Unmanned aerial vehicle distribution center site selection method based on fuzzy mathematical programming particle swarm optimization

Abstract

The invention provides an unmanned aerial vehicle distribution center site selection method based on a fuzzy mathematical programming particle swarm algorithm, aims to complete position selection of a park distribution center under multi-target and complex constraint conditions under the background of low-altitude economy, intelligent logistics and unmanned distribution, and comprises the following steps: carrying out detailed modeling characterization on a park multi-unmanned aerial vehicle distribution center site selection problem; delivery time and operation cost targets are subjected to target reduction through fuzzy mathematical programming, solving under complex constraint conditions is facilitated, the particle swarm optimization optimizes the search process through an elitism strategy, a limited number of Pareto solutions are obtained through an epsilon-constraint method, convergence is gradually carried out to an optimal solution, and the optimal solution is obtained. The method is suitable for multi-unmanned-aerial-vehicle distribution in an unattended park, the load and cruising ability of the unmanned aerial vehicles, energy consumption, no-fly zone distribution and other scenes with complex constraint conditions are considered, and an efficient and accurate unmanned aerial vehicle distribution center site selection scheme can be provided.

Description

Technical Field

[0001] The present invention relates to the field of logistics technology, and in particular to a method for selecting a drone distribution center site based on a fuzzy mathematical programming particle swarm algorithm. Background Art

[0002] With the rapid development of the low-altitude economy, drone delivery, as an important part of modern logistics, is becoming an important means to realize smart logistics and unmanned delivery. In scenarios such as industrial parks, drone delivery can realize unmanned services in all areas and all weather, which not only effectively reduces labor costs, but also significantly improves delivery efficiency and flexibility. However, although the delivery scenarios in industrial parks seem to be small in scale and the environment is relatively fixed, there are actually many complex constraints, such as no-fly zones, load and endurance restrictions of drones, and delivery time conflicts between multiple demand nodes. These constraints make the distribution problems within the industrial park not only complex, but also put higher requirements on site selection and optimization methods. Traditional methods are difficult to achieve efficient optimization effects in such an environment, resulting in many challenges in practical applications.

[0003] In the problem of distribution center site selection, the rationality of site selection is directly related to distribution efficiency, operating costs and service quality. Traditional site selection methods are usually divided into qualitative methods and quantitative methods. Qualitative methods (such as hierarchical analysis method and fuzzy evaluation method) rely on expert experience. Although they can provide certain references when information is incomplete or uncertainty is strong, they are highly subjective and difficult to cope with optimization needs under complex constraints. Quantitative methods (such as the center of gravity method and p-median model) are optimized through mathematical modeling, but when dealing with multi-objective and multi-constraint problems, they are usually unable to effectively balance conflicting goals.

[0004] In the campus distribution scenario, if the location of the distribution center is inappropriate, it will bring a series of practical problems. For example, unreasonable site selection may lead to a significant increase in drone flight paths, resulting in longer flight time and increased energy consumption, thereby significantly increasing operating costs. In addition, due to delivery time constraints, if the location of the distribution center is not reasonably distributed, it may also lead to the inability to complete the delivery tasks of all demand nodes within the specified time, seriously affecting the service quality. Especially in the campus, drone delivery is also affected by spatial restrictions such as no-fly zones, which makes flight path planning more complicated and further aggravates the difficulty of the site selection problem. Therefore, how to comprehensively consider delivery time, operating costs and multiple constraints in multi-objective optimization has become a core problem that needs to be solved urgently.

[0005] With the improvement of information technology and computing power, swarm intelligence optimization algorithms are widely used in complex optimization problems. Among them, particle swarm optimization has shown superior solving ability to traditional methods due to its global search ability and efficient computing characteristics, especially in static scenes with good convergence effect. However, particle swarm optimization still has shortcomings in multi-objective optimization. Due to the single fitness function, particle swarm optimization is difficult to balance conflicting objectives in multi-objective optimization, such as delivery time and operating cost, and is prone to fall into local optimal solutions. At the same time, the distribution of solutions is not balanced enough, and it is impossible to fully explore possible Pareto optimal solutions. This defect makes it difficult for particle swarm optimization to achieve satisfactory optimization results when facing problems with complex constraints and conflicting objectives such as campus distribution.

