes, urban low-altitude logistics has higher flexibility. The establishment of ground infrastructure, especially facilities that support vertical take-off and landing aircraft operations, also known as vertical airports, is key to the successful implementation of urban low-altitude logistics systems. As the take-off and landing nodes for aircraft to transport goods, vertical airports are transit stations and hubs for cargo consolidation, distribution and last-mile delivery. They overcome the challenges of traditional urban logistics through the advantages of air transportation and promote the seamless transportation of goods in urban environments.

[0003] It is a major challenge to determine the location of these low-altitude logistics hub nodes and design a safe and efficient route network to ensure the economy and efficiency of the entire low-altitude logistics system. On the one hand, the hub network design problem is an NP-hard problem. On the other hand, the urban low-altitude environment is complex, with dense buildings and dense populations. It is necessary to consider the third-party safety risks to the urban population caused by the crash of low-altitude logistics aircraft due to control or navigation failures. However, when designing the urban low-altitude logistics network, the impact of third-party safety risks on network design is not fully considered, and the conflicts of interest between different stakeholders are ignored. Summary of the invention

[0004] In view of the above problems, the present invention provides a method for optimizing the design of urban low-altitude logistics route networks based on adaptive evolution, which solves the technical problem of ignoring safety factors in the optimization of low-altitude logistics route networks in the prior art.

[0005] The present invention provides an urban low-altitude logistics route network design optimization method based on adaptive evolution, comprising the following steps:

[0006] Step S1, gridding the area of ​​low-altitude logistics planning, obtaining take-off and landing facility nodes, and determining the low-altitude logistics network model to be optimized based on the take-off and landing facility nodes;

[0007] Step S2, establishing an objective function for optimizing the low-altitude logistics network model, the objective function comprising: a total network cost function established based on transportation demand costs and the costs of building hubs and hub routes, and a third-party security risk function established based on the population density of the transportation area;

[0008] Step S3, determining the constraint conditions for optimizing the low-altitude logistics network model, wherein the constraint conditions include network topology constraints, flow distribution constraints, and range restriction constraints;

[0009] Step S4, using an adaptive evolutionary algorithm, based on the objective function and the constraint conditions, to optimize the low-altitude logistics network model to be optimized, and obtain a Pareto frontier optimization result of the low-altitude logistics network model;

[0010] Step S5: determining the optimal urban low-altitude logistics route network based on the Pareto front optimization result.

[0011] Preferably, the step S1 specifically includes:

[0012] Step S1-1, dividing the area of ​​low-altitude logistics planning into grids of uniform size, clustering the logistics demand points in the grids, and using the cluster center points obtained by clustering as take-off and landing facility nodes;

[0013] Step S1-2: Construct the directed graph G corresponding to the low-altitude logistics network model to be optimized<N,E> , the take-off and landing facilities are regarded as a node set N of a directed graph, N = {1, ..., |N|}, |N| represents the total number of all nodes; the edge E represents the flight path between two nodes; the nodes of the directed graph include non-hub nodes and hub nodes; the nodes and edges in the directed graph are encoded:

[0014] For node coding, a 0-1 binary list coding is used, where 1 means that the node at the index is selected as a hub node, otherwise it is a non-hub node;

[0015] For edge coding, 0-1 symmetric matrix coding is used, where 1 means that the connection between the node pairs represented by the row and column indices is activated, otherwise, there is no connection between the node pairs.

[0016] Preferably, in step S2, the total network cost function includes the variable cost of transportation demand and the fixed cost required for building hubs and hub routes, and is expressed as:

[0017]

[0018] Among them, w ij represents the transportation demand from node i to node j of the starting point-end point; c ij ,c ik ,c lj ,c kl are the transportation costs from node i to node j, node i to node k, node l to node j, and node k to node l respectively; y ijklis a 0-1 decision variable. If its value is 1, it means that the first hub node through which the transportation demand from node i to node j passes is k, and the last hub node is l; α is the economic discount coefficient between hub nodes; f ijkl is a 0-1 decision variable. If its value is 1, it means that the transportation demand from node i to node j passes through the hub arc kl; β is the economic penalty coefficient between non-hub nodes; s ij is a 0-1 decision variable. If its value is 1, it means that the transportation demand from node i to node j is directly transported without passing through the hub node; f k represents the cost of building hub node k; x k is a 0-1 decision variable. If its value is 1, it means that the decision node k is a hub node; g kl is the fixed cost required to activate the edge between hub node k and hub node l; z kl is a 0-1 decision variable. If its value is 1, it means that the edge between the hub nodes k and l is activated;

[0019] The expression of the third-party security risk function is:

[0020]

[0021] Among them, r ij ,r ik ,r lj ,r kl They are the third-party safety transportation risks from node i to node j, node i to node k, node l to node j, and node k to node l;

[0022] The third party security transportation risk ij The specific calculation expression is:

[0023]

[0024] Among them, a, b∈N, and a≠b, r ab The third-party safety transportation risk of the affected area that the aircraft passes through from node a to node b; A exp (a,b) is the potential area exposed to aircraft crashes on the route from node a to node b; ρ(x,y) is the affected area A exp Population density at grid (x,y) in grid (i,j).

