Urban low-altitude three-dimensional logistics network optimization method considering noise constraint

Abstract

The invention relates to an urban low-altitude three-dimensional logistics network optimization method considering noise constraint, belongs to the technical field of low-altitude airline network design, and solves the problem that environmental influence and distribution efficiency cannot be considered in the prior art. The method comprises the following specific steps: performing grid division based on geographic information of a city planning area to obtain logistics network parameters; constructing an urban low-altitude three-dimensional logistics network model with a multi-layer undirected graph structure in a grid based on take-off and landing nodes, connecting edges and flight height layers by combining logistics network parameters; constructing a target function which aims at minimizing the total cost of the network and minimizing the flight safety risk of the network; the construction constraint conditions comprise a network construction constraint, a flow distribution constraint, a voyage constraint and a noise constraint constructed in combination with a noise tolerance value; the urban low-altitude three-dimensional logistics route network meeting the noise constraint condition is obtained by using the target function and the constraint condition, and the noise influence of a logistics system is reduced while the low-altitude logistics network efficiency is optimized.

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 three-dimensional logistics network optimization method considering noise constraints. Background Art

[0002] With the rapid development of low-altitude aircraft technology and its application in the logistics industry, low-altitude aircraft delivery has gradually become an important part of the urban logistics system. Traditional logistics network design methods mainly focus on factors such as transportation costs, delivery time and route planning. However, in urban environments, the noise problem caused by the operation of low-altitude aircraft is becoming increasingly apparent, especially in residential and commercial areas. The noise from low-altitude aircraft takeoffs and landings and during flight may cause serious interference to people's daily lives. That is, the existing logistics network methods fail to take into account both delivery efficiency and environmental impact. Therefore, there is an urgent need for a new method that can effectively reduce the noise impact of low-altitude logistics systems while optimizing the efficiency of logistics networks. Summary of the invention

[0003] In view of the above analysis, an embodiment of the present invention aims to provide an urban low-altitude three-dimensional logistics network optimization method taking into account noise constraints, so as to solve the problem in the prior art that environmental impact and distribution efficiency cannot be taken into account at the same time.

[0004] The purpose of the present invention is mainly achieved through the following technical solutions:

[0005] The embodiment of the present invention provides a method for optimizing an urban low-altitude three-dimensional logistics network considering noise constraints, comprising the following steps:

[0006] Based on the geographic information of the planned area of ​​the city, the planned area is gridded to obtain logistics network parameters; wherein the logistics network parameters include noise tolerance values ​​of noise-sensitive locations in the planned area;

[0007] In combination with the logistics network parameters, a multi-layer undirected graph structured urban low-altitude three-dimensional logistics network model is constructed in the grid based on take-off and landing nodes, edges and flight altitude layers; wherein the edges represent the flight paths of low-altitude aircraft between different take-off and landing nodes;

[0008] Construct an objective function to minimize the total network cost and minimize the network flight safety risk;

[0009] Constructing constraint conditions; wherein the constraint conditions include network construction constraints, flow distribution constraints and range constraints, and noise constraints constructed in combination with the noise tolerance value;

[0010] The urban low-altitude logistics network model is solved by using the objective function and constraint conditions to obtain an urban low-altitude three-dimensional logistics route network that meets the noise constraint conditions.

[0011] Furthermore, the objective function of minimizing the total network cost is constructed based on the fixed construction cost and variable transportation demand cost required for building hub nodes and connecting edges, which is expressed as:

[0012]

[0013] Among them, F k is the cost of building a hub node at node k; The construction cost required to activate the connection at level h between hubs k and l; The construction cost required to activate the h-level connection between non-hub i and hub k; The construction cost required to activate the connection at level h between non-hub i and non-hub j; w ij is the demand of OD pairs from node i to node j, where OD pairs represent the departure node and the destination node; The unit flow flight cost when the aircraft chooses the hth layer from node i to node j; α is the economic discount coefficient between hub nodes; x k is a 0-1 decision variable. If its value is 1, it means that node k is a hub node. is a 0-1 decision variable. If its value is 1, it means that there is an edge between hub node k and hub node l at layer h; is a 0-1 decision variable. If its value is 1, it means that there is an edge between non-hub node i and hub node k at layer h; is a 0-1 decision variable. If its value is 1, the OD demand for (i, j) passes through the hub edge kl at the h layer. is a 0-1 decision variable. If its value is 1, the OD demand for (i, j) passes through the access edge ik of the h layer. is a 0-1 decision variable. If its value is 1, the OD demand for (i, j) is distributed through the h-layer edge lj; is a 0-1 decision variable. If its value is 1, non-hub node i and non-hub node j have a connection in layer h; N is the total number of take-off and landing nodes; H is the flight altitude layer set.

[0014] Furthermore, the objective function of minimizing network flight safety risk is expressed as:

[0015]

[0016] in, The safety risk of a flight when a low-altitude aircraft selects layer h from node i to node j.

[0017] Furthermore, constructing the constraint condition includes:

[0018] The constraints of network construction constraints include that hub edges can only be established between hub nodes; the connectivity of the hub network; there is at least one hub node in the network and access / distribution edges can only exist between non-hub nodes and hub nodes;

[0019] The constraints of the flow distribution constraints include the distribution of the flow between the origin and the destination through the hub node or direct transportation of the non-hub edge; activating the edges that collect and distribute the OD flow; and balancing the flow of OD, distribution or collection edges, and hub nodes;

[0020] Range Constraints Constraints include the distance between nodes at all altitude levels being less than the range of low-altitude aircraft.

