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

Abstract

The present application relates to the technical field of low-altitude air route network design, and particularly relates to a city low-altitude logistics air route network design optimization method based on adaptive evolution, comprising: carrying out grid division on a region of low-altitude logistics planning to determine a low-altitude logistics network model to be optimized; establishing a network total cost function based on a transportation demand cost and a cost of constructing a hub and a hub air route, and a third-party safety risk function based on a population density of a transportation region; determining constraint conditions for optimizing the low-altitude logistics network model, the constraint conditions comprising network topology constraints, flow distribution constraints and voyage limit constraints; adopting an adaptive evolution algorithm to optimize the low-altitude logistics network to be optimized based on the objective function and the constraint conditions to obtain a Pareto frontier optimization result of the low-altitude logistics network; and the present application can give consideration to economic cost and safety factors in the optimization of a logistics air route network.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of low-altitude air route network design, and particularly relates to a city low-altitude logistics air route network design optimization method based on adaptive evolution. BACKGROUND

[0002] City low-altitude logistics is a new concept in the field of city air traffic, which involves the application of advanced aircraft, such as unmanned aerial vehicles, to transport goods in urban areas. Compared with the traditional ground transportation logistics mode, city low-altitude logistics has higher flexibility. The establishment of ground infrastructure, especially facilities supporting the operation of vertical take-off and landing aircraft, also known as vertical airports, is the key to the successful implementation of city low-altitude logistics systems. As the take-off and landing nodes of aircraft transporting goods, vertical airports are transfer stations and hub points for goods integration, distribution and last-mile delivery, overcoming the challenges of traditional city logistics through the advantages of air transportation and promoting seamless transportation of goods in the city environment.

[0003] Determining the locations of these low-altitude logistics hub nodes and designing a safe and efficient air route network to ensure the economic and efficient nature of the entire low-altitude logistics system is a major challenge. On the one hand, the hub network design problem is an NP-hard problem, and on the other hand, the city low-altitude environment is complex, with dense buildings and dense population, and the third-party safety risks caused by the crash of low-altitude logistics aircraft due to control or navigation failures and other factors to the population in the urban area need to be considered. However, the impact of third-party safety risks on network design is not fully considered in the design of city low-altitude logistics networks, and the conflicts of interest of different stakeholders are ignored. SUMMARY

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

[0005] The present application provides a city low-altitude logistics air route network design optimization method based on adaptive evolution, comprising the following steps:

[0006] Step S1, performing grid division on the region planned for low-altitude logistics to obtain take-off and landing facility nodes, and determining a low-altitude logistics network model to be optimized from 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 network total cost function established based on transportation demand cost and the cost of constructing hubs and hub air routes, and a third-party safety risk function established based on the population density of the transportation region;

[0008] Step S3, determining a constraint condition for optimizing the low-altitude logistics network model, the constraint condition including a network topology constraint, a flow distribution constraint and a flight range limit constraint;

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

[0010] Step S5, determining an 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 a region of low-altitude logistics planning into uniform grids, clustering logistics demand points in the grids, and taking cluster center points obtained by clustering as take-off and landing facility nodes;

[0013] Step S1-2, constructing a directed graph G=<N, E> corresponding to the low-altitude logistics network model to be optimized, taking take-off and landing facilities as a node set N of the directed graph, N={1,…,|N|}, |N| representing a total number of all nodes; an edge E representing a flight path between two nodes; the nodes of the directed graph including non-hub nodes and hub nodes; and coding the nodes and edges in the directed graph:

[0014] For node coding, 0-1 binary list coding is adopted, 1 representing that a 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 adopted, 1 representing that a connection between a node pair represented by row and column indexes is activated, otherwise, there is no connection between the node pair.

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

[0017]

[0018] wherein w ij represents a transportation demand amount of a node i to a node j of a start-end point; c ij , c ik , c lj , and c kl are transportation costs of the node i to the node j, the node i to a node k, the node l to the node j, and the node k to the node l, respectively; y ijklis a 0-1 decision variable, and 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; a is the economic discount coefficient between hub nodes; f ijkl is a 0-1 decision variable, and if its value is 1, it means that the transportation demand from node i to node j passes through the hub arc k-l; b is the economic penalty coefficient between non-hub nodes; s ij is a 0-1 decision variable, and if its value is 1, it means that the transportation demand from node i to node j does not pass through a hub node and is directly transported; f k represents the cost of building a hub node k; x k is a 0-1 decision variable, and if its value is 1, it means that node k is determined to be a hub node; g kl is the fixed cost required to activate the connection between hub node k and hub node l; z kl is a 0-1 decision variable, and if its value is 1, it means that the connection between hub node k and l is activated;

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

[0020]

[0021] wherein r ij , r ik , r lj , and r kl are the third-party security transportation risks of nodes i to j, i to k, l to j, and k to l, respectively;

[0022] The specific calculation expression of the third-party security transportation risk r ij is:

[0023]

[0024] wherein a, b ∈ N, and a≠b, r ab is the third-party security transportation risk of the affected area through which the aircraft passes 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; p(x, y) is the population density of the grid (x, y) in the affected area A exp (i, j).