[0025] Preferably, in step S3, the network topology constraint is used to ensure that the premise for activating the hub edge is that both nodes of the edge are hub nodes, the network formed between the hubs is connected, and there is at least one hub node in the logistics network, and the expression is:

[0026] C1:z kl ≤xk k,l∈N,k <l

[0027] C2:z kl ≤x l k,l∈N,k <l

[0028] C3:

[0029] C4:

[0030] C5:

[0031] C6:∑ k∈N x k ≥1

[0032] C7:s ij +x j ≤1i,j∈N

[0033] C8:s ij +x i ≤1i,j∈N

[0034] in, is the connectivity variable, and the connectivity of the hub network is ensured by defining a spanning tree with its root node at the hub node k. The value of 1 indicates that the spanning tree starting from the hub node k passes through the hub node i k To hub node j k The edge of The value of 1 indicates that the spanning tree starting from the hub node k passes through the hub node j. k To hub node i k The edge of

[0035] The flow allocation constraint is used to ensure that each transport demand pair is transported by only one path, that transport demands that cannot be transported directly can only be transported by using open hubs, and that the flow is balanced. The expression is:

[0036] C9:s ij +∑ k∈n ∑ l∈N y ijkl =1i,j∈N

[0037] C10:∑ l∈N y ijkl +∑ l∈N,l≠k y ijlk ≤x k i,j,k∈N

[0038] C11:∑ j∈N ∑ l∈N,l≠k f ijkl -∑j∈N ∑ l∈N,l≠k f ijlk =∑ j∈N ∑ l∈N w ij y ijkl -∑ j∈N ∑ l∈ N w ij y ijlk i,k∈N

[0039] C12:f ijkl ≤w ij z kl i,j,k,l∈N,k <l

[0040] The range constraint is used to ensure that all activated edges and transport paths meet the aircraft range, and the expression is:

[0041] C13:

[0042] C14:

[0043] C15:d kl z kl ≤Dk,l∈N,k <l

[0044] C16:

[0045] Where D is the range of the aircraft.

[0046] Preferably, the step S4 specifically includes:

[0047] Step S4-1: Initialize the basic parameters of the adaptive evolutionary algorithm, which include: population size N c , the number of take-off and landing facility nodes |N|, the number of maximum fitness calculations, and the length of the first-in-first-out queue that records operator usage |SW|;

[0048] Step S4-2: Generate N based on random greedy strategy c individuals as the initial population, and the initial population as the contemporary population; the value of the objective function of the individual is calculated, and the value of the objective function is used as the fitness of the individual; the individual is generated by: establishing a directed graph consisting of a hub node set and a non-hub node set, and the directed graph is used as the individual;

[0049] Step S4-3: For the contemporary population, a binary tournament strategy is used to select and obtain selected individuals;

[0050] Step S4-4, determining a candidate crossover mutation operator combination, using a multi-armed bandit selection mechanism, and performing adaptive selection based on the credit value of the candidate crossover mutation operator combination to obtain a screened crossover mutation operator combination;

[0051] Step S4-5: For the selected individuals, use the screened crossover and mutation operator combination to perform crossover and mutation processing to obtain child individuals, calculate the fitness of the child individuals, add the child individuals to the offspring population, and determine the offspring population;

[0052] Step S4-6, updating the credit value of the candidate crossover mutation operator combination;

[0053] Step S4-7, return to step S4-3, until the number of individuals in the offspring population reaches a preset population size;

[0054] Step S4-8: merge the contemporary population and the offspring population, and perform quick sorting on the merged population based on the non-dominated rule, and select the top N c The population formed by each individual updates the contemporary population;

[0055] Step S4-9, determine whether the maximum number of fitness calculations has been reached. If not, return to step S4-3; otherwise, complete the adaptive evolution and use the contemporary population as the Pareto frontier optimization result of the low-altitude logistics network model.

[0056] Preferably, the step S4-2 specifically includes:

[0057] Step S4-2-1, establish a directed graph of |N| nodes, between 1 and A random number k is generated, and k nodes are randomly selected from all nodes to form the hub node set H, and the other nodes form the non-hub node set;

[0058] Step S4-2-2: determine whether the hub node set H can generate a feasible solution that satisfies the range restriction constraint and the network topology constraint; the determination method is specifically as follows:

[0059] Add the edges between hub nodes whose distance is less than the flight distance to the directed graph. If the directed graph is not connected, it is determined that no feasible solution can be generated;

[0060] Otherwise, if all hub nodes can be connected to at least one hub node while satisfying the range constraint, it is determined that a feasible solution can be generated;

[0061] Step S4-2-3: If no feasible solution can be generated, return to step S4-2-1 until it is determined that a feasible solution can be generated, and obtain the directed graph corresponding to the feasible solution;

[0062] Step S4-2-4: for the hub node set in the directed graph corresponding to the feasible solution, activate the edges between the hub nodes that meet the range constraint, and for each non-hub node, select a random number of non-hub access / distribution edges on the premise of meeting the range constraint, and randomly select non-hub direct edges that meet the range constraint;

[0063] Step S4-2-5, determine whether the directed graph satisfies the flow distribution constraint, obtain the directed graph that satisfies the flow distribution constraint as the individual; calculate the objective function value of the individual, and use the objective function value as the fitness of the individual.

[0064] Preferably, step S4-4 specifically includes:

[0065] Step S4-4-1, determining a crossover operator, wherein the crossover operator performs crosswise modification on the node coding and the edge coding in the directed graph; determining a mutation operator, wherein the mutation operator performs variability modification on the node coding and the edge coding in the directed graph;

[0066] Step S4-4-2, obtaining a plurality of crossover-mutation operator combinations by combining the crossover operator and the mutation operator as the candidate crossover-mutation operator combinations;

[0067] Step S4-4-3: Select the candidate crossover mutation operator combination using a confidence upper bound algorithm to obtain a screened crossover mutation operator combination.

[0068] Preferably, the step S4-4-3 specifically includes: screening the crossover mutation operator combination, the expression is:

[0069]

[0070] Among them, op is the crossover mutation operator combination after screening; FRR u is the credit value of the combinatorial operator u; C′ is the proportional factor that adjusts the trade-off between development and exploration during the search process, OPs is the set of candidate crossover mutation combinatorial operator combinations, n v ,n u are the frequencies of the combined operators v,u∈OPs in the most recent |SW| times of use of operators;

[0071] FRR u The expression is:

[0072]

[0073] Among them, Reward u is the fitness improvement rate FIR obtained after all the combined operators u are used in the most recent |SW| times of using the operators u The sum of

[0074]

[0075] Among them, FIR u P represents the fitness improvement rate of the combined operator u. p’ is the set of parent individuals, |P p’ | represents the size of the parent individual set, where p'∈P p’ is the parent individual. c’ P p’ The generated set of offspring individuals, |P c’ | represents the size of the offspring individual set, c'∈P c’ For offspring individuals.