[0021] Furthermore, the take-off and landing nodes and the edges are encoded to obtain the encoded representation of the urban low-altitude logistics network model solution, including:

[0022] A 0-1 binary list encoding is used to represent the decision of whether the take-off and landing node is a hub node, where the hub node is the main distribution center in the logistics network;

[0023] A 0-1 symmetric matrix encoding is used to represent the decision of whether the edge of each altitude layer is activated;

[0024] The network topology is obtained by projecting the edges of the logistics network onto the ground. The network topology is encoded using a 0-1 symmetric matrix encoding to verify the network construction constraints.

[0025] Furthermore, a crossover operator is established based on the coded representation for solving the problem using a collaborative evolutionary optimization method, wherein the crossover operator includes:

[0026] Forward single-point crossover, the crossover operation includes one-way crossover of the node chromosomes, randomly selecting a crossover point k, exchanging the gene segments of the node chromosomes of the two parent individuals starting from the crossover point, and obtaining two child node chromosomes; bidirectional crossover of the edge chromosomes, by exchanging the first k×k sub-blocks of each matrix encoding, to obtain two edge chromosomes; based on the two crossed node chromosomes and edge chromosomes, obtain the corresponding two child individuals; wherein the parent individual is the coded representation of the solution, including the node chromosome and the edge chromosome, the node chromosome is the list encoding of the take-off and landing nodes, and the edge chromosome is the matrix encoding of the network edges;

[0027] The backward single-point crossover operation is different from the forward single-point crossover operation in that the crossover operation of the edge chromosome is to exchange each k×k sub-block after the matrix encoding;

[0028] Forward multi-point crossover, the crossover operation includes randomly selecting two or more crossover points, and according to the positions of the crossover points, alternately exchanging the segments between the crossover points for the node chromosomes; exchanging the gene segments between the crossover points for the edge chromosomes in the form of forward crossover;

[0029] Backward multi-point crossover,The crossover operation is different from the forward multi-point crossover operation in that the exchange of edge chromosomes adopts the backward exchange method.

[0030] Further, the collaborative evolution optimization method is used to solve the problem, including:

[0031] Initializing the main population and the auxiliary population using a coding representation that satisfies the range constraint; wherein the coding representation is generated using a hub set obtained by a random strategy;

[0032] The main population evolves based on the combination of the crossover operator and the mutation operator under the consideration of noise constraints to generate a sub-population;

[0033] The auxiliary population evolves based on the combination of the crossover operator and the mutation operator without considering the noise constraint to generate a descendant population;

[0034] The main population and the auxiliary population complete the next generation individual selection of the population under the cooperative mechanism of offspring sharing; wherein the individual is represented by a code;

[0035] Determine whether the maximum number of fitness calculations has been reached; if so, obtain the Pareto frontier of individuals in the current main population; if not, perform the above steps again;

[0036] The final solution is selected from the solution set of the Pareto frontier to obtain the urban low-altitude three-dimensional logistics network and the route network of the logistics network.

[0037] Furthermore, the hub set obtained by the random strategy includes:

[0038] in 1 and A random number k is generated between, where N represents the number of take-off and landing nodes in the network;

[0039] Randomly select k take-off and landing nodes to form a hub set;

[0040] It is determined whether the hub set generates feasible individuals that satisfy the range constraints of the low-altitude aircraft.

[0041] Furthermore, the mutation operation of the mutation operator includes:

[0042] Single-point random mutation is used for node chromosomes; random exchange mutation is used for edge chromosomes. A pair of hub nodes or non-hub nodes are randomly selected to exchange all edges of all height layers of the two nodes.

[0043] Furthermore, constructing the noise constraint includes:

[0044] Calculate the sound exposure level of a low-altitude aircraft based on the impact of a low-altitude aircraft on a certain point on the ground during the duration of a flight from take-off and landing node i to take-off and landing node j;

[0045] Calculate the equivalent sound level of low-altitude aircraft to noise-sensitive locations based on the sound exposure level to obtain the noise model;

[0046] The noise model is combined with the noise tolerance value to construct a noise constraint, which is expressed as:

[0047] Leq s ≤L s ,

[0048] Among them, Leq s L is the equivalent sound level of the noise sensitive site s affected by low-altitude aircraft; s is the maximum noise tolerance value of noise-sensitive location s.

[0049] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0050] 1. The present invention proposes to establish a low-altitude three-dimensional logistics network model based on the goal of minimizing the total cost of the logistics network and the flight safety risk by taking the impact of the noise generated by low-altitude aircraft flying in the city on the ground as a constraint, so as to ensure that when designing the logistics network, the efficiency of the urban low-altitude logistics system is fully utilized, while minimizing the impact on noise-sensitive areas;

[0051] 2. A matrix-based bidirectional crossover operator was designed, and the collaborative evolutionary optimization algorithm was used to solve the logistics network, thereby improving the distribution efficiency of the urban low-altitude three-dimensional logistics network.

[0052] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.