[0006] Fuzzy mathematical programming has advantages in dealing with multi-objective optimization problems under complex constraint scenarios. By introducing fuzzy sets and membership functions, it can effectively describe and deal with uncertainties and fuzzy constraints, thereby achieving flexible modeling of objective trade-offs and decision-making processes. Summary of the invention

[0007] In view of the shortcomings of the prior art, the present invention provides a UAV distribution center site selection method based on fuzzy mathematical programming and particle swarm algorithm, which aims to complete the location selection of the park distribution center under multi-objective and complex constraints, and balance the delivery time and operating cost goals.

[0008] To achieve the above objectives, the present invention is implemented through the following technical solutions: a method for selecting a multi-UAV distribution center in a park based on fuzzy mathematical programming particle swarm algorithm, comprising the following steps:

[0009] Step 1: Model the delivery scenario in detail, taking into account complex constraints, including the geographical location of customers in the park, the technical parameters of the drone (load capacity, endurance, etc.), the distribution of no-fly zones, and the location of potential delivery centers;

[0010] Step 2: Simplify the two objectives of delivery time and operation cost through fuzzy mathematical programming, construct a membership function to normalize multiple objectives, and reduce the complexity of solution;

[0011] Step 3: Use the particle swarm algorithm to solve the optimization problem after the transformed target simplification, determine the optimal number and location of distribution centers, and output the final configuration plan.

[0012] In step 1, the modeling of the drone delivery scenario involves the following key factors: the geographical location of the on-campus customers, the technical parameters of the drone (load and endurance), the distribution of no-fly zones, and the location of potential delivery centers. The specific modeling process is as follows:

[0013] Assuming that the distribution demand point is located in a small-scale scenario such as a park, the location of each customer is represented by a two-dimensional coordinate system, and the geographical location of customer i is P i (x i ,y i ) Where: i = 1, 2, ..., N represents the customer number, there are N customers in total, and the geographical locations of all customers can be represented as a set of coordinate points {P 1 (x 1 ,y 1 ),P 2 (x 2 ,y 2 ),...,P N (x N ,y N )}.

[0014] In order to simulate the flight capability of UAVs, the following technical parameters are introduced: the maximum load of each UAV is W max , represents the maximum cargo weight that the drone can carry, and the maximum flight distance of each drone is D max , which is calculated based on the battery life and flight efficiency of the drone and is related to the load. Suppose the current load of the drone is W and the empty weight is W 0 , the battery capacity is Q, the voltage is v, and the energy conversion efficiency is η, then the maximum flight distance can be expressed by the following formula:

[0015]

[0016] The flight speed of the drone is V. It is usually assumed that the flight speed is within a fixed value V, and the unit is the distance flown per second (meters / second). The maximum flight time of each drone is T. max , which limits the flight duration of the drone, and it will not be able to return after this time.

[0017] In the delivery scenario, there may be some no-fly zones that drones cannot cross. The no-fly zones are modeled as follows: Assume that there are F no-fly zones, and each no-fly zone j can be represented by a circular area with the center coordinates (x j ,y j ), with a radius of r j , that is, the mathematical model of the no-fly zone is a circular area: C j (x j ,y j ,r j )wherein, j=1,2,...,F represents the number of the no-fly zone.

[0018] The impact of each no-fly zone is that when a drone is flying from a distribution center to a customer, if the flight path overlaps with a no-fly zone, it must detour around the no-fly zone. The detour time and path length will increase the delivery time.

[0019] In the distribution task, the potential distribution center is located in the preset candidate location area. Assume that there are M candidate distribution center locations, represented by C k (x k ,y k ), where k = 1, 2, ..., M represents the number of the distribution center. There are M distribution center candidate locations. The drone can depart from one distribution center and go to another distribution center for charging or loading after completing the delivery.

[0020] Based on the above modeling content, the calculation method of the delivery path can be defined. The key lies in how to calculate the flight time of the drone from the delivery center to the customer based on the location of the delivery center and the customer location, and set the delivery center C k To Customer P i The flight time T flight (C k ,P i )for: and In addition, if the flight path passes through a no-fly zone, it is necessary to detour around the no-fly zone.