[0076] Preferably, in step S4-5, the fitness of the sub-individual is calculated by: taking the objective function value of the sub-individual as the fitness of the sub-individual;

[0077] The step S4-6 specifically includes: updating the FRR of the candidate crossover mutation operator combination u The value of and updates the first-in-first-out queue SW that records the usage of operators.

[0078] Compared with the prior art, the present invention has at least the following beneficial effects:

[0079] (1) The present invention realizes the multi-objective optimization design of the low-altitude logistics network by introducing a comprehensive objective function based on transportation demand cost, construction cost and population density, and combining constraints such as network topology, flow distribution and range restriction. The adaptive evolutionary algorithm is adopted to take into account factors such as cost, efficiency and safety in the network design process, thereby reducing the distribution cost and the safety risk of the third party and improving the distribution efficiency.

[0080] (2) The present invention introduces a multi-armed bandit mechanism and a binary tournament strategy into the optimization algorithm, adaptively selects a combination of crossover and mutation operators, and improves the intelligence and convergence efficiency of the algorithm. The Pareto frontier optimization results finally obtained provide a reliable decision-making basis for the optimal route deployment of the urban low-altitude logistics network, achieving the improvement of distribution efficiency and the balance of multiple objectives.

[0081] (3) The present invention constructs a low-altitude logistics network model to be optimized by gridding the low-altitude logistics planning area and establishing take-off and landing facility nodes. Through precise model design and grid division, the basic layout problem of the low-altitude logistics network in complex urban areas is solved, providing a clear structural framework for subsequent optimization, and effectively improving the scientificity and applicability of network planning. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] The drawings are only for the purpose of illustrating particular embodiments and are not to be construed as limiting the invention.

[0083] Figure 1 A flow chart of the urban low-altitude logistics route network design optimization method based on adaptive evolution provided by the present invention.

[0084] Figure 2 A flow chart of the adaptive evolution process provided by the present invention.

[0085] Figure 3 Schematic diagram of the adaptive operator selection mechanism provided by the present invention.

[0086] Figure 4 A schematic diagram of node coding and network edge coding provided by the present invention.

[0087] Figure 5 Schematic diagram of the crossover operator provided by the present invention.

[0088] Figure 6 Schematic diagram of the mutation operator provided by the present invention. DETAILED DESCRIPTION

[0089] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. In addition, the present invention can also be implemented in other ways different from those described herein, and therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

[0090] In order to illustrate the effectiveness of the method proposed by the present invention, the above technical solution of the present invention is described in detail below through a specific embodiment. Figure 1 As shown, a method for optimizing the design of urban low-altitude logistics route networks based on adaptive evolution is disclosed, and the specific implementation steps are as follows:

[0091] Step S1, gridding the area of ​​low-altitude logistics planning, obtaining take-off and landing facility nodes, and determining the low-altitude logistics network to be optimized based on the take-off and landing facility nodes.

[0092] In this step, the area of ​​low-altitude logistics planning is divided into grids, the logistics demand points within the grids are clustered, and the cluster center points obtained by clustering are used as take-off and landing facility nodes.

[0093] The grid division divides the area of ​​low-altitude logistics planning into grids of uniform size. The take-off and landing facility nodes can be site facilities for take-off and landing of drones or other low-altitude logistics tools, and the take-off and landing facility nodes are set at locations where the logistics demand obtained by clustering is concentrated.

[0094] The urban low-altitude logistics network design problem is modeled and the directed graph G corresponding to the low-altitude logistics network to be optimized is constructed.<N,E> The specific process includes taking the take-off and landing facilities as a node set N of a directed graph, N = {1, ..., |N|}, representing the location of each take-off and landing facility, |N| represents the total number of all nodes; the edge E represents the flight path between two nodes. The nodes of the directed graph of the present invention include non-hub nodes and hub nodes. The hub nodes can be used as key transfer and distribution points in the low-altitude logistics network, and the nodes other than the hub nodes are non-hub nodes.

[0095] The present invention encodes the nodes and edges in the directed graph. Specifically, suppose there are |N| take-off and landing facility nodes;

[0096] In node coding, 0-1 binary list coding is adopted, where 1 means that the node at the index is selected as a hub node, otherwise it is a non-hub node;

[0097] The edges are encoded using a 0-1 symmetric matrix, where 1 means that the connection between the node pair represented by the row and column index is activated, otherwise, there is no connection between the node pairs.

[0098] like Figure 4 As shown, there are 6 take-off and landing facility nodes, among which nodes 2, 3, and 4 are selected as hub nodes, and the edges between hub node pairs 2-3 and 2-4 are activated. At the same time, the access / distribution edges 1-2, 1-3, 3-6, and 4-5 between non-hub nodes and hub nodes are activated, and the non-hub node direct edge 5-6 is activated.

[0099] Step S2: Establish an objective function for optimizing the low-altitude logistics network, wherein the objective function includes: a total network cost function established based on the transportation demand cost and the cost of building hubs and hub routes, and a third-party safety risk function established based on the population density of the transportation area.

[0100] In this step, the objective function of the urban low-altitude logistics network design problem model is constructed, and the objective function includes the total network cost function and the third-party security risk function. The target effect of the evaluation is to minimize the total network cost and minimize the third-party security risk of the network.