[0054] Figure 1 It is a flow chart of a method for optimizing a low-altitude urban three-dimensional logistics network according to an embodiment of the present invention;

[0055] Figure 2 A flowchart of the collaborative evolution of an embodiment of the present invention;

[0056] Figure 3 A schematic diagram of crossover mutation operator selection according to an embodiment of the present invention;

[0057] Figure 4 A schematic diagram of a decision example and corresponding double-layer coding according to an embodiment of the present invention;

[0058] Figure 5 A schematic diagram of a single-point crossover in a crossover operator according to an embodiment of the present invention;

[0059] Figure 6 A schematic diagram of a multi-point crossover in a crossover operator according to an embodiment of the present invention;

[0060] Figure 7 Schematic diagram of a mutation operator according to an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0062] A specific embodiment of the present invention discloses a method for optimizing an urban low-altitude three-dimensional logistics network considering noise constraints, such as Figure 1 As shown, the following steps are included:

[0063] Step S1: Based on the geographic information of the planned area of ​​the city, grid division is performed in the planned area to obtain logistics network parameters; wherein the logistics network parameters include noise tolerance values ​​of noise-sensitive locations in the planned area;

[0064] Step S2, combining the logistics network parameters to construct a multi-layer undirected graph structure of an urban low-altitude three-dimensional logistics network model in a grid based on take-off and landing nodes, edges and flight altitude layers; wherein the edges represent the flight paths of low-altitude aircraft between different take-off and landing nodes;

[0065] Step S3: construct an objective function with the goal of minimizing the total network cost and minimizing the network flight safety risk;

[0066] Step S4, constructing constraint conditions; wherein the constraint conditions include network construction constraints, flow distribution constraints and flight constraints, and noise constraints constructed in combination with the noise tolerance value;

[0067] Step S5: using the objective function and constraint conditions, solving the urban low-altitude logistics network model to obtain an urban low-altitude three-dimensional logistics route network that meets the noise constraint conditions.

[0068] Through the above method, by introducing noise constraints into the multi-altitude network model, combining the constraints of network construction constraints, flow distribution constraints and flight constraints, a city low-altitude logistics network model is constructed with the goal of reducing the total cost of the logistics network and flight safety risks. Based on the objective function and constraints, an urban low-altitude logistics route network that takes both economy and safety into consideration under noise constraints is obtained, which optimizes the efficiency of the logistics network and effectively reduces the noise impact of the low-altitude aircraft logistics system.

[0069] Logistics network parameters include the noise tolerance value of noise-sensitive points, the flight altitude of low-altitude aircraft, the logistics demand at the take-off and landing node locations, the performance data of low-altitude aircraft and the distance of the flight routes between take-off and landing points at different altitudes, transportation costs and flight safety risks for third parties (referred to as flight safety risks).

[0070] Specifically, in step S1, obtaining logistics network parameters includes:

[0071] S11, based on the geographic information of the planned area of ​​the city, gridding the planned area, marking noise-sensitive locations (i.e., noise-sensitive points), and determining the noise tolerance values ​​of the noise-sensitive points;

[0072] The geographic information of the planning area includes building distribution, height, roads and open spaces, population density distribution, acoustic environment planning, etc. Noise sensitive points include residential areas, schools, hospitals, etc.

[0073] S12, cluster the logistics demand points in the grid to the grid center, and use the grid center as the take-off and landing node location to calculate the logistics demand w between each node ij ;

[0074] S13. According to the low-altitude aircraft management regulations and safety isolation requirements, the flight altitudes of low-altitude aircraft are divided into three levels: low, medium and high;

[0075] S14. Obtain performance data of low-altitude aircraft, including size, deadweight, load, flight altitude range, speed and noise generation characteristics of low-altitude aircraft;

[0076] S15. Calculate the distance, transportation cost and third-party safety risk of the flight route between take-off and landing points at different altitudes.

[0077] For example, at a certain altitude h, considering the buildings at this altitude as obstacles, the A* algorithm is used to calculate the distance between take-off and landing nodes. Among them, i∈N is the take-off and landing facility node.

[0078] Shipping costs and distance Into a linear relationship.

[0079] Combined with the performance data of low-altitude aircraft, the safety operation risk between each take-off and landing point is calculated based on the following formula:

[0080]

[0081] in, is the risk value of the affected area that a low-altitude aircraft passes through from node i to node j at altitude level h; n start and n goal are the first and last discrete points that divide the edge (i, j) into discrete segments; x n is the position of the nth discrete point; The discrete point x is h altitude layer n Third-party security risks; and are the discrete points x at h altitude layers respectively n and x n-1 The number of casualties per hour; t(x n-1 , x n ) is the number of discrete points x n-1 To discrete point x n Flight time; P crash is the failure probability of low-altitude aircraft; is the population of the falling area, S hit is the area affected by the low-altitude aircraft crash, which is determined by the size of the low-altitude aircraft, σ p (x n ) is a discrete point x n Population density of the place; is the casualty rate caused by falling from the h-th altitude layer, S c =0.5,α=10 6 , β=100, m is the mass of the low-altitude aircraft (including its own weight and load), R I is the resistance shielding coefficient, h is the falling height, ρ A is the air density and g is the acceleration due to gravity.

[0082] Specifically, before constructing the urban low-altitude three-dimensional logistics network model in step S2, a noise propagation model for low-altitude aircraft takeoff and landing and flight is established. The specific steps include:

[0083] S21. Calculate the low-altitude aircraft sound exposure level to reflect the impact of a low-altitude aircraft on a certain point on the ground during the duration of a flight from take-off and landing node i to take-off and landing node j;

[0084] Specifically, the sound exposure level is defined as:

[0085]

[0086] in, is the effective sound level, t1 and t2 are the maximum sound level L during the flight max The time it takes for the signal to drop by 10 dB.

[0087] The sound exposure level is further discretized to obtain the discretized sound exposure level:

[0088]

[0089] Among them, T0 is 1 second, is the sound level at the ith second.