[0025] Preferably, in step S3, the network topology constraints are used to ensure that the premise of hub connection activation is that both nodes of the connection are hub nodes, to ensure that the network formed between hubs has connectivity, and to ensure that 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 ≤ 1, i, j ∈ N

[0033] C8: s ij + x i ≤ 1, i, j ∈ N

[0034] wherein, is a connectivity variable, which ensures the connectivity of the hub network by defining the spanning tree of the root node at the hub node k, the value of is 1 indicates that the spanning tree from the hub node k passes through the edge between the hub node i k and the hub node j k , the value of is 1 indicates that the spanning tree from the hub node k passes through the edge between the hub node j k and the hub node i k ;

[0035] The flow allocation constraint is used to ensure that each transportation demand is transported by only one path, to ensure that the transportation demand that cannot be directly transported can only be transported by using the open hub, and to ensure the flow balance, and the expression is:

[0036] C9: s ij + ∑ k∈n ∑ l∈N y ijkl = 1, i, 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 voyage limit constraint is used to ensure that all activated edges and transportation paths satisfy the aircraft voyage, and the expression is:

[0041] C13:

[0042] C14:

[0043] C15:d kl z kl ≤Dk,l∈N,k<l

[0044] C16:

[0045] wherein D is the voyage of the aircraft.

[0046] Preferably, the step S4 specifically comprises:

[0047] Step S4-1, initializing the basic parameters of the adaptive evolutionary algorithm, the basic parameters including: population size N c , the number of take-off and landing facilities nodes |N|, the maximum number of times of fitness calculation, and the length |SW| of the first-in-first-out queue recording the usage of the operator;

[0048] Step S4-2, generating N c individuals based on a random greedy strategy as an initial population, taking the initial population as a current population; calculating the value of the objective function of the individuals, taking the value of the objective function as the fitness of the individuals; the generation mode of the individuals is: establishing a directed graph composed of a hub node set and a non-hub node set, taking the directed graph as the individual;

[0049] Step S4-3, for the current population, selection is performed by using a binary tournament strategy to obtain selected individuals;

[0050] Step S4-4, determining a candidate crossover mutation operator combination, adopting a multi-armed tiger machine selection mechanism, and adaptively selecting based on credit values of the candidate crossover mutation operator combination to obtain a screened crossover mutation operator combination;

[0051] Step S4-5, performing crossover and mutation processing on the selected individual by using the screened crossover mutation operator combination to obtain a child individual, calculating fitness of the child individual, adding the child individual to an offspring population, and determining the offspring population;

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

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

[0054] Step S4-8, merging the current population and the offspring population, performing fast sorting on the merged population based on a non-dominated rule, selecting a population formed by the first N individuals after sorting to update the current population, and returning to step S4-3. c

[0055] Step S4-9, determining whether a maximum fitness calculation number is reached, if not, returning to step S4-3, otherwise completing adaptive evolution and taking the current population as a Pareto front optimization result of the low-altitude logistics network model.

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

[0057] Step S4-2-1, establishing a directed graph of |N| nodes, generating a random number k between 1 and |N|, and randomly selecting k nodes from all nodes to form a hub node set H and other nodes to form a non-hub node set.

[0058] Step S4-2-2, determining whether the hub node set H can generate a feasible solution meeting the voyage limit constraint and the network topology constraint, and the determination manner specifically comprises:

[0059] adding an edge between hub nodes with a distance less than the voyage to the directed graph, and if the directed graph is not connected, determining that a feasible solution cannot be generated;

[0060] otherwise, if all hub nodes can be connected to at least one hub node under the condition of meeting the voyage limit constraint, it is determined that a feasible solution can be generated;

[0061] Step S4-2-3, if a feasible solution cannot be generated, returning to step S4-2-1 until it is determined that a feasible solution can be generated, and obtaining a 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, activating the edges between hub nodes satisfying the flight range limit constraint, for each non-hub node, selecting a random number of non-hub access / distribution edges under the premise of satisfying the flight range limit constraint, and randomly selecting non-hub direct edges satisfying the flight range limit constraint;

[0063] Step S4-2-5, judging whether the directed graph satisfies the flow allocation constraint, obtaining the directed graph satisfying the flow allocation constraint as the individual; calculating the objective function value of the individual, and taking the objective function value as the fitness of the individual.

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

[0065] Step S4-4-1, determining a crossover operator that modifies the node encoding and the edge encoding in the directed graph in a crossover manner; and determining a mutation operator that modifies the node encoding and the edge encoding in the directed graph in a mutation manner;

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

[0067] Step S4-4-3, selecting the candidate crossover mutation operator combinations by using a confidence upper bound algorithm to obtain screened crossover mutation operator combinations.