[0101] Specifically, the total network cost function includes the variable cost of transportation demand and the fixed cost required for building hubs and hub routes, and is expressed as:

[0102]

[0103] Among them, w ij represents the transportation demand from node i to node j of the starting point-end point; c ij ,c ik ,clj ,c kl are the transportation costs from node i to node j, node i to node k, node l to node j, and node k to node l respectively; y ijkl is a 0-1 decision variable. If its value is 1, it means that the first hub node through which the transportation demand from node i to node j passes is k, and the last hub node is l; α is the economic discount coefficient between hub nodes; f ijkl is a 0-1 decision variable. If its value is 1, it means that the transportation demand from node i to node j passes through the hub arc kl; β is the economic penalty coefficient between non-hub nodes; s ij is a 0-1 decision variable. If its value is 1, it means that the transportation demand from node i to node j is directly transported without passing through the hub node; f k represents the cost of building hub node k; x k is a 0-1 decision variable. If its value is 1, it means that the decision node k is a hub node; g kl is the fixed cost required to activate the edge between hub node k and hub node l; z kl It is a 0-1 decision variable. If its value is 1, it means that the edge between the hub nodes k and l is activated.

[0104] The total network cost function provided by the present invention introduces an economic discount coefficient and an economic penalty coefficient to make a trade-off between hub node transportation and direct transportation. It can take into account the economy of the transportation path, balance the investment in infrastructure construction, and minimize the overall cost of the low-altitude logistics network.

[0105] In some embodiments, the decision variable y ijkl 、f ijkl 、s ij The calculation steps include:

[0106] (1) Construct the cost parameter matrix C = [c ij ] |N|×|N| And the security risk parameter matrix R = [r ij ] |N|×|N| , perform bi-norm normalization on C and R to obtain the normalized cost matrix and normalized safety risk matrix C n =[c ij n ] |N|×|N| , R n =[r ij n ] |N|×|N| , where c ij n ,r ij n represents the normalized c ij and r ij , |N| is the number of nodes;

[0107] (2) Based on the hub node set H, based on C n , R n Construct the weighted cost of the network edge (i, j) with the edge attributes The expression is:

[0108]

[0109] Among them, N\H represents the difference between N and H, w1 and w2 are weighting coefficients, both set to 0.5. The weighted cost matrix is ​​expressed as

[0110] (3) Calculate the weighted cost of unit flow of any hub pair (k, l) using the Dijkstra algorithm Calculate the weighted cost per unit flow of transport demand pair (i,j) When direct edges are not considered, The calculation expression is:

[0111]

[0112] Among them, A i ,A j Respectively represent the hub sets connected to nodes i and j;

[0113] When considering direct edges, The calculation expression is:

[0114]

[0115] Among them, SL represents the set of directly connected edges between non-hub nodes.

[0116] (4) will have the smallest The path between the node pairs with the value is determined as the shortest path, and the decision variable y is determined by the shortest path ijkl 、f ijkl 、s ij The value of .

[0117] In some embodiments, the transportation cost c from node i to node j is ij , the transportation cost is linearly related to the distance, and the specific calculation expression is:

[0118] c ij =ηd ij

[0119]

[0120] Among them, η is the linear coefficient, d ij represents the Euclidean distance between node i and node j, (xi ,y i ) and (x j ,y j ) are the position coordinates of node i and node j respectively.

[0121] The expression of the third-party security risk function is:

[0122]

[0123] Among them, r ij ,r ik ,r lj ,r kl They are the third-party security transportation risks from node i to node j, node i to node k, node l to node j, and node k to node l.

[0124] In some embodiments, the third party security transport risk ij The specific calculation expression is:

[0125]

[0126] Among them, a, b∈N, and a≠b, r ab The third-party safety transportation risk of the affected area that the aircraft passes through from node a to node b; A exp (a,b) is the potential area exposed to aircraft crashes on the route from node a to node b; ρ(x,y) is the affected area A exp Population density at grid (x,y) in grid (i,j).

[0127] The third-party safety risk function of the present invention comprehensively considers the safety transportation risks between different nodes and introduces the calculation of population density, so that the risk assessment is not only based on the path itself, but also deeply considers the population distribution characteristics of the areas that may be affected along the way, and can more accurately identify and quantify the potential safety risks in the network transmission process.

[0128] Step S3: determining the constraints for optimizing the low-altitude logistics network, wherein the constraints include network topology constraints, flow distribution constraints, and range restriction constraints.

[0129] For the directed graph of the urban low-altitude logistics network design problem, it is necessary to construct constraints on the directed graph based on the requirements of the real-world logistics network. The constraints include: network topology constraints, flow distribution constraints and range limit constraints.

[0130] Specifically, the expression of the network topology constraint is:

[0131] C1:z kl ≤x k k,l∈N,k <l

[0132] C2:z kl ≤x l k,l∈N,k <l

[0133] C3:

[0134] C4:

[0135] C5:

[0136] C6:∑ k∈N x k ≥1

[0137] C7:s ij +x j ≤1i,j∈N

[0138] C8:s ij +x i ≤1i,j∈N

[0139] in, is the connectivity variable, and the connectivity of the hub network is ensured by defining a spanning tree with its root node at the hub node k. The value of 1 indicates that the spanning tree starting from the hub node k passes through the hub node i k To hub node j k The edge of The value of 1 indicates that the spanning tree starting from the hub node k passes through the hub node j. k To hub node i k edge.

[0140] Constraints C1 and C2 ensure that the premise for activating hub edges is that both nodes of the edge are hub nodes; constraints C3, C4, and C5 ensure that the network formed between hubs has connectivity; and constraint C6 ensures that there is at least one hub node in the logistics network.

[0141] The expression of the flow distribution constraint is:

[0142] C9:s ij +∑ k∈N ∑ l∈N y ijkl =1i,j∈N

[0143] C10:∑ l∈N y ijkl +∑ l∈N,l≠k y ijlk ≤x k i,j,k∈N

[0144] C11:∑j∈N ∑ l∈N,l≠k f ijkl -∑ j∈N ∑ l∈N,l≠k f ijlk =∑ j∈N ∑ l∈N w ij y ijkl -∑ j∈N ∑ l∈ N w ij y ijlk i,k∈N

[0145] C12:f ijkl ≤w ij z kl i,j,k,l∈N,k <l

[0146] Constraint C9 ensures that each transport demand pair is transported by only one path; constraint C10 ensures that transport demands that cannot be transported directly can only be transported using open hubs; constraints C11 and C12 are flow balance constraints.