[0090] S22. Based on the low-altitude aircraft sound exposure level, calculate the low-altitude aircraft equivalent sound level to quantify the impact of low-altitude aircraft flying over noise-sensitive points throughout the day; the expression for the equivalent sound level of low-altitude aircraft on noise-sensitive points is:

[0091]

[0092] Among them, Leq s is the equivalent sound level received by the noise sensitive point, is the number of flights of the low-altitude aircraft from take-off and landing point i to take-off and landing point j at altitude h, and T is the observation time, which is set to 1 day.

[0093] S23. Based on the equivalent sound level of low-altitude aircraft to ground noise-sensitive locations and the corresponding maximum noise tolerance value, a noise constraint is constructed, which is expressed as:

[0094] Leq s ≤L s ,

[0095] Among them, Leq s is the equivalent sound level of low-altitude aircraft received by the noise sensitive point s, L s is the maximum noise tolerance value of the noise sensitive point location s.

[0096] Specifically, the noise constraint is introduced into the low-altitude three-dimensional logistics network model, and the urban low-altitude three-dimensional logistics network model is constructed based on the logistics network parameters and the multi-layer undirected graph, which includes:

[0097] Exemplarily, the undirected graph is represented as G=<N, E, H>, N={1,…, |N|} represents the take-off and landing nodes, E represents the edges, and H={1,…, |H|} is the set of flight altitude layers. The edges include node edges (i, j, h) on the same layer h∈H, or altitude switching connections of the same take-off and landing node i∈N. Since only the altitude level changes on the take-off and landing nodes are considered, the altitude switching edges are hidden edges in the network, that is, the altitude switching edges of the same take-off and landing point must exist by default. Therefore, the edges are by default the connections between different take-off and landing nodes on the same layer h∈H, indicating the flight path of the low-altitude aircraft between different take-off and landing points, with a distance Shipping costs and flight safety risks Each edge corresponds to a specific flight altitude, which is divided into low-level, middle-level and high-level to meet the low-altitude logistics network and flight flow distribution plan that meets the noise constraints. In addition, the noise sensitive point set N s To introduce an additional point set in the undirected graph, the noise-sensitive point s∈N of a low-altitude aircraft flight on the edge (i, j, h) s The noise impact is measured using the sound exposure level express.

[0098] Specifically, in step S3, an objective function is constructed with the goal of minimizing the total network cost and minimizing the network flight safety risk, including:

[0099] Minimizing the total network cost includes the fixed construction cost required to build hubs and network edges and the variable cost of transportation demand, which can be expressed as:

[0100]

[0101] Among them, network edges are all edges in the logistics network; F k is the cost of building a hub node at node k; The construction cost required to activate the connection at level h between hubs k and l; The construction cost required to activate the h-level connection between non-hub i and hub k; The construction cost required to activate the connection at level h between non-hub i and non-hub j; w ij is the demand of the origin-destination (OD) node, i.e., the demand of OD from node i to node j; The unit flow flight cost when the aircraft chooses the hth layer from node i to node j; α is the economic discount coefficient between hub nodes; x k is a 0-1 decision variable. If its value is 1, it means that node k is a hub node. is a 0-1 decision variable. If its value is 1, it means that there is an edge between hub node k and hub node l at layer h; is a 0-1 decision variable. If its value is 1, it means that there is an edge between non-hub node i and hub node k at layer h; is a 0-1 decision variable. If its value is 1, the OD demand for (i, j) passes through the hub edge kl at the h layer. is a 0-1 decision variable. If its value is 1, the OD demand for (i, j) passes through the access edge ik of the h layer. is a 0-1 decision variable. If its value is 1, the OD demand for (i, j) passes through the h-layer distribution link lj; is a 0-1 decision variable. If its value is 1, non-hub node i and non-hub node j have an edge in layer h. The construction cost F of hub node k is obtained through professional calculation. k , the construction cost of the hub edge in the network Access / distribution edge construction costs The construction cost of the direct edge Access edges are edges from non-hub nodes to hub nodes; distribution edges are edges from hub nodes to non-hub nodes.

[0102] Minimize network flight safety risks:

[0103]

[0104] in, The safety risk of a flight when a low-altitude aircraft selects layer h from node i to node j.

[0105] Specifically, in step S4, the constraints of the model are constructed, including network construction constraints, flow distribution constraints, flight constraints and noise constraints;

[0106] Exemplarily, the projection of network edges on the ground constitutes a network topology, and the network construction constraints that the network topology needs to satisfy are:

[0107] C1:z kl ≤x k k,l∈N,k<l

[0108] C2:z kl ≤x l k,l∈N,k<l

[0109] C3:

[0110] C4:

[0111] C5:∑ i∈N，i≠j T kij ≥xk +x j -1 j, k∈N, j≠k

[0112] C6:∑ i∈N，i≠j T kij ≤x k j, k∈N, j≠k

[0113] C7:T kij +T kji ≤z ij k,i,j∈N,i<j

[0114] C8:∑ k∈N x k ≥1

[0115] C9:

[0116] C10:

[0117] C11:

[0118] C12:

[0119] Among them, constraints C1-C4 ensure that hub edges can only be established between hub nodes. kl is a 0-1 variable. If it is 1, it means there is an edge between hub k and hub l.