[0068] Preferably, the step S4-4-3 specifically comprises: screening the crossover mutation operator combinations, and the expression is:

[0069]

[0070] Wherein, op is the screened crossover mutation operator combination; FRR u is the credit value of the combination operator u; C' is a proportion factor for adjusting the balance between development and exploration in the search process, OPs is a set of candidate crossover mutation combination operators, n v , u are the frequencies of the combination operators v, u e OPs in the last |SW| times of using the operators, respectively;

[0071] FRR u The expression of is:

[0072]

[0073] Wherein, Reward u is the sum of the fitness improvement rates FIR u obtained after all uses of the combination operator u in the last |SW| times of using the operators.

[0074]

[0075] wherein FIR u improvement rate of fitness of the table combination operator u. p’ P is a parent individual set, |P p’ | represents the size of the parent individual set, wherein p' ∈ P p’ P is a parent individual. c’ P is a parent individual set. p’ P is a generated child individual set, |P c’ | represents the size of the child individual set, wherein c' ∈ P c’ P is a child individual.

[0076] Preferably, in the step S4-5, the fitness of the child individual is calculated in the manner that the objective function value of the child individual is taken as the fitness of the child individual.

[0077] The step S4-6 specifically comprises: updating the value of the FRR u of the candidate combination of the crossover and mutation operators, and updating the first-in-first-out queue SW recording the usage of the operators.

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

[0079] (1) The present application realizes the multi-objective optimization design of the low-altitude logistics network by introducing a comprehensive objective function based on the transportation demand cost, the construction cost and the population density, and combining the constraint conditions such as network topology, flow distribution and voyage limit. The adaptive evolutionary algorithm is adopted, and the factors such as cost, efficiency and safety are considered in the network design process, so as to reduce the distribution cost and the safety risk of the third party, and improve the distribution efficiency.

[0080] (2) The multi-armed tiger mechanism and the binary tournament strategy are introduced in the optimization algorithm, the combination of the crossover and mutation operators is adaptively selected, the intelligence and the convergence efficiency of the algorithm are improved, and the obtained Pareto front optimization result provides a reliable decision basis for the optimal route deployment of the urban low-altitude logistics network, and realizes the improvement of the distribution efficiency and the balance of the multi-objective.

[0081] (3) The present application divides the low-altitude logistics planning area into grids, establishes a drop facility node, and constructs a low-altitude logistics network model to be optimized. Through the accurate model design and the grid division, the basic layout problem of the low-altitude logistics network in the complex urban area is solved, a clear structure framework is provided for the subsequent optimization, and the scientificity and the applicability of the network planning are effectively improved. BRIEF DESCRIPTION OF DRAWINGS

[0082] The accompanying drawings are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the principles of the application.

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

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

[0085] Figure 3 A schematic diagram of the adaptive operator selection mechanism provided by the application.

[0086] Figure 4 A schematic diagram of the node encoding and network edge encoding provided by the application.

[0087] Figure 5 A schematic diagram of the crossover operator provided by the application.

[0088] Figure 6 A schematic diagram of the mutation operator provided by the application. DETAILED DESCRIPTION

[0089] In order to enable the above-mentioned objects, features and advantages of the application to be more clearly understood, the application will be further described below with reference to the drawings and specific embodiments. It should be noted that the embodiments of the application and the features in the embodiments can be combined with each other without conflict. In addition, the application can also be implemented in other ways different from those described herein, and therefore, the protection scope of the application is not limited by the specific embodiments disclosed below.

[0090] In order to illustrate the effectiveness of the method provided by the application, the above technical solutions of the application will be described in detail below through a specific embodiment. As shown in Figure 1 The adaptive evolution-based urban low-altitude logistics route network design optimization method provided by the application is disclosed, and the specific implementation steps are as follows:

[0091] Step S1, performing grid division on the region planned for low-altitude logistics, obtaining take-off and landing facility nodes, and determining the low-altitude logistics network to be optimized from the take-off and landing facility nodes.

[0092] In this step, the region planned for low-altitude logistics is divided into grids, and the logistics demand points in the grids are clustered, and the cluster center points obtained by clustering are taken as the take-off and landing facility nodes.

[0093] The grid division divides the region planned for low-altitude logistics into grids of uniform size. The take-off and landing facility nodes can be the sites where unmanned aerial vehicles or other low-altitude logistics tools take off and land, and the take-off and landing facility nodes are arranged at positions where the logistics demand is concentrated.

[0094] A model is constructed to represent the design problem of urban low-altitude logistics networks, and a directed graph G corresponding to the low-altitude logistics network to be optimized is generated.<N,E> The specific process includes treating the takeoff and landing facilities as a set of nodes N in a directed graph, where N = {1, ..., |N|}, representing the location of each takeoff and landing facility, and |N| representing the total number of nodes; and connecting edges E to represent the flight path between two nodes. The nodes in the directed graph of this invention include non-hub nodes and hub nodes. Hub nodes can serve as key transshipment and distribution points in the low-altitude logistics network, while nodes other than hub nodes are non-hub nodes.