[0147] The expression of the range limit constraint is:

[0148] C13:

[0149] C14:

[0150] C15:d kl z kl ≤Dk,l∈N,k <l

[0151] C16:

[0152] Where D is the range of the aircraft.

[0153] Step S4: Adopting an adaptive evolutionary algorithm, based on the objective function and the constraint conditions, the low-altitude logistics network to be optimized is optimized to obtain a Pareto frontier optimization result of the low-altitude logistics network.

[0154] The present invention adopts an adaptive evolutionary algorithm to optimize the design of the urban low-altitude logistics route network, which specifically includes the following steps:

[0155] Step S4-1: Initialize basic parameters of the adaptive evolutionary algorithm.

[0156] Specifically, the basic parameters of the algorithm include the population size N c, the number of take-off and landing facility nodes |N|, the maximum number of fitness calculations maxFEs, and the length of the first-in-first-out queue that records operator usage in the adaptive operator selection mechanism |SW|.

[0157] Step S4-2: Generate N based on random greedy strategy c Individuals are used as the initial population, and the initial population is used as the contemporary population. The method for generating individuals in the present invention is to establish a directed graph consisting of a hub node set and a non-hub node set, and use the directed graph as individuals. Specifically, it includes:

[0158] Step S4-2-1, establish a directed graph of |N| nodes, between 1 and A random number k is generated, and k nodes are randomly selected from all nodes to form the hub node set H, and the other nodes form the non-hub node set;

[0159] Step S4-2-2: determine whether the hub node set H can generate a feasible solution that satisfies the range restriction constraint and the network topology constraint; the determination method is specifically as follows:

[0160] Add the edges between hub nodes whose distance is less than the flight distance to the directed graph. If the directed graph is not connected, it is determined that no feasible solution can be generated;

[0161] Otherwise, if all hub nodes can be connected to at least one hub node while satisfying the range constraint, it is determined that a feasible solution can be generated.

[0162] Step S4-2-3: If no feasible solution can be generated, return to step S4-2-1 until it is determined that a feasible solution can be generated, and obtain the directed graph corresponding to the feasible solution.

[0163] Step S4-2-4: for the hub node set in the directed graph corresponding to the feasible solution, activate the edges between the hub nodes that meet the range constraint, and for each non-hub node, select a random number of non-hub access / distribution edges on the premise of meeting the range constraint, and randomly select non-hub direct edges that meet the range constraint;

[0164] like Figure 4 As shown, the non-hub access / distribution edge refers to the edge between a non-hub node and a hub node; the non-hub direct edge refers to the edge between hub nodes.

[0165] Step S4-2-5, determine whether the directed graph satisfies the flow distribution constraint, obtain the directed graph that satisfies the flow distribution constraint as the individual; calculate the objective function value of the individual, and use the objective function value as the fitness of the individual.

[0166] Step S4-3: For the contemporary population, a binary tournament strategy is used to select and obtain selected individuals;

[0167] Step S4-4, determining a candidate crossover mutation operator combination, using a multi-armed bandit selection mechanism, and performing adaptive selection based on the credit value of the crossover mutation operator combination to obtain a screened crossover mutation operator combination;

[0168] Step S4-4-1, determine a crossover operator, the crossover operator will cross-modify the node coding and the edge coding in the directed graph; determine a mutation operator, the mutation operator will mutate the node coding and the edge coding in the directed graph.

[0169] The crossover-mutation operator combination is obtained by combining the crossover operator and the mutation operator.

[0170] like Figure 5 As shown, the crossover operator of the present invention is used to modify the node coding and edge coding in a directed graph. In the following text, the node coding and edge coding are referred to as chromosomes, each coding value in the node coding and edge coding is referred to as a gene, and the node coding and edge coding before and after the modification are referred to as the parent and the child, respectively.

[0171] The crossover operator of the present invention adopts 8 operators, including forward and backward single-point crossover, two-point crossover, multi-point crossover and uniform crossover, customized based on the problem, to realize the generation of offspring from parent generation.

[0172] Specifically, in the forward single-point crossover operator, a crossover point τ∈[1,2,…,|N|] is randomly selected at the same position of the parent chromosome, and the node chromosomes of the two daughter chromosomes are generated by exchanging the genes behind the crossover point; the link chromosomes of the daughter chromosomes are generated by exchanging the blocks consisting of the back τ rows and columns of size τ*τ. The backward single-point crossover operator is similar to the forward single-point crossover operator, but the genes representing the link decisions of the two daughter chromosomes are obtained by exchanging the blocks consisting of the first τ rows and columns of size τ*τ. The forward two-point crossover operator randomly selects two crossover points, exchanges the genes of the parent between the two points, and generates two daughter genes; among them, the gene part of the node decision directly exchanges the part between the two points to generate the node decision gene of the daughter chromosome, and the forward crossover method is used to exchange the link decision chromosomes in the vertical and horizontal directions. The backward two-point crossover operator, the operation of the gene part of the node decision is the same as the forward two-point crossover operator, and the link decision chromosome uses the backward crossover method to obtain the corresponding part of the daughter chromosome.

[0173] Forward multi-point crossover random selection Crossover points, the genes of the parents are exchanged between two adjacent selection points to produce new offspring; the forward crossover method is used to exchange the link decision chromosomes in the vertical and horizontal directions. Backward multi-point crossover uses similar steps to forward multi-point crossover, the difference is that the backward crossover method is used to exchange the link decision chromosomes in the vertical and horizontal directions. In forward uniform crossover, a probability array with the same length as the parent element is randomly generated, and the parent genes are exchanged according to the predefined probability value. If the elements of the array exceed the predefined threshold, set to 0.5. The genes with the corresponding index are exchanged to produce offspring; the genes of node decision are exchanged using standard uniform crossover, while the genes of link decision are operated on two-dimensional matrices using the forward exchange method. Backward uniform crossover uses similar steps to forward multi-point crossover, the difference is that it exchanges the genes representing the link matrix in a backward two-dimensional crossover manner.