[0021] In order to ensure the safety and rationality of the UAV's flight, it is necessary to set constraints on the flight path. The flight distance of the UAV cannot exceed its maximum flight distance D max ,Right now: The flight time of the drone cannot exceed its maximum flight time T max ,Right now: If the path is affected by a no-fly zone, the detour time T detour (C k ,P i ) cannot exceed a certain proportion ρ of the flight time:

[0022] In step 2, two objective functions are introduced: the delivery time objective and the operating cost objective. These two objectives are conflicting and reflect the timeliness and economy of the delivery task respectively. Ultimately, they need to be converted through fuzzy mathematical programming and optimized through particle swarm algorithm.

[0023] Delivery time refers to the total flight time of the drone from the distribution center to each customer, which is affected by the flight time and the detour time in the no-fly zone. Assuming there are M distribution centers and N customers, the delivery time objective function T total It can be expressed as the weighted sum of the flight time of all customers. The specific formula is:

[0024]

[0025] Where: T flight (C k ,P i ) is the distribution center C k To Customer P i Flight time, T detour (C k ,P i ) is the detour time. If the flight path is affected by a no-fly zone, the additional detour time needs to be calculated. ki is a binary variable, indicating that the distribution center C k Responsible for delivery to customer P i , if distribution center C k Responsible for Customer P i For delivery, then x ki =1, otherwise x ki =0,d(C k ,P i ) is the distribution center C k To Customer P i The Euclidean distance of , V is the flight speed of the drone.

[0026] The operating costs mainly include the construction cost of the distribution center, the maintenance cost of the drone, the flight cost, and the battery charging cost. The specific operating cost objective function C total It can be expressed as:

[0027]

[0028] Where: C center (C k ) is to establish distribution center C k The required fixed construction cost, assumed to be constant, C flight (C k ,P i ) is the drone from the distribution center C k To Customer P i The flight cost is usually estimated based on the flight distance and flight time; C flight (C k ,P i )=α·d(C k ,P i ), where α is the flight cost per unit distance, C battery (C k ,P i ) is the cost of charging the drone battery, which is usually determined by the flight time and the battery charging cost; C battery (C k ,Pi )=β·T flight (C k ,P i ), where β is the battery charging cost per unit flight time.

[0029] In order to compare these two targets under a unified standard, they first need to be normalized to the interval [0,1].

[0030] set up and are the optimal values ​​of delivery time and operating cost respectively, and the normalized target T norm and C norm It can be expressed as:

[0031]

[0032] in: and are the lower limits of delivery time and operating cost, respectively, and are the predetermined minimum values. and They are the upper limits of delivery time and operating cost respectively, usually the maximum values ​​under the worst case scenario.

[0033] The membership function is used to fuzzy the two normalized targets. The role of the membership function is to map the target value to a numerical interval [0,1] representing the degree of satisfaction, where 1 means that the target is fully satisfied and 0 means that the target is not satisfied at all.

[0034] For the delivery time target T norm and operating cost target C norm , respectively construct the membership function μ T (T norm ) and μ C (C norm ):

[0035]

[0036] μ T (T norm ) and μ C (C norm ) represent the membership of the delivery time target and the operating cost target respectively. The delivery time target T processed by the membership function norm As the main optimization target, the operating cost target C processed by the membership function norm After adding constraints and fuzzy mathematical programming, the problem can be expressed as:

[0037] maxμ T (T norm )

[0038]

[0039] Where: μ T (T norm ) is the membership degree of the delivery time target, represents the optimization target, μ C (C norm ) is the membership degree of the operating cost target. As a constraint, ε is a constant that represents the tolerance of the constraint, ensuring that the operating cost does not exceed a certain upper limit while optimizing the delivery time.

[0040] In step 3, the basic idea of ​​the particle swarm algorithm is to search for the optimal solution to the problem by simulating the foraging process of a flock of birds. In PSO, each particle represents a potential solution, and the position and velocity of the particle represent a solution in the solution space and the search step length of the solution, respectively. Each particle will update its position and velocity according to its historical optimal position and the global optimal position.

[0041] The particle updates its position and velocity using the following formula:

[0042]

[0043] in: is the velocity of particle i at time t; is the position of particle i at time t; is the historical optimal position of particle i; g (best) is the global optimal position; w is the inertia weight, which controls the exploration ability of the particle; c 1 ,c 2 are the individual and social learning factors, respectively, controlling the dependence of particles on individual and group experience; r 1 ,r 2 is a random number, usually in the range [0,1];

[0044]

[0045] in is the new position of particle i at time t+1.