[0095] This invention encodes the nodes and edges in the directed graph. Specifically, there are |N| landing facility nodes.

[0096] In node encoding, a 0-1 binary list encoding is used, where 1 indicates that the node at that index is selected as the hub node, and otherwise it is a non-hub node;

[0097] The edges are encoded using a 0-1 symmetric matrix, where 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.

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

[0099] Step S2: Establish an objective function for optimizing the low-altitude logistics network. The objective function includes: a total network cost function based on transportation demand costs and the cost of building hubs and hub routes, and a third-party safety risk function 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. The objective function includes the total network cost function and the third-party security risk function. The objective effect to be evaluated 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 costs of transportation demand and the fixed costs required to construct hubs and hub routes, and is expressed as follows:

[0102]

[0103] Among them, w ij c represents the transportation demand from node i to node j (origin-end point); ij ,c ik ,clj c kl is the transportation cost from node i to node j, node i to node k, node l to node j and node k to node l, respectively; ijkl is a 0-1 decision variable, and if its value is 1, it indicates 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; ijkl is a 0-1 decision variable, and if its value is 1, it indicates that the transportation demand from node i to node j passes through the hub arc k-l; β is the economic penalty coefficient between non-hub nodes; ij is a 0-1 decision variable, and if its value is 1, it indicates that the transportation demand from node i to node j does not pass through the hub node and is directly transported; k represents the cost of building the hub node k; k is a 0-1 decision variable, and if its value is 1, it indicates that the decision node k is a hub node; kl is the fixed cost required to activate the connection between the hub node k and the hub node l; kl is a 0-1 decision variable, and if its value is 1, it indicates that the connection between the hub node k and the hub node l is activated.

[0104] The total network cost function provided by the application can balance the transportation between the hub node and the direct transportation by introducing the economic discount coefficient and the economic penalty coefficient, can consider the economy of the transportation path, can balance the investment of the infrastructure construction at the same time, and realizes the minimization of the overall cost of the low-altitude logistics network.

[0105] In some embodiments, the calculation steps of the decision variables y ijkl , f ijkl , s ij include:

[0106] (1) constructing the cost parameter matrix C = [c ij ] |N|×|N| and the safety risk parameter matrix R = [r ij ] |N|×|N| , and performing two norm normalization on C and R to obtain the normalized cost matrix and the normalized safety risk matrix C n = [c ij n ] |N|×|N| , R n = [r ij n ] |N|×|N| , wherein c ij n and r ij n represent the normalized c ij and r ij , and |N| is the number of nodes.

[0107] (2) According to the hub node set H, the weighted cost of the network edge (i,j) is constructed based on C n , R n and the edge attribute The expression is:

[0108]

[0109] Where N\H represents the difference set of N and H, w1 and w2 are weighting coefficients, both of which are set to 0.5. The weighted cost matrix is represented as

[0110] (3) The weighted cost of the unit flow of (k,l) of any hub pair is calculated by Dijkstra algorithm The weighted cost of the unit flow of the transport demand pair (i,j) is calculated When the direct connection edge is not considered, The calculation expression is:

[0111]

[0112] Where A i and A j represent the hub sets connected to nodes i and j, respectively;

[0113] When the direct connection edge is considered, The calculation expression is:

[0114]

[0115] Where SL represents the direct connection edge set between non-hub nodes.

[0116] (4) The path between the node pair with the smallest value is determined as the shortest path, and the values of the decision variables y ijkl , f ijkl , s ij are determined by the shortest path.

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

[0118] c ij = ηd ij

[0119]

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

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

[0122]

[0123] wherein r ij , r ik , r lj , and r kl are the third-party safety transportation risks of nodes i to j, i to k, l to j, and k to l respectively.

[0124] In some embodiments, the specific calculation expression of the third-party safety transportation risk r ij is:

[0125]

[0126] wherein a, b ∈ N, and a ≠ b, r ab is the third-party safety transportation risk of the affected area passed by the aircraft from node a to node b; A exp (a, b) is the potential area exposed to aircraft crash on the route from node a to node b; and ρ(x, y) is the population density of the grid (x, y) in the affected area A exp (i, j).

[0127] The third-party safety risk function of the present application 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 possible affected area along the way, which can more accurately identify and quantify the potential safety risks in the network transmission process.

[0128] Step S3, determining the constraint conditions for optimizing the low-altitude logistics network, the constraint conditions including network topology constraints, flow distribution constraints, and flight range constraints.