[0120] Constraints C5, C6, and C7 ensure the connectivity of the hub network composed of hub nodes. kij is a 0-1 variable. If it is 1, it means that the spanning tree starting from hub k passes through the hub edge ij;

[0121] Constraint C8 ensures that there is at least one hub node in the network to provide parking, charging, maintenance and other support services for low-altitude aircraft;

[0122] Constraints C9 and C10 indicate that access / distribution edges can only exist between non-hub nodes and hub nodes;

[0123] Constraints C11 and C12 indicate that non-hub direct edges can only be constructed between non-hub nodes.

[0124] Exemplarily, the traffic distribution constraint is:

[0125] C13:

[0126] C14:

[0127] C15:

[0128] C16:

[0129] C17:

[0130] C18:

[0131]

[0132] C19:

[0133] C20:

[0134] Among them, constraints C13 and C14 restrict the flow between OD pairs to either be distributed through hubs or directly transported through non-hub edges;

[0135] Constraints C15 and C16 indicate that the edges used to collect and distribute OD flows are activated. Collecting OD flows refers to the logistics demand from non-hub nodes to hub nodes; in contrast, distributing OD flows refers to the flow from hub nodes to non-hub nodes.

[0136] Constraints C17 and C18 are the flow balance equations of OD pairs, distribution or collection edges, and hub nodes;

[0137] Constraints C19 and C20 ensure that the hub edge through which the OD pair (i, j) passes is activated.

[0138] Exemplarily, the range constraint includes that the distance between nodes at all altitude levels is less than the range of the low-altitude aircraft:

[0139] C21:

[0140] C22:

[0141] C23:

[0142] C24:

[0143] Where D is the range of the low-altitude aircraft.

[0144] Exemplarily, the noise constraint of the noise sensitive point is:

[0145] C25:

[0146]

[0147] Among them, the left part of the expression of C25 is the equivalent sound level of the noise sensitive point obtained based on the noise model.

[0148] Specifically, in step S5, in order to solve the urban low-altitude three-dimensional logistics network model, it is necessary to encode the take-off and landing nodes and network edges, construct a coded representation of the logistics solution, and calculate the objective function value corresponding to the coded representation of each solution; wherein the logistics solution is the solution to the urban low-altitude three-dimensional logistics network model.

[0149] Exemplarily, there are N take-off and landing nodes and H altitude layers; the organizational structure of the urban low-altitude three-dimensional logistics network is designed using a hub-and-spoke network structure, including dividing the take-off and landing nodes into take-off and landing hub nodes and radiation nodes. The take-off and landing hub node is the main distribution center in the city, responsible for centralized management and scheduling of multiple logistics routes and maintenance of low-altitude aircraft, etc. The radiation node is the take-off and landing point of the non-hub node distributed in various areas of the city, which is used to receive and send packages. The selection of the take-off and landing hub and the activation of the edge are part of the optimization decision to build a logistics network, and the network topology formed by the projection of the network edge on the ground satisfies the hub-and-spoke network structure. The specific coding includes:

[0150] In the take-off and landing node encoding, 0-1 binary list encoding is used to make node decisions x in the solution k To indicate, 1 means the node at this index is selected as the hub node, otherwise it is a non-hub node;

[0151] The edge decision of each height layer is encoded by a 0-1 symmetric matrix, where 1- means that the connection between the node pairs represented by the row and column indexes is activated, otherwise, there is no connection between the node pairs; the nature of the edge is determined by the node type corresponding to the matrix index, thereby determining the decision The value of .

[0152] The projection of network edges on the ground is encoded in a 0-1 symmetric matrix to verify the network construction constraints. 1- indicates 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.

[0153] Encoding example: Figure 4 As shown, there are 6 take-off and landing nodes and 3 altitude levels, among which nodes 2, 3, and 4 are selected as hub nodes, the connection between hub node pair 2-3 at altitude level 1 and altitude level 2 is activated, and the connection between hub node pair 2-4 at altitude level 3 is activated. At the same time, the access / distribution connection 1-2 between non-hub nodes and hub nodes is activated at altitude level 2, 1-3 is activated at altitude level 1, 3-6 is activated at altitude level 1 and altitude level 2, 4-5 is activated at altitude level 1, altitude level 2, and altitude level 3, and the non-hub node direct connection 5-6 is activated at altitude level 3.

[0154] The take-off and landing nodes and edges of the logistics network in the solution are represented by encoding, and the distribution path of the OD pair (i, j) in the model is calculated based on the weighted shortest path based on this network. The corresponding decision variables can be calculated through the edges and their properties in the path. The value is set to 1. Based on the decision variables, the objective function value can be calculated.

[0155] Furthermore, the co-evolutionary optimization algorithm is used to solve the low-altitude three-dimensional logistics network, such as Figure 2 As shown, the specific steps include:

[0156] S51, initializing basic parameters of the collaborative evolution optimization algorithm;

[0157] Specifically, the basic parameters include the population size N c , the number of take-off and landing nodes N, the maximum number of fitness calculations maxFEs, the number of crossover mutation combination operators n, and the length of the sliding window |SW| that records the operator usage in the operator selection mechanism;

[0158] S52, using the hub set formed by the random strategy to generate individuals that meet the range constraints, thereby constructing a population and completing the initialization of the main population and the auxiliary population; wherein the individual is a coded representation of the solution, corresponding to a solution;

[0159] Specifically, the algorithm main population and auxiliary population are initialized, that is, random strategies are used to generate N c Individuals, the specific way to randomly generate individuals is as follows:

[0160] S521, in 1 and Generate a random number k between

[0161] S522, randomly select k nodes to form a hub set N H ;

[0162] S523, determining whether the hub set obtained in S522 can generate feasible individuals that meet the range constraints of the low-altitude aircraft;

[0163] Specifically, all edges between hub nodes whose altitude layer distance is less than the flight range are added to the graph G. If the graph is not connected, it is impossible to generate a feasible solution; otherwise, the feasibility of non-hub nodes is further evaluated. If all non-hub nodes can be connected to at least one hub node while satisfying the flight range constraint, the solution is considered feasible.