[0046] In order to evaluate the quality of particles, a fitness function (objective function) is defined, and the fitness is calculated based on the particle position update. In this problem, the fitness function is the combination of the normalized delivery time target and the operating cost target. The goal of the particle swarm algorithm is to maximize the membership of the delivery time target, while taking the membership of the operating cost target as a constraint.

[0047] Specifically, the fitness function is:

[0048] f(x)=μ T (Tnorm );

[0049] The particle swarm algorithm continuously optimizes the target through multiple iterations and searches for the optimal solution. The key steps in each iteration process include position update, speed update and fitness evaluation. The specific steps are as follows:

[0050] In the initialization stage, a certain number of particles are randomly generated, each particle corresponds to a distribution center configuration plan (i.e., the number and location of distribution centers), the position of each particle is the solution to the problem to be optimized, and the speed represents the search step.

[0051] Calculate the fitness value of each particle according to the membership function μ T (T norm ) and μ C (C norm ) to evaluate the quality of each particle.

[0052] According to the update formula of the particle swarm algorithm (the aforementioned speed update and position update formula), the speed and position of the particles are updated.

[0053] Update the individual optimum and the global optimum. If the fitness of the current particle is better than its historical optimal fitness, update the historical optimal position of the particle; if the fitness of the current particle is better than the global optimal fitness, update the global optimal position.

[0054] Check whether the termination condition is met (for example, the maximum number of iterations is reached or the fitness converges). If the termination condition is met, the optimal solution is output; if not, return to the update step to continue iterating.

[0055] After multiple iterations of optimization, the particle swarm algorithm will converge to the optimal solution, which is the optimal number and location configuration of distribution centers. In each iteration, the position of the particle corresponds to a different distribution center configuration, and the fitness reflects the pros and cons of the configuration. After multiple iterations, the particle position corresponding to the global optimal solution is the optimal distribution center configuration.

[0056] For the new problem obtained by transformation, ε increases in a certain step size between 0 and 1. A Pareto solution is obtained each time it is increased, and finally a finite number of Pareto solutions are obtained. Each solution obtained is calculated, and the one with the largest value is taken as the final location selection plan. The output final configuration plan includes: the optimal number of distribution centers, the specific location of each distribution center, and the optimal values ​​of delivery time and operating cost under the constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a general flow chart of the location selection method of drone distribution center based on fuzzy mathematical programming and particle swarm algorithm;

[0058] Figure 2 It is a specific step diagram of the location selection method of drone distribution center based on fuzzy mathematical programming particle swarm algorithm;

[0059] Figure 3 It is a specific scenario diagram of the drone delivery center site selection method based on fuzzy mathematical programming and particle swarm algorithm. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] Embodiment 1

[0062] Combination Figure 1 , the present invention provides a UAV distribution center site selection method based on fuzzy mathematical programming particle swarm algorithm, which realizes the optimization process through three main steps:

[0063] Step 1: Problem Modeling

[0064] The modeling of multi-drone delivery scenarios considers complex constraints, including the geographical location of customers within the park, the technical parameters of drones (load capacity and endurance), the distribution of no-fly zones, and key factors in the site selection areas of potential distribution centers.

[0065] Step 2: Fuzzy Mathematical Programming Objective Transformation

[0066] In this step, the two objectives of delivery time and operating cost are conflicting. After characterizing the objective function, fuzzy mathematical programming must be used to simplify the objectives and transform the original complex problem into a simple new problem for solution.

[0067] Step 3: Particle swarm algorithm optimization and solution

[0068] Each particle of the particle swarm algorithm represents a potential position selection scheme. The position and velocity of the particle represent a solution in the solution space and the search step of the solution respectively. The position and velocity of each particle are updated according to its historical optimal position and the global optimal position. Through the ε-constraint method, ε increases between 0 and 1, and a finite number of Pareto solutions are obtained, among which the optimal solution is selected.

[0069] Combination Figure 2 , the present invention provides a detailed technical implementation flow chart, further illustrating the specific implementation method of each step, Figure 2The specific unfolding process of three main steps is demonstrated, including fuzzy mathematical programming transformation, particle swarm algorithm solution and the final distribution center configuration output.