[0174] The mutation operator of the present invention is used to modify the gene in the node coding and edge coding in the directed graph. The mutation operator includes a SLAM operator and a CenCS operator. Figure 6 Describe the specific operation of the mutation operator. Specifically, the SLAM operator applies a simple bit mutation to the node decision array, including adding or removing a hub; for the link decision matrix, a pair of hub nodes or a pair of non-hub nodes are randomly selected, and all links connected to the selected node pair are exchanged to form new child nodes. The CenCS operator mutates the chromosome through the newly defined centrality. The expression of the newly defined centrality of node i is:

[0175]

[0176] Where N is the node set; |N| is the number of nodes; w ij is the transportation demand between node i and node j; is d ij The standardized value of For r ij The standardized value of .

[0177] For the mutation of the hub decision chromosome, a node is randomly selected. If the node is currently a hub, another hub is randomly selected and the node with a lower centrality value is converted to a non-hub node. Conversely, if the node is a non-hub node, another non-hub node is randomly selected and the node with a higher centrality value is converted to a hub node.

[0178] Step S4-4-2, obtaining a plurality of crossover-mutation operator combinations by combining the crossover operator and the mutation operator as the candidate crossover-mutation operator combinations;

[0179] Table 1

[0180] Operator Crossover operator Mutation Operator Operator Crossover operator Mutation Operator 1 Even cross (front / back) none 7 Single point crossover (front / rear) none 2 Even cross (front / back) SLAM 8 Two-point crossover (front / back) none 3 Even cross (front / back) CenCS 9 none SLAM 4 Multi-point crossover (front / rear) none 10 none CenCS 5 Multi-point crossover (front / rear) SLAM 11 none none 6 Multi-point crossover (front / rear) CenCS

[0181] As shown in Table 1, the present invention combines the crossover operator and the mutation operator, and adopts the 11 crossover mutation operator combinations in Table 1 as the crossover mutation operator combinations. In the case of forward and reverse crossover operators, the selection probability P is introduced. d , when P d ≤0.5, forward crossover is applied, otherwise, backward crossover is used.

[0182] Step S4-4-3: Use the confidence upper bound algorithm to screen the candidate crossover mutation operator combinations to obtain the screened crossover mutation operator combinations.

[0183] The multi-armed bandit selection strategy uses a confidence upper bound algorithm to screen the crossover mutation operator combination, and the expression is:

[0184]

[0185] Among them, op is the crossover mutation operator combination after screening; FRR u is the credit value of the combinatorial operator u; C′ is the proportional factor that adjusts the trade-off between development and exploration during the search process. OPs = {1,…,11} is the set of candidate crossover and mutation combinatorial operators. n v ,n u are the frequencies of the combined operators v,u∈OPs in the most recent |SW| times of use of operators.

[0186] FRR u The expression is:

[0187]

[0188] Among them, Reward u It is the sum of the domination-based fitness improvement rates obtained after all combined operators u are used in the most recent |SW| times of using the operators.

[0189] The fitness improvement rate based on domination is used to measure the performance of an operator combination in one application. The expression is:

[0190]

[0191] Among them, FIR u P represents the fitness improvement rate of the combined operator u. p’ is the set of parent individuals, |P p’ | represents the size of the parent individual set, where p'∈P p’ is the parent individual. c’ P p’ The generated set of offspring individuals, |P c’| represents the size of the offspring individual set, c'∈p c’ For offspring individuals.

[0192] Step S4-5, for the selected individuals, use the screened crossover and mutation operator combination to perform crossover and mutation processing to obtain child individuals, calculate the fitness of the child individuals, and add the child individuals to the offspring population to determine the offspring population;

[0193] In this step, the fitness of the sub-individual is calculated in the same manner as the objective function value, and the objective function value of the sub-individual is used as the fitness of the sub-individual.

[0194] Step S4-6: Update the credit value of the candidate crossover mutation operator combination.

[0195] Specifically, the FRR of the candidate crossover mutation operator combination is updated according to the expression in step S4-4. u The value of and updates the first-in-first-out queue SW that records the usage of operators.

[0196] Step S4-7, return to step S4-3, until the number of individuals in the offspring population reaches a preset population size;

[0197] Step S4-8: merge the contemporary population and the offspring population, and perform quick sorting on the merged population based on the non-dominated rule, and select the top N c The population formed by individuals updates the contemporary population.

[0198] The non-dominated rule is a ranking criterion in this field, which is used to evaluate the quality of solutions, especially to deal with the situation where multiple objectives conflict with each other.

[0199] Step S4-9, determine whether the maximum number of fitness calculations has been reached. If not, return to step S4-3; otherwise, complete the adaptive evolution and use the contemporary population as the Pareto frontier optimization result of the low-altitude logistics network.

[0200] The Pareto front refers to the set of solutions found so far that cannot be further improved on one objective without compromising another objective. In the present invention, the optimal Pareto front of the model represents the completion of the trade-off between economic cost and safety, and obtains an urban low-altitude logistics route network that takes both economy and safety into consideration.

[0201] Step S5: determining the optimal urban low-altitude logistics route network based on the Pareto front optimization result.

[0202] The Pareto front is the optimal contemporary population, which has multiple individuals representing the route network. The logistics route network corresponding to the optimal individual is selected as the optimal urban low-altitude logistics route network.

[0203] In some embodiments, the method of selecting the best individual in the present invention may include: (1) using weighted scoring and taking the individual with the highest score as the best individual; (2) visualizing the solutions in the Pareto front and selecting the individual that best meets the requirements as the best individual; (3) selecting individuals that meet preset constraints from the Pareto front as the best individual; (4) using a clustering method to determine the best individual, etc. Those skilled in the art may use a variety of existing methods to determine the best individual, and the present invention does not limit the method of selecting the best individual.