[0164] S524. If the selected hub node set and non-hub node set fail to create a feasible solution, the hub node set is deleted from the candidate hub node set, and a new hub set is generated until a feasible solution is obtained.

[0165] S525. In the generated feasible hub node set, for any pair of hub nodes, randomly select the altitude layers between the nodes that meet the range constraints for activation; for each non-hub node, on the premise of meeting the range constraints, select a random number of access / distribution edges, and randomly activate the connections between the altitude layers of these edges; finally, randomly select non-hub direct edges that meet the range constraints, and randomly activate the connections between the altitude layers of these edges.

[0166] S53. The main population evolves under noise constraints to produce a subpopulation; the details are as follows:

[0167] S531. For the contemporary population, a binary tournament strategy based on the constraint dominance principle is used to select the selected individuals;

[0168] S532, use the multi-armed bandit selection strategy to select the crossover mutation operator combination, such as Figure 3 As shown, the crossover and mutation operators are obtained;

[0169] The crossover operator uses (forward / backward) single-point crossover and multi-point crossover designed based on the coding characteristics. d The value of determines the crossover direction. d ≤0.5, forward crossover is applied, otherwise, backward crossover is used. In forward crossover, the crossover unit includes the first k elements in rows and columns, k represents the crossover point, and the operation is performed on all matrix encodings. In contrast, in backward crossover, the crossover unit contains the last Nk elements in rows and columns, N represents the number of nodes in the network.

[0170] There are four types of crossover operations, including forward single-point crossover (FS), backward single-point crossover (BS), forward multi-point crossover (FM) and backward multi-point crossover (BM). The solution encoding is represented as a parent individual, including the node chromosome and the edge chromosome. The node chromosome is the list encoding of the take-off and landing nodes, and the edge chromosome is the matrix encoding of the network edges. Figure 5As shown in , the specific operation of single-point crossover in the crossover operator is described. FS is a one-way crossover. A crossover point k is randomly selected within the length of the node chromosome. This position will determine the gene exchange of the two parent individuals before and after this point. The gene segments of the node chromosomes of the two parent individuals starting from the crossover point are exchanged to generate two new offspring node chromosomes. For the edge chromosomes, a bidirectional crossover is used. The offspring edge chromosomes are generated by exchanging the first k×k sub-blocks of each matrix; based on the two crossed node chromosomes and edge chromosomes, the corresponding two offspring individuals are obtained. What is different from the FS chromosome operation in the backward single-point crossover (BS) is the way the edge chromosomes are exchanged. The offspring edge chromosomes are obtained by exchanging the k×k sub-blocks after each matrix. As shown Figure 6 As shown in the figure, forward multipoint crossover (FM) randomly selects two or more crossover points, and according to the positions of the crossover points, alternately exchanges the segments between the crossover points for the node chromosomes of the parent individuals. For the connecting chromosomes of the parent individuals, the gene segments between the crossover points are exchanged in the form of forward crossover. In backward multipoint crossover (BM), unlike the FM chromosome operation, the exchange of connecting chromosomes adopts the backward exchange method.

[0171] like Figure 7 As shown, the nodes in the mutation operator adopt single-point random mutation; the edge chromosome adopts random exchange mutation, and the edge matrix adopts a pair of hub nodes or non-hub nodes randomly selected to exchange all the edges of all height layers of the two nodes. The mutation operator is denoted as SLAM. Figure 7 As an example of an operator, the bit at index 3 of the node chromosome is changed from 1 to 0. For each edge chromosome, a hub pair (2,4) is selected, the elements of the 2nd and 4th rows are swapped, and the elements of the 2nd and 4th columns are swapped.

[0172] Among them, six crossover mutation operator combinations are described in Table 1 as candidate operators.

[0173] Table 1

[0174] Operator Crossover operator Mutation Operator 1 Single point crossover (front / rear) none 2 Single point crossover (front / rear) SLAM 3 Multi-point crossover (front / rear) none 4 Multi-point crossover (front / rear) SLAM 5 none SLAM 6 none none

[0175] The multi-armed bandit selection strategy adopts a confidence upper bound algorithm to select crossover and mutation operators, and the expression is:

[0176]

[0177] Among them, op is the selected crossover mutation combination operator; FRR i is the credit value of combinatorial operator i; C is the proportional factor that adjusts the trade-off between exploitation and exploration during the search process.

[0178] OPs = {1, ..., 11} is a set of candidate crossover mutation combination operators.j is the frequency of the combinatorial operator j∈OPs in the most recent |SW| applications.

[0179] Specifically, FRR i The expression is:

[0180]

[0181] Among them, Reward i It is the sum of the fitness improvement rates based on domination obtained after all applications of the combined operator i in the most recent |SW| applications. The fitness improvement rate based on domination is used to measure the performance of an application of the operator combination. The expression is:

[0182]

[0183] Among them, FIR i represents the fitness improvement rate of the crossover and mutation operator combination i. p is the set of parent individuals, |P p | represents the set of parent individuals, 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.