[0070] First, the objective function of the distribution center location problem is constructed. Assuming that the delivery time target is T total , the operating cost target is C total , and define their membership functions μ respectively. T (T norm ) and μ C (C norm ), the objectives are normalized by fuzzy mathematical programming method, and the normalized objectives are T norm and C norm ,

[0071] These objective functions are defined as:

[0072]

[0073] μ T (T norm ) and μ C (C norm ) represent the membership of the delivery time target and the operating cost target respectively. The delivery time target T processed by the membership function norm As the main optimization target, the operating cost target C processed by the membership function norm After adding constraints and fuzzy mathematical programming, the problem can be expressed as:

[0074] maxμ T (T norm )

[0075]

[0076] Where: μ T (T norm ) is the membership degree of the delivery time target, represents the optimization target, μ C (C norm ) is the degree of membership of the operating cost target, and as a constraint, it represents the tolerance of the constraint, ensuring that the operating cost does not exceed a certain upper limit while optimizing the delivery time.

[0077] Combination Figure 2 ,The present invention provides a specific scenario of the UAV delivery center site selection method based on fuzzy mathematical programming and particle swarm algorithm.

[0078] The small-scale park is a logistics distribution environment with a limited geographical scope and full-area and all-weather unmanned demand. It occurs in a closed or semi-closed area of ​​several square kilometers, such as an industrial park, university campus, commercial complex, etc.; the number of distribution demand nodes generally does not exceed 50 to 100, and the distribution demand is relatively stable in time and has small dynamic changes; the number of drones involved in the distribution is between 5 and 10, and is managed through distributed scheduling.

[0079] Although the scale of the problem is relatively small, the spatial constraints within the campus scenario are significant, including no-fly zones, flight path restrictions, and UAV endurance and load constraints. UAVs cannot fly over no-fly zones and must strictly meet endurance and load restrictions.

[0080] Combination Figure 3 ,The present invention provides a UAV distribution center site selection method based on ,fuzzy mathematical programming particle swarm algorithm ,At this stage, first a number of particles are randomly generated, ,each particle represents a potential distribution center configuration scheme (i.e., ,the number and location of distribution centers), the position of the particle represents the ,solution of the configuration, and the speed represents the step length in the ,particle search space.

[0081] The particle updates its position and velocity using the following formula:

[0082]

[0083] in: is the velocity of particle i at time t; is the position of particle i at time t; is the historical optimal position of particle i; g (best) is the global optimal position; w is the inertia weight, which controls the exploration ability of the particle; c 1 ,c 2 are the individual and social learning factors, respectively, controlling the dependence of particles on individual and group experience; r 1 ,r 2 is a random number, usually in the range [0,1];

[0084]

[0085] in is the new position of particle i at time t+1. After each iteration, the particle updates its position and velocity according to its fitness evaluation function (i.e., the value of the objective function).

[0086] Finally, for the new problem obtained by transformation, ε increases in a certain step size between 0 and 1, and a Pareto solution is obtained each time it is increased, and finally a finite number of Pareto solutions are obtained. The fitness function is calculated for each solution obtained, and the one with the largest value is taken as the final location selection plan. The particle swarm algorithm will return the optimal configuration plan of the distribution center, that is, the specific location and number of each distribution center. According to the algorithm optimization process, the final delivery time and operating cost target values ​​will be in the optimal compromise state, meeting the optimization requirements of the problem.

[0087] Through the above steps, the present invention can effectively select the site for multiple drone delivery centers in the park, balance the delivery time and operating costs, and obtain an efficient and feasible configuration plan.

[0088] Embodiment 2

[0089] A method for selecting a drone distribution center site using a fuzzy mathematical programming particle swarm algorithm is an urban and rural distribution method based on machine learning or deep learning. During the implementation of the present invention, in addition to the existing park distribution center site selection method, its application scope is further expanded to be applicable to other distribution scenarios of different types and scales; in addition to small-scale parks, this method can be applied to environments such as urban distribution or rural distribution. In urban distribution scenarios, due to the more complex geographical environment of the city, there are more traffic congestion and distribution demand nodes, and the existing model can be adjusted on this basis, taking into account the traffic conditions, road flow and distribution demand changes in different regions. To meet these challenges, the particle swarm algorithm can be appropriately modified, such as introducing a dynamic weight mechanism based on traffic flow, so that the algorithm can be adaptively optimized according to real-time traffic data.