[0129] For the directed graph of the urban low-altitude logistics network design problem, it is necessary to implement the constraint conditions of the directed graph based on the requirements of the real-world logistics network, including: network topology constraints, flow distribution constraints, and flight range 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 e N, k < l

[0133] C3:

[0134] C4:

[0135] C5:

[0136] C6: å k∈N x k ≥ 1

[0137] C7: s ij + x j ≤ 1 i, j e N

[0138] C8: s ij + x i ≤ 1 i, j e N

[0139] wherein, is a connectivity variable, which ensures the connectivity of the hub network by defining the spanning tree of the root node at the hub node k, the value of 1 indicates that the spanning tree from the hub node k passes through the edge between the hub node i k and the hub node j k , the value of 1 indicates that the spanning tree from the hub node k passes through the edge between the hub node j k and the hub node i k .

[0140] The constraint conditions C1, C2 ensure that the prerequisite for the activation of the hub edge is that both nodes of the edge are hub nodes; the constraint conditions C3, C4, C5 ensure that the network formed between the hubs has connectivity; the constraint condition C6 ensures that there is at least one hub node in the logistics network.

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

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

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

[0144] C11: åj∈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 transportation demand is transported by only one path; constraint C10 ensures that the transportation demands that cannot be directly transported can only be transported by using the open hubs; constraints C11 and C12 are flow balance constraints.

[0147] The expression of the voyage limit constraint is as follows:

[0148] C13:

[0149] C14:

[0150] C15:d kl z kl ≤Dk,l∈N,k<l

[0151] C16:

[0152] wherein D is the voyage of the aircraft.

[0153] In step S4, the low-altitude logistics network to be optimized is optimized based on the objective function and the constraints by using the adaptive evolutionary algorithm, and a Pareto front optimization result of the low-altitude logistics network is obtained.

[0154] The adaptive evolutionary algorithm is used to optimize the design of the urban low-altitude logistics route network, and the method specifically comprises the following steps:

[0155] In step S4-1, the basic parameters of the adaptive evolutionary algorithm are initialized.

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

[0157] Step S4-2, generating N individuals based on a random greedy strategy, taking the initial population as a current population. The generation of the individuals of the present application is as follows: establishing a directed graph composed of a hub node set and a non-hub node set, and taking the directed graph as an individual. Specifically, the process includes: c

[0158] Step S4-2-1, establishing a directed graph of |N| nodes, generating a random number k between 1 and , and randomly selecting k nodes from all nodes to form a hub node set H, and other nodes to form a non-hub node set;

[0159] Step S4-2-2, judging whether the hub node set H can generate a feasible solution meeting the flight range constraint and the network topology constraint. The judgment method is specifically as follows:

[0160] adding an edge between the hub nodes with a distance less than the flight range to the directed graph, and if the directed graph is not connected, it is determined that a feasible solution cannot be generated;

[0161] otherwise, if all hub nodes can be connected to at least one hub node under the condition of meeting the flight range constraint, it is determined that a feasible solution can be generated.

[0162] Step S4-2-3, if a feasible solution cannot be generated, returning to step S4-2-1 until it is determined that a feasible solution can be generated, and obtaining 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, activating the edges between the hub nodes meeting the flight range constraint, and for each non-hub node, selecting a random number of non-hub access / distribution edges under the premise of meeting the flight range constraint, and randomly selecting non-hub direct edges meeting the flight range constraint;

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

[0165] Step S4-2-5, judging whether the directed graph meets the flow allocation constraint, and obtaining the directed graph meeting the flow allocation constraint as the individual; calculating the objective function value of the individual, and taking the objective function value as the fitness of the individual.

[0166] ​Step S4-3, for the current population, selection is performed using a binary tournament strategy to obtain selected individuals;

[0167] Step S4-4, a candidate crossover mutation operator combination is determined, an adaptive selection is performed based on credit values of the crossover mutation operator combination using a multi-armed bandit selection mechanism to obtain a screened crossover mutation operator combination;

[0168] Step S4-4-1, a crossover operator is determined, which cross-modifies the node encoding and the edge encoding in the directed graph; a mutation operator is determined, which mutation-modifies the node encoding and the edge encoding in the directed graph.

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

[0170] As shown in the following table, the crossover operator of the present application is used to modify the node encoding and the edge encoding in the directed graph, in the following, the node encoding and the edge encoding are referred to as chromosomes, each encoding value in the node encoding and the edge encoding is referred to as a gene, and the node encoding and the edge encoding before and after modification are referred to as parent and offspring respectively. Figure 5

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

[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 two child node chromosomes are generated by exchanging genes in the rear part of the crossover point; the edge chromosome of the child chromosome is generated by exchanging a block composed of the last τ rows with a size of τ*τ. The backward single-point crossover operator is similar to the forward single-point crossover operator, but the genes representing the edge decision of the two child chromosomes are obtained by exchanging a block composed of the first τ rows with a size of τ*τ. The forward two-point crossover operator randomly selects two crossover points, and exchanges the genes of the parent between the two points to generate two child genes; wherein, the node decision gene part is directly exchanged between the two points to generate the node decision gene of the child chromosome, and the link decision chromosome is exchanged in the vertical and horizontal directions using the forward crossover method. The backward two-point crossover operator, the operation of the node decision gene part is the same as the forward two-point crossover operator, and the link decision chromosome adopts the backward crossover method to obtain the corresponding part of the child chromosome.