[0184] c<p means that the offspring individual c dominates the parent individual p, p<c means that the parent individual p dominates the offspring individual c, and p==c means that the parent individual p and the offspring individual c do not dominate each other.

[0185] S533, for the selected individuals, use the crossover mutation operator combination selected in step S532 to operate, obtain a child individual (i.e., a new solution), and add it to the offspring population of the main population;

[0186] S534, calculating the objective function value and constraint violation of the sub-individual obtained in S533, and updating the credit value of the crossover mutation operator combination in the multi-armed bandit operator selection strategy;

[0187] Specifically, the FIR is calculated according to the expression in S532 i value, and update the first-in-first-out queue SW that records the operator usage; when the main population selects individuals for the next generation update, individuals with smaller objective function values ​​and lower constraints are given priority to form a new generation of population.

[0188] S535, repeat steps S531-S534 until the offspring population reaches half of the set population size;

[0189] S54, the auxiliary population evolves by relaxing (ignoring) the noise constraint to generate a sub-population; the details are as follows:

[0190] S541. For the contemporary population, a target-dominated binary tournament strategy is used to select and obtain the selected individuals;

[0191] S542, using the same operations as steps S532-S534 to evolve the auxiliary population;

[0192] S543, repeat steps S541-S542 until the offspring population reaches half of the set population size;

[0193] S55. The main population and the auxiliary population complete the next generation individual selection of the population under the collaborative mechanism of offspring sharing, respectively, with and without considering the noise constraint. The specific operations are as follows:

[0194] S551, merge the main population, the offspring of the main population, and the offspring of the auxiliary population, calculate the fitness of the individuals in the new population, and select N under the condition of considering the noise constraint. c Individuals make up the main population;

[0195] S552, merge the auxiliary population, the offspring of the main population, and the offspring of the auxiliary population, calculate the fitness of the individuals in the new population, and select N without considering the noise constraint. c Individuals form the auxiliary population;

[0196] S56, determine whether the maximum number of fitness calculations has been reached, if so, obtain the Pareto frontier of individuals in the current main population; otherwise, perform steps S53-S55 again;

[0197] S57. In the Pareto front solution set, the final solution is selected based on the decision maker's preference, and the urban low-altitude three-dimensional logistics network and the required distribution path are output. The distribution path is a directed urban low-altitude three-dimensional logistics route network.

[0198] Compared with the prior art, this embodiment provides an urban low-altitude three-dimensional logistics network optimization method taking into account noise constraints. By introducing the noise impact of low-altitude aircraft on the ground into the urban low-altitude logistics network model in the form of constraints, an urban low-altitude logistics network model is constructed with the goal of reducing the total cost of the logistics network and flight safety risks. Ultimately, the problem of balancing the efficiency of the urban three-dimensional logistics network and the impact of environmental noise is solved. At the same time, based on the bidirectional crossover operator of the matrix, the collaborative evolutionary optimization algorithm is used to solve the logistics network to further improve the efficiency of logistics distribution.

[0199] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0200] 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 urban low-altitude three-dimensional logistics network considering noise constraints, characterized in that: The steps include: Based on the geographic information of the planned area of ​​the city, the planned area is gridded to obtain logistics network parameters; wherein the logistics network parameters include noise tolerance values ​​of noise-sensitive locations in the planned area; In combination with the logistics network parameters, a multi-layer undirected graph structure of an urban low-altitude three-dimensional logistics network model is constructed in a grid based on take-off and landing nodes, edges and flight altitude layers; wherein the edges represent the flight paths of low-altitude aircraft between different take-off and landing nodes; Construct an objective function to minimize the total network cost and minimize the network flight safety risk; Constructing constraint conditions; wherein the constraint conditions include network construction constraints, flow distribution constraints and range constraints, and noise constraints constructed in combination with the noise tolerance value; The urban low-altitude logistics network model is solved by using the objective function and constraint conditions to obtain an urban low-altitude three-dimensional logistics route network that meets the noise constraint conditions.

2. According to the method for optimizing urban low-altitude three-dimensional logistics network considering noise constraints in claim 1, it is characterized in that: The objective function of minimizing the total network cost is constructed based on the fixed construction cost and variable transportation demand cost required to build hub nodes and edges, which is expressed as: Among them, F k is the cost of building a hub node at node k; The construction cost required to activate the connection at level h between hubs k and l; The construction cost required to activate the h-level connection between non-hub i and hub k; The construction cost required to activate the connection at level h between non-hub i and non-hub j; w ij is the demand of OD pair from node l to node j, where OD pair represents the departure node and the destination node; The unit flow flight cost when the aircraft chooses the hth layer from node i to node j; α is the economic discount coefficient between hub nodes; x k is a 0-1 decision variable. If its value is 1, it means that node k is a hub node. is a 0-1 decision variable. If its value is 1, it means that there is an edge between hub node k and hub node l at layer h; is a 0-1 decision variable. If its value is 1, it means that there is an edge between non-hub node i and hub node k at layer h; is a 0-1 decision variable. If its value is 1, 0D's demand for (i, j) passes through the hub edge kl at layer h; is a 0-1 decision variable. If its value is 1, the demand for (i, j) goes through the access edge ik at layer h. is a 0-1 decision variable. If its value is 1, the demand for (i, j) is distributed through the h-layer edge lj; is a 0-1 decision variable. If its value is 1, non-hub node i and non-hub node j have a connection in layer h; N is the total number of take-off and landing nodes; H is the flight altitude layer set.