[0090] In addition, urban distribution may involve more distribution demands and more complex constraints. At this time, more optimization objectives can be introduced, such as traffic distribution of road networks and management of delivery time windows, so as to improve the adaptability and accuracy of the algorithm.

[0091] In addition to the existing optimization framework based on fuzzy mathematical programming and particle swarm algorithm, more advanced algorithms can be introduced to further improve the intelligence level of the system. For example, combined with reinforcement learning technology, the various parameters in the particle swarm algorithm can be adjusted through adaptive learning in each distribution scenario, thereby improving the robustness and adaptability of the algorithm in a dynamic environment. By allowing the system to autonomously learn and adjust in the ever-changing distribution needs, it can effectively solve the problems of improving distribution efficiency and satisfying constraints in complex environments. Taking into account issues such as energy consumption and environmental protection, more constraints can be introduced in the optimization process, such as energy consumption and carbon emissions of drones, so as to achieve a more environmentally friendly and sustainable distribution solution.

Claims

1. A fuzzy mathematical programming particle swarm algorithm method for selecting the location of a UAV distribution center, characterized in that: The method comprises the following steps: Step S1: Modeling the delivery scenario; Step S2: Simplify the two objectives of delivery time and operation cost through fuzzy mathematical programming, construct a membership function to normalize multiple objectives, and reduce the complexity of solution; Step S3: Use the particle swarm algorithm to solve the optimization problem after the transformed target simplification, determine the optimal number and location of distribution centers, and output the final configuration plan.

2. The method for selecting a drone distribution center site based on fuzzy mathematical programming and particle swarm algorithm according to claim 1 is characterized by: The modeling of the multi-UAV delivery scenario in the park considers the following key factors: the geographical location of customers in the park, the technical parameters of the UAVs, the distribution of no-fly zones, and the location areas of potential distribution centers.

3. The method for selecting a drone distribution center site based on fuzzy mathematical programming and particle swarm algorithm according to claim 2 is characterized by: The two objectives of delivery time and operation cost conflict with each other. After characterizing the objective function, fuzzy mathematical programming is used to simplify the objective and transform the original complex problem into a simple new problem for solution.

4. The method for selecting a drone distribution center site based on fuzzy mathematical programming and particle swarm algorithm according to claim 3 is characterized by: Each particle of the particle swarm algorithm represents a potential position selection scheme. The position and velocity of the particle represent a solution in the solution space and the search step of the solution respectively. The position and velocity of each particle are updated according to its historical optimal position and the global optimal position. Through the ε-constraint method, ε increases between 0 and 1, and a finite number of Pareto solutions are obtained, among which the optimal solution is selected.

5. The method for selecting a UAV distribution center site based on fuzzy mathematical programming and particle swarm algorithm according to claim 4 is characterized by: The park selected for drone delivery meets the following conditions: The logistics distribution environment with limited geographical scope and full-area and all-weather unmanned demand occurs in closed or semi-closed areas of several square kilometers, specifically industrial parks, university campuses, and commercial complexes; the number of distribution demand nodes is controlled at 50-100, the distribution demand is stable in time, with small dynamic changes, the number of drones involved in the distribution is 5-10, and they are managed through distributed scheduling. The spatial constraints in small-scale scenarios are significant, including no-fly zones, flight path restrictions, and drone endurance and load constraints.

6. The method for selecting a drone distribution center site based on fuzzy mathematical programming and particle swarm algorithm according to claim 5 is characterized by: The specific modeling and complex constraint methods are as follows: First, the distribution demand point is located in the park. The location of each customer is represented by a two-dimensional coordinate. The geographical location of customer i is P i (x i ,y i ), where i = 1, 2, ..., N represents the customer number, there are N customers in total, and the geographical locations of all customers are represented by a set of coordinate points {P1(x1, y1), P2(x2, y2), ..., P N (x N ,y N )}, the maximum load of each drone is W max , represents the maximum cargo weight that the drone can carry, and the maximum flight distance of each drone is D max , which is calculated based on the battery life and flight efficiency of the drone and the comprehensive load. The flight speed of the drone is V. Assuming the flight speed is within the fixed value V, the unit is the distance flown per second. The maximum flight time of each drone is T max ,This time limits the flight duration of the drone. It will not be able to fly beyond this time. The drone departs from one distribution center and goes to another distribution center for charging or loading after completing the delivery; In the delivery scenario, there are no-fly zones, which drones cannot cross. The modeling of no-fly zones is as follows: First, there are F no-fly zones, each of which is represented by a circular area with the center coordinates (x j ,y j ), with a radius of r j , that is, the mathematical model of the no-fly zone is a circular area: C j (x j ,y j ,r j ) where j = 1, 2, ..., F represents the number of the no-fly zone. In the delivery task, the potential delivery center is located in the preset candidate location area. Assume that there are M candidate delivery center locations, represented by C k (x k ,y k ), where: k = 1, 2, ..., M represents the number of the distribution center, and there are M distribution center candidate locations in total.