[0173] The forward multi-point crossover randomly selects ​At a crossover point, 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 as forward multi-point crossover, with the difference 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 of the same length as the parent is randomly generated, and the parent genes are exchanged according to the predefined probability value, and if the element of the array exceeds the predefined threshold value, it is set to 0.5. Then the genes with the corresponding index are exchanged to produce offspring; the genes of the node decision are exchanged by standard uniform crossover, and the genes of the link decision are operated in a two-dimensional matrix by the forward exchange method. Backward uniform crossover uses similar steps as forward multi-point crossover, with the difference that it exchanges the genes representing the link matrix in the backward two-dimensional crossover manner.

[0174] The mutation operator of the present application is used to mutate the genes in the node encoding and edge encoding in the graph. The mutation operator includes a SLAM operator and a CenCS operator, Figure 6 The specific operation of the mutation operator is described. Specifically, the SLAM operator applies a simple bit mutation to the node decision array, including adding or deleting 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 a new sub-node. The CenCS operator mutates the chromosome by newly defined centrality, and 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 the standardized value of d ij ; and r is the standardized value of r ij .

[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 into 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 into a hub node.

[0178] Step S4-4-2, a plurality of crossover mutation operator combinations are obtained 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 Uniform crossover (front / back) No 7 Single point crossover (front / back) No 2 Uniform crossover (front / back) SLAM 8 Two point crossover (front / back) No 3 Uniform crossover (front / back) CenCS 9 No SLAM 4 Multi-point crossover (front / back) No 10 No CenCS 5 Multi-point crossover (front / back) SLAM 11 No No 6 Multi-point crossover (front / back) CenCS

[0181] As shown in Table 1, the present application combines the crossover operator and the mutation operator, adopts the combination of the 11 crossover mutation operators in Table 1 as the combination of the crossover mutation operators. Among them, 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 adopted.

[0182] Step S4-4-3, the candidate crossover mutation operator combination is screened by using the confidence upper bound algorithm to obtain the screened crossover mutation operator combination.

[0183] The multi-armed bandit selection strategy screens the crossover mutation operator combination by using the confidence upper bound algorithm, and the expression is:

[0184]

[0185] Among them, op is the screened crossover mutation operator combination; FRR u is the credit value of the combination operator u; C' is the proportion factor for adjusting the balance between development and exploration in the search process. OPs={1,…,11} is the candidate crossover mutation operator combination set. n v ,n u are the frequencies of the combination operators v, u∈OPs in the last |SW| times of using the operators.

[0186] The expression of FRR u is:

[0187]

[0188] Among them, Reward u is the sum of the dominance-based fitness improvement rates obtained after all uses of the combination operator u in the last |SW| times of using the operators.

[0189] The dominance-based fitness improvement rate is used to measure the performance of the application of the operator combination once. The expression is:

[0190]

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

[0192] Step S4-5, for the selected individual, cross and mutation processing is performed using the screened combination of crossover and mutation operators to obtain a child individual, the fitness of the child individual is calculated, the child individual is added to the offspring population, and the offspring population is determined;

[0193] In this step, the fitness of the child individual is also calculated using the objective function value, and the objective function value of the child individual is taken as the fitness of the child individual.

[0194] Step S4-6, update the credit value of the candidate crossover and mutation operator combination.

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

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

[0197] Step S4-8, merge the current population and the offspring population, sort the merged population quickly based on the non-dominated rule, and select the first N c individuals to form a population to update the current population.

[0198] The non-dominated rule is a sorting criterion in the art for evaluating the pros and cons of solutions, especially for handling multiple conflicting objectives.

[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 take the current population as the Pareto front optimization result of the low-altitude logistics network.

[0200] The Pareto front refers to a set of solutions in the current found solution set that cannot be further improved in one objective without compromising another objective. In the present application, the optimal Pareto front of the model represents the completion of the trade-off between economic cost and safety, and the economic and safe urban low-altitude logistics route network is obtained.

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

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

[0203] In some embodiments, the way of selecting the optimal individual in the present application can include: (1) using weighted scores and selecting the individual with the highest score as the optimal individual; (2) visualizing the solutions in the Pareto front and selecting the individual that best meets the requirements as the optimal individual; (3) screening the individuals that meet the preset constraints from the Pareto front as the optimal individual; (4) using a clustering method to determine the optimal individual, and the like. Those skilled in the art can determine the optimal individual in a variety of existing ways, and the present application does not limit the way of selecting the optimal individual.

[0204] In the present application, the optimal Pareto front of the model represents that the economic cost and safety are balanced, and the urban low-altitude logistics route network that takes into account both economy and safety is obtained.