3. The method for optimizing urban low-altitude three-dimensional logistics network considering noise constraints according to claim 2 is characterized in that: The objective function of minimizing network flight safety risk is expressed as: in, The flight safety risk when selecting layer h for a low-altitude aircraft from node i to node j.

4. The method for optimizing urban low-altitude three-dimensional logistics network considering noise constraints according to claim 1 is characterized in that: Constructing the constraints includes: The constraints of network construction constraints include that hub edges can only be established between hub nodes; the connectivity of the hub network; there is at least one hub node in the network and access / distribution edges can only exist between non-hub nodes and hub nodes; The constraints of the flow distribution constraints include the distribution of the flow between the origin and the destination through the hub node or direct transportation of the non-hub edge; activating the edges that collect and distribute the OD flow; and balancing the flow of OD, distribution or collection edges, and hub nodes; Range Constraints Constraints include the distance between nodes at all altitude levels being less than the range of low-altitude aircraft.

5. The method for optimizing urban low-altitude three-dimensional logistics network considering noise constraints according to claim 1 is characterized in that: Encoding the take-off and landing nodes and the edges to obtain the coded representation of the urban low-altitude logistics network model solution includes: A 0-1 binary list encoding is used to represent the decision of whether the take-off and landing node is a hub node, where the hub node is the main distribution center in the logistics network; A 0-1 symmetric matrix encoding is used to represent the decision of whether the edge of each altitude layer is activated; The network topology is obtained by projecting the edges of the logistics network onto the ground. The network topology is encoded using a 0-1 symmetric matrix encoding to verify the network construction constraints.

6. The method for optimizing urban low-altitude three-dimensional logistics network considering noise constraints according to claim 5 is characterized in that: A crossover operator is established based on the encoding representation for solving the problem using the co-evolutionary optimization method. The crossover operator includes: Forward single-point crossover, the crossover operation includes one-way crossover of the node chromosomes, randomly selecting a crossover point k, exchanging the gene segments of the node chromosomes of the two parent individuals starting from the crossover point, and obtaining two child node chromosomes; bidirectional crossover of the edge chromosomes, by exchanging the first k×k sub-blocks of each matrix encoding, to obtain two edge chromosomes; based on the two crossed node chromosomes and edge chromosomes, obtain the corresponding two child individuals; wherein the parent individual is the coded representation of the solution, including the node chromosome and the edge chromosome, the node chromosome is the list encoding of the take-off and landing nodes, and the edge chromosome is the matrix encoding of the network edges; The backward single-point crossover operation is different from the forward single-point crossover operation in that the crossover operation of the edge chromosome is to exchange each k×k sub-block after the matrix encoding; Forward multi-point crossover, the crossover operation includes randomly selecting two or more crossover points, and according to the positions of the crossover points, alternately exchanging the segments between the crossover points for the node chromosomes; exchanging the gene segments between the crossover points for the edge chromosomes in the form of forward crossover; Backward multi-point crossover,The crossover operation is different from the forward multi-point crossover operation in that the exchange of edge chromosomes adopts the backward exchange method.

7. The method for optimizing urban low-altitude three-dimensional logistics network considering noise constraints according to claim 6 is characterized in that: The collaborative evolution optimization method is used to solve the problem, including: Initializing the main population and the auxiliary population using a coding representation that satisfies the range constraint; wherein the coding representation is generated using a hub set obtained by a random strategy; The main population evolves based on the combination of the crossover operator and the mutation operator under the consideration of noise constraints to generate a sub-population; The auxiliary population evolves based on the combination of the crossover operator and the mutation operator without considering the noise constraint to generate a descendant population; The main population and the auxiliary population complete the next generation individual selection of the population under the cooperative mechanism of offspring sharing; wherein the individual is represented by a code; Determine whether the maximum number of fitness calculations has been reached; if so, obtain the Pareto frontier of individuals in the current main population; if not, perform the above steps again; The final solution is selected from the solution set of the Pareto frontier to obtain the urban low-altitude three-dimensional logistics network and the route network of the logistics network.

8. The method for optimizing urban low-altitude three-dimensional logistics network considering noise constraints according to claim 7 is characterized in that: The hub set obtained by random strategy includes: in 1 and A random number k is generated between, where N represents the number of take-off and landing nodes in the network; Randomly select k take-off and landing nodes to form a hub set; It is determined whether the hub set generates feasible individuals that satisfy the range constraints of the low-altitude aircraft.

9. The method for optimizing urban low-altitude three-dimensional logistics network considering noise constraints according to claim 7 is characterized in that: The mutation operation of the mutation operator includes: Single-point random mutation is used for node chromosomes; random exchange mutation is used for edge chromosomes. A pair of hub nodes or non-hub nodes are randomly selected to exchange all edges of all height layers of the two nodes.

10. The method for optimizing urban low-altitude three-dimensional logistics network considering noise constraints according to any one of claims 1 to 9, characterized in that: Constructing the noise constraint includes: Calculate the sound exposure level of a low-altitude aircraft based on the impact of a low-altitude aircraft on a certain point on the ground during the duration of a flight from take-off and landing node i to take-off and landing node j; Calculate the equivalent sound level of low-altitude aircraft to noise-sensitive locations based on the sound exposure level to obtain the noise model; The noise model is combined with the noise tolerance value to construct a noise constraint, which is expressed as: Leq s ≤L s , Among them, Leq s L is the equivalent sound level of the noise sensitive site s affected by low-altitude aircraft; s is the maximum noise tolerance value of noise-sensitive location s.

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