7. The method for selecting a drone distribution center site based on fuzzy mathematical programming and particle swarm algorithm according to claim 3 is characterized by: The delivery time considered is T total , operating costs C total The two objectives are expressed as: Where: T flight (C k ,P i ) is the distribution center C k To Customer P i The flight time, x ki is a binary variable, indicating that the distribution center C k Responsible for delivery to customer P i , if distribution center C k Responsible for Customer P i For delivery, then x ki =1, otherwise x ki =0,d(C k ,P i ) is the distribution center C k To Customer P i The Euclidean distance, V is the flight speed of the drone; Where: C center (C k ) is to establish distribution center C k The required fixed construction cost, assumed to be constant, C flight (C k ,P i ) is the drone from the distribution center C k To Customer P i The flight cost is usually estimated based on the flight distance and flight time; C flight (C k ,P i )=α·d(C k ,P i ), where α is the flight cost per unit distance, C battery (C k ,P i ) is the cost of charging the drone battery, which is usually determined by the flight time and the battery charging cost; C battery (C k ,P i )=β·T flight (C k ,P i ), where β is the battery charging cost per unit flight time; set up and are the optimal values ​​of delivery time and operating cost respectively, and the normalized target T norm and C norm It can be expressed as: in: and are the lower limits of delivery time and operating cost, respectively, and are the predetermined minimum values. and are the upper limits of delivery time and operating cost, respectively, which are usually the maximum values ​​in the worst case. For the delivery time target T norm and operating cost target C norm , respectively construct the membership function μ T (T norm ) and μ C (C norm ): μ T (T norm ) and μ C (C norm ) represent the membership of the delivery time target and the operating cost target respectively. The delivery time target T processed by the membership function norm As the main optimization target, the operating cost target C processed by the membership function norm After adding constraints and fuzzy mathematical programming, the problem can be expressed as:

8. The method for selecting a drone distribution center site based on fuzzy mathematical programming and particle swarm algorithm according to claim 4 is characterized by: The particle updates its position and velocity using the following formula: in: is the velocity of particle i at time t; is the position of particle i at time t; is the historical optimal position of particle i; g (best) is the global optimal position; w is the inertia weight, which controls the exploration ability of the particle; c 1 ,c 2 are individual and social learning factors, respectively, controlling the dependence of particles on individual and group experience; r1, r2 are random numbers in the range of [0,1]; in is the new position of particle i at time t+1; In order to evaluate the quality of particles, the fitness objective function is defined, and the fitness is calculated according to the particle position update, and the fitness function is: f(x)=μ T (T norm ); For the new problem obtained by transformation, ε increases in a certain step size between 0 and 1. A Pareto solution is obtained each time it is increased, and finally a finite number of Pareto solutions are obtained. f(x) is calculated for each solution obtained, and the one with the largest value is taken as the final site selection plan.

9. The method for selecting a drone distribution center site based on fuzzy mathematical programming and particle swarm algorithm according to claim 8 is characterized by: The formula f(x) = μ T (T norm ) The two objectives of delivery time and operation cost are transformed through fuzzy mathematical programming, so that the optimization process can focus on the time objective while ensuring that the cost objective is also effectively optimized. First, the delivery time and operation cost are normalized to obtain the normalized time objective T norm and cost target C norm ; And the normalized time target T norm represents the optimal delivery time expected under given constraints. The membership function is evaluated by μ T Whether this time goal meets the set optimization criteria, providing a value to measure the degree of goal achievement; Formula f(x) = μ T (T norm ) represents the function value of the degree of achievement of the time target at a specific moment, and this value will be used as the fitness function in the particle swarm algorithm.

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