[0205] The detailed description of the application, although using a specific order to depict various actions or steps, should be understood that such actions or steps are required to be performed in the specific order shown or in a sequential order, or all the illustrated actions or steps should be performed to achieve the desired results. In certain circumstances, multi-tasking and parallel processing can be advantageous. Similarly, although the above discussion contains a number of specific implementation details, these should not be interpreted as limiting the scope of the disclosure. Certain features described in the context of separate embodiments can also be combined in a single implementation. Conversely, various features described in the context of a single implementation can also be separated and implemented in multiple implementations. The above description is only the preferred specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any changes or replacements within the technical scope disclosed by the present application can be easily thought by those skilled in the art, which should be covered in the protection scope of the present application.

[0206] The above description is only the preferred specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any changes or replacements within the technical scope disclosed by the present application can be easily thought by those skilled in the art, which should be covered in the protection scope of the present application.

Claims

1. An adaptive evolution-based optimization method for urban low-altitude logistics route network design, characterized in that, The method comprises the following steps: Step S1, grid division is performed on a region of low-altitude logistics planning, and take-off and landing facility nodes are obtained, and the low-altitude logistics network model to be optimized is determined by the take-off and landing facility nodes; Step S2, a target function for optimizing the low-altitude logistics network model is established, the target function comprising: a network total cost function established based on transportation demand cost and cost of constructing hubs and hub routes, and a third-party safety risk function established based on population density of a transportation region; Step S3, a constraint condition for optimizing the low-altitude logistics network model is determined, the constraint condition comprising a network topology constraint, a flow distribution constraint and a flight range limit constraint; Step S4, an adaptive evolutionary algorithm is adopted to optimize the low-altitude logistics network model to be optimized based on the target function and the constraint condition, and a Pareto front optimization result of the low-altitude logistics network model is obtained; Step S5, an optimal urban low-altitude logistics route network is determined based on the Pareto front optimization result; In step S2, the network total cost function comprises variable cost of transportation demand and fixed cost required for constructing hubs and hub routes, and the expression is as follows: wherein, denotes the start-end node denotes the transportation demand from node to node , , denotes the transportation cost from node to node , node to node , node to node and node to node ; is a 0-1 decision variable, if its value is 1, it means that the first hub node of the transportation demand from node to node is and the last hub node is ; is the economic discount factor between hub nodes; is a 0-1 decision variable, if its value is 1, it means that the transportation demand from node to node passes through hub arc ; is the economic penalty factor between non-hub nodes; is a 0-1 decision variable, if its value is 1, it means that the transportation demand from node to node does not pass through hub nodes directly; denotes the cost of building hub node ; is a 0-1 decision variable, if its value is 1, it means that node is decided to be a hub node; is the fixed cost of activating the edge between hub node and hub node ; is a 0-1 decision variable, if its value is 1, it means that the edge between hub node and is activated; The expression of the third-party safety risk function is as follows: wherein, , , are third party security transportation risks from node to node , from node to node , from node to node , and from node to node , respectively. The specific calculation expression of the third-party safety transportation risk is as follows: wherein, , and , is a third party safety transport risk of an affected area flown over by the aircraft from node to node ; is a potential area exposed to a plane crash for a flight from node to node ; is a population density of a grid in the affected area ; In step S3, the network topology constraint is used to ensure that the prerequisite for activating a hub edge is that both nodes of the edge are hub nodes, to ensure that the network formed between hubs has connectivity, and to ensure that there is at least one hub node in the logistics network, and the expression is as follows: C1： C2： C3： C4： C5： C6： C7： C8： wherein, , is a connectedness variable, which, by defining the spanning tree of the root node at the hub node , ensures the connectedness of the hub network, a value of 1 indicates that the spanning tree from the hub node passes through the edge from the hub node to the hub node , a value of 1 indicates that the spanning tree from the hub node passes through the edge from the hub node to the hub node ; The flow distribution constraint is used to ensure that each transportation demand is transported by only one path, to ensure that transportation demand that cannot be directly transported can only be transported by using an open hub, and to ensure flow balance, and the expression is as follows: C9： C10： C11： C12： The flight range limit constraint is used to ensure that all activated edges and transportation paths meet the flight range of an aircraft, and the expression is as follows: C13： C14： C15： C16： wherein, is the range of the aircraft.

2. The adaptive-evolution-based urban low-altitude logistics route network design optimization method according to claim 1, characterized in that, The step S1 specifically comprises: Step S1-1, the region of low-altitude logistics planning is divided into uniform grids, and logistics demand points in the grids are clustered, and cluster center points obtained by clustering are taken as take-off and landing facility nodes; Step S1-2, constructing a directed graph corresponding to the low-altitude logistics network model to be optimized , taking the take-off and landing facilities as the node set of the directed graph , , indicating the total number of all nodes; edges , indicating the path of flight between two nodes; the nodes of the directed graph include non-hub nodes and hub nodes; encoding the nodes and edges in the directed graph: For node coding, 0-1 binary list coding is adopted, 1 indicates that a node at an index is selected as a hub node, otherwise, it is a non-hub node; For edge coding, 0-1 symmetric matrix coding is adopted, 1 indicates that the connection between a node pair represented by row and column indexes is activated, otherwise, there is no connection between the node pair.