[0204] In the present invention, the optimal Pareto frontier of the model represents the trade-off between economic cost and safety, and obtains an urban low-altitude logistics route network that takes both economy and safety into consideration.

[0205] Although the specific embodiments of the present invention depict various actions or steps in a specific order, this should be understood as requiring such actions or steps to be performed in the specific order shown or in a sequential order, or requiring all illustrated actions or steps to be performed to obtain the desired results. Under certain circumstances, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be interpreted as limiting the scope of the present disclosure. Certain features described in the context of a separate embodiment can also be implemented in a single implementation in combination. On the contrary, the various features described in the context of a single implementation can also be implemented in multiple implementations individually or in any suitable sub-combination. The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or replacements that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

[0206] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for optimizing the design of urban low-altitude logistics route networks based on adaptive evolution, characterized in that: The following steps are involved: Step S1, gridding the area of ​​low-altitude logistics planning, obtaining take-off and landing facility nodes, and determining the low-altitude logistics network model to be optimized based on the take-off and landing facility nodes; Step S2, establishing an objective function for optimizing the low-altitude logistics network model, the objective function comprising: a total network cost function established based on transportation demand costs and the costs of building hubs and hub routes, and a third-party security risk function established based on the population density of the transportation area; Step S3, determining the constraint conditions for optimizing the low-altitude logistics network model, wherein the constraint conditions include network topology constraints, flow distribution constraints, and range restriction constraints; Step S4, using an adaptive evolutionary algorithm, based on the objective function and the constraint conditions, to optimize the low-altitude logistics network model to be optimized, and obtain a Pareto frontier optimization result of the low-altitude logistics network model; Step S5: determining the optimal urban low-altitude logistics route network based on the Pareto front optimization result.

2. The method for optimizing the design of urban low-altitude logistics route network based on adaptive evolution according to claim 1 is characterized in that: The step S1 specifically includes: Step S1-1, dividing the area of ​​low-altitude logistics planning into grids of uniform size, clustering the logistics demand points in the grids, and using the cluster center points obtained by clustering as take-off and landing facility nodes; Step S1-2: Construct the directed graph G corresponding to the low-altitude logistics network model to be optimized<N,E> , the take-off and landing facilities are regarded as a node set N of a directed graph, N = {1, ..., |N|}, |N| represents the total number of all nodes; the edge E represents the flight path between two nodes; the nodes of the directed graph include non-hub nodes and hub nodes; the nodes and edges in the directed graph are encoded: For node coding, a 0-1 binary list coding is used, where 1 means that the node at the index is selected as a hub node, otherwise it is a non-hub node; For edge coding, 0-1 symmetric matrix coding is used, where 1 means that the connection between the node pairs represented by the row and column indices is activated, otherwise, there is no connection between the node pairs.

3. The method for optimizing the design of urban low-altitude logistics route network based on adaptive evolution according to claim 2 is characterized in that: In step S2, the total network cost function includes the variable cost of transportation demand and the fixed cost required for building hubs and hub routes, and is expressed as: Among them, w ij represents the transportation demand from node i to node j of the starting point-end point; c ij ,c ik ,c lj ,c kl are the transportation costs from node i to node j, node i to node k, node l to node j, and node k to node l respectively; y ijkl is a 0-1 decision variable. If its value is 1, it means that the first hub node through which the transportation demand from node i to node j passes is k, and the last hub node is l; α is the economic discount coefficient between hub nodes; f ijkl is a 0-1 decision variable. If its value is 1, it means that the transportation demand from node i to node j passes through the hub arc kl; β is the economic penalty coefficient between non-hub nodes; s ij is a 0-1 decision variable. If its value is 1, it means that the transportation demand from node i to node j is directly transported without passing through the hub node; f k represents the cost of building hub node k; x k is a 0-1 decision variable. If its value is 1, it means that the decision node k is a hub node; g kl is the fixed cost required to activate the edge between hub node k and hub node l; z kl is a 0-1 decision variable. If its value is 1, it means that the edge between the hub nodes k and l is activated; The expression of the third-party security risk function is: Among them, r ij ,r ik ,r lj ,r kl They are the third-party safety transportation risks from node i to node j, node i to node k, node l to node j, and node k to node l; The specific calculation expression of the third-party safe transportation risk is: Among them, a, b∈N, and a≠b, r ab The third-party safety transportation risk of the affected area that the aircraft passes through from node a to node b; A exp (a,b) is the potential area exposed to aircraft crashes on the route from node a to node b; ρ(x,y) is the affected area A exp Population density at grid (x,y) in grid (i,j).

4. The method for optimizing the design of urban low-altitude logistics route network based on adaptive evolution according to claim 3 is characterized in that: In step S3, the network topology constraint is used to ensure that the premise for the activation of the hub edge is that both nodes of the edge are hub nodes, the network formed between the hubs is connected, and there is at least one hub node in the logistics network. The expression is: C1:z kl ≤x k k,l∈N,k<l C2:z kl ≤x l k,l∈N,k <l C3： C4： C5： C6:∑ k∈N x k ≥1 C7:s ij +x j ≤1i,j∈N C8:s ij +x i ≤1i,j∈N in, is the connectivity variable, and the connectivity of the hub network is ensured by defining a spanning tree with its root node at the hub node k. The value of 1 indicates that the spanning tree starting from the hub node k passes through the hub node i k To hub node j k The edge of The value of 1 indicates that the spanning tree starting from the hub node k passes through the hub node j. k To hub node i k The edge of The flow allocation constraint is used to ensure that each transport demand pair is transported by only one path, that transport demands that cannot be transported directly can only be transported by using open hubs, and that the flow is balanced. The expression is: C9:s ij +∑ k∈N ∑ l∈N y ijkl =1i,j∈N C10:∑ l∈N y ijkl +∑ l∈N,l≠k y ijlk ≤x k i,j,k∈N C11:∑ j∈N ∑ l∈N,l≠k f ijkl -∑ j∈N ∑ l∈N,l≠k f ijlk =∑ j∈N ∑ l∈N w ij y ijkl -∑ j∈N ∑ l∈N w ij y ijlk i,k∈N C12:f ijkl ≤w ij z kl i,j,k,l∈N,k<l The range constraint is used to ensure that all activated edges and transport paths meet the aircraft range, and the expression is: C13： C14： C15:d kl with kl ≤D k ,l∈N,k <l C16： Where D is the range of the aircraft.