3. The adaptive evolution-based urban low-altitude logistics route network design optimization method according to claim 2, characterized in that, The step S4 specifically comprises: Step S4-1, initializing the basic parameters of the adaptive evolution algorithm, including: population size , number of take-off and landing facilities nodes , maximum number of times of fitness calculation, and length of the first-in-first-out queue recording the use of the operator ; Step S4-2, generating based on a random greedy strategy An individual is generated as an initial population, the initial population is taken as a current population, a value of the objective function of the individual is calculated, the value of the objective function is taken as the fitness of the individual, and the individual is generated in the following manner: a directed graph composed of a hub node set and a non-hub node set is established, and the directed graph is taken as the individual. Step S4-3, for a current population, a binary tournament strategy is adopted for selection, and selected individuals are obtained; Step S4-4, a candidate crossover and mutation operator combination is determined, a multi-armed tiger machine selection mechanism is adopted, adaptive selection is performed based on credit values of the candidate crossover and mutation operator combination, and a screened crossover and mutation operator combination is obtained; Step S4-5, for the selected individuals, the screened crossover and mutation operator combination is adopted for crossover and mutation processing, sub-individuals are obtained, fitness of the sub-individuals is calculated, the sub-individuals are added to a child population, and the child population is determined; Step S4-6, credit values of the candidate crossover and mutation operator combination are updated; Step S4-7, return to step S4-3 until the number of individuals of the offspring population reaches the preset population size; Step S4-8, merging the current population and the offspring population, fast sorting the merged population based on non-dominated rules, and selecting the first population formed by the individuals to update the current population; Step S4-9, determine whether the maximum number of fitness calculations is reached, if not, return to step S4-3; otherwise, complete the adaptive evolution, and take the current population as the Pareto front optimization result of the low-altitude logistics network model.

4. The adaptive evolution-based urban low-altitude logistics route network design optimization method according to claim 3, characterized in that, The step S4-2 specifically comprises: Step S4-2-1, establishing a directed graph of nodes, generating a random number between 1 and randomly selecting a set of hub nodes from all nodes , other nodes constitute a set of non-hub nodes; Step S4-2-2, judging the hub node set whether a feasible solution satisfying the voyage limit constraint and the network topology constraint can be generated; the judging manner is specifically: Adding edges between hub nodes with a distance less than the flight range to the directed graph, and if the directed graph is not connected, determining that a feasible solution cannot be generated; Otherwise, if all hub nodes can be connected to at least one hub node under the flight range constraint, determining that a feasible solution can be generated; Step S4-2-3, if a feasible solution cannot be generated, return to step S4-2-1 until a feasible solution is determined to 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 hub nodes that satisfy the flight range constraint, and for each non-hub node, select a random number of non-hub access / distribution edges under the premise of satisfying the flight range constraint, and randomly select non-hub direct edges that satisfy the flight range constraint; Step S4-2-5, determine whether the directed graph satisfies the flow allocation constraint, obtain the directed graph satisfying the flow allocation constraint as the individual, and calculate the objective function value of the individual, taking the objective function value as the fitness of the individual.

5. The adaptive-evolution-based urban low-altitude logistics route network design optimization method according to claim 4, characterized in that, The step S4-4 specifically comprises: Step S4-4-1, determine a crossover operator that modifies the node encoding and edge encoding in the directed graph in a crossover manner, and determine a mutation operator that modifies the node encoding and edge encoding in the directed graph in a mutation manner; Step S4-4-2, combine the crossover operator and the mutation operator to obtain a plurality of crossover mutation operator combinations as the candidate crossover mutation operator combinations; Step S4-4-3, select the candidate crossover mutation operator combinations by using a confidence upper bound algorithm to obtain screened crossover mutation operator combinations.

6. The adaptive evolution-based urban low-altitude logistics route network design optimization method according to claim 5, characterized in that, The step S4-4-3 specifically comprises: screening the crossover mutation operator combinations, and the expression is: wherein, is the selected crossover mutation operator combination; is the combined operator credit value; is a scaling factor that adjusts the trade-off between exploitation and exploration during the search process, is a set of candidate crossover mutation operator combinations, is the combined operator frequency of use of the operator in the last times. The expression is: wherein, is the most recent combination operator all fitness improvement rates obtained after being used sum; wherein, Table combination operator a fitness improvement rate, a parent individual set, denotes a size of the parent individual set, wherein a parent individual, is a generated offspring individual set, denotes a size of the offspring individual set, an offspring individual.

7. The adaptive-evolution-based urban low-altitude logistics route network design optimization method according to claim 6, characterized in that, In the step S4-5, the fitness calculation method of the sub-individual is to take the objective function value of the sub-individual as the fitness of the sub-individual; The step S4-6 specifically comprises updating the values of the candidate crossover mutation operator combinations and updating a first-in-first-out queue recording operator usage .

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