5. The method for optimizing the design of urban low-altitude logistics route network based on adaptive evolution according to claim 4 is characterized in that: The step S4 specifically includes: Step S4-1: Initialize the basic parameters of the adaptive evolutionary algorithm, which include: population size N c , the number of take-off and landing facility nodes |N|, the number of maximum fitness calculations, and the length of the first-in-first-out queue that records operator usage |SW|; Step S4-2: Generate N based on random greedy strategy c individuals as the initial population, and the initial population as the contemporary population; the value of the objective function of the individual is calculated, and the value of the objective function is used as the fitness of the individual; the individual is generated by: establishing a directed graph consisting of a hub node set and a non-hub node set, and the directed graph is used as the individual; Step S4-3: For the contemporary population, a binary tournament strategy is used to select and obtain selected individuals; Step S4-4, determining a candidate crossover mutation operator combination, using a multi-armed bandit selection mechanism, and performing adaptive selection based on the credit value of the candidate crossover mutation operator combination to obtain a screened crossover mutation operator combination; Step S4-5: For the selected individuals, use the screened crossover and mutation operator combination to perform crossover and mutation processing to obtain child individuals, calculate the fitness of the child individuals, add the child individuals to the offspring population, and determine the offspring population; Step S4-6, updating the credit value of the candidate crossover mutation operator combination; Step S4-7, return to step S4-3, until the number of individuals in the offspring population reaches a preset population size; Step S4-8: merge the contemporary population and the offspring population, and perform quick sorting on the merged population based on the non-dominated rule, and select the top N c The population formed by each individual updates the contemporary population; Step S4-9, determine whether the maximum number of fitness calculations has been reached. If not, return to step S4-3; otherwise, complete the adaptive evolution and use the contemporary population as the Pareto frontier optimization result of the low-altitude logistics network model.

6. The method for optimizing the design of urban low-altitude logistics route network based on adaptive evolution according to claim 5 is characterized in that: The step S4-2 specifically includes: Step S4-2-1, establish a directed graph of |N| nodes, between 1 and A random number k is generated, and k nodes are randomly selected from all nodes to form the hub node set H, and the other nodes form the non-hub node set; Step S4-2-2: determine whether the hub node set H can generate a feasible solution that satisfies the range restriction constraint and the network topology constraint; the determination method is specifically as follows: Add the edges between hub nodes whose distance is less than the flight distance to the directed graph. If the directed graph is not connected, it is determined that no feasible solution can be generated; Otherwise, if all hub nodes can be connected to at least one hub node while satisfying the range constraint, it is determined that a feasible solution can be generated; Step S4-2-3: If no feasible solution can be generated, return to step S4-2-1 until it is determined that a feasible solution can be generated, and obtain the directed graph corresponding to the feasible solution; Step S4-2-4: for the hub node set in the directed graph corresponding to the feasible solution, activate the edges between the hub nodes that meet the range constraint, and for each non-hub node, select a random number of non-hub access / distribution edges on the premise of meeting the range constraint, and randomly select non-hub direct edges that meet the range constraint; Step S4-2-5, determine whether the directed graph satisfies the flow distribution constraint, obtain the directed graph that satisfies the flow distribution constraint as the individual; calculate the objective function value of the individual, and use the objective function value as the fitness of the individual.

7. The method for optimizing the design of urban low-altitude logistics route network based on adaptive evolution according to claim 6 is characterized in that: Step S4-4 specifically includes: Step S4-4-1, determining a crossover operator, wherein the crossover operator performs crosswise modification on the node coding and the edge coding in the directed graph; determining a mutation operator, wherein the mutation operator performs variability modification on the node coding and the edge coding in the directed graph; Step S4-4-2, obtaining a plurality of crossover-mutation operator combinations by combining the crossover operator and the mutation operator as the candidate crossover-mutation operator combinations; Step S4-4-3: select the candidate crossover mutation operator combination using a confidence upper bound algorithm to obtain a screened crossover mutation operator combination.

8. The method for optimizing the design of urban low-altitude logistics route network based on adaptive evolution according to claim 7 is characterized in that: The step S4-4-3 specifically includes: screening the crossover mutation operator combination, the expression is: Among them, op is the crossover mutation operator combination after screening; FRR u is the credit value of the combinatorial operator u; C′ is the proportional factor that adjusts the trade-off between development and exploration during the search process, OPs is the set of candidate crossover mutation combinatorial operator combinations, n v ,n u are the frequencies of the combined operators v,u∈OPs in the most recent |SW| times of use of operators; FRR u The expression is: Among them, Reward u is the fitness improvement rate FIR obtained after all the combined operators u are used in the most recent |SW| times of using the operators u The sum of Among them, FIR u P represents the fitness improvement rate of the combined operator u. p’ is the set of parent individuals, |P p’ | represents the size of the parent individual set, where p'∈P p’ is the parent individual. c’ P p’ The generated set of offspring individuals, |P c’ | represents the size of the offspring individual set, c'∈P c’ For offspring individuals.

9. The method for optimizing the design of urban low-altitude logistics route network based on adaptive evolution according to claim 8 is characterized in that: In step S4-5, the fitness of the sub-individual is calculated by taking the objective function value of the sub-individual as the fitness of the sub-individual; The step S4-6 specifically includes: updating the FRR of the candidate crossover mutation operator combination u The value of and updates the first-in-first-out queue SW that records the usage of operators.

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