A Multi-Objective Optimization Based on Particle Swarm Algorithm for Ensuring Equipment Reservation Algorithm

Abstract

The present invention provides a multi-objective optimization-based equipment reservation algorithm for support based on the particle swarm algorithm, which includes the following steps: S1, establishing a mathematical model algorithm; S2, quantifying the preset indicators by means of hierarchical weighting; S3, arranging the preset points of support equipment and allocating the preset quantities, and simplifying them by using graph algorithms to make the preset storage localized or approximately localized; S4, dividing the simplified local vertex clusters, which are some independent regions, and the algorithm uses the particle swarm algorithm in each independent region for multi-objective optimization. The present invention can improve the rapid response ability of maintenance support services. When necessary, for optimizing the execution efficiency of the algorithm and moderately considering the influence of climate factors, the number of support equipment required for each preset location can be generated according to the shortest response time.

Description

Technical Field

[0001] The present invention relates to the technical field of aviation maintenance equipment support, and particularly relates to a multi-objective optimization support equipment reservation algorithm based on a particle swarm algorithm. Background Art

[0002] To improve the response speed of support services, first consider laying out support resource sites according to the optimization of the transportation network. It is necessary to construct a multi-objective optimization layout model of support resource sites that better meets regulatory requirements and actual needs starting from the resource arrival time, site construction cost, and functional positioning of the line.

[0003] Existing models mainly focus on discussing related issues using traditional optimization techniques:

[0004] The advantages and disadvantages of the P-center model, P-median model, set covering model, and maximum covering model in layout;

[0005] Starting from multiple perspectives such as response time, shortest distance, and minimum cost, multi-objective optimization is used to layout support sites;

[0006] After discretizing time, a dynamic programming model of time series is established, considering the multiple allocations of support facilities;

[0007] On the basis of having multiple fault points and known demands, consider the location problem suitable for large-scale emergencies;

[0008] With the goal of maximizing the covered support equipment, perform multi-objective linear programming of support resources;

[0009] Use a genetic algorithm with stochastic simulation to solve the layout model of support sites in the transportation network, and then obtain the optimal site allocation.

[0010] Whether in terms of computing performance or feasibility, the above-mentioned various models have an appropriate gap from the current required pre-set model of aviation maintenance equipment, and new methods need to be explored to construct an optimized pre-set plan for aviation maintenance equipment as quickly as possible. Summary of the Invention

[0011] In view of this, the present invention provides a multi-objective optimization support equipment reservation algorithm based on a particle swarm algorithm to solve the above problems.

[0012] To solve the above technical problems, the present invention provides a multi-objective optimization support equipment reservation algorithm based on a particle swarm algorithm, including the following steps:

[0013] S1. Establish a mathematical model algorithm;

[0014] S2. Quantify the preset indicators by means of hierarchical weighting;

[0015] S3. Ensure the arrangement of equipment preset points and the allocation of preset quantities, and simplify them using graph algorithms to localize or approximately localize the preset storage.

[0016] S4. Divide each simplified local vertex cluster, which are independent regions, and the algorithm uses the particle swarm algorithm to perform multi-objective optimization in each independent region.

[0017] Furthermore, the mathematical model algorithm is as follows:

[0018] Let the input planned task J involve m airports, and the set of airports is A = {a 1 , a 2 , …, a m}, where the number of aircraft types P = {p k , p 1 , …, p 2 , …, p t} that need to be guaranteed at airport a p are N 1 = {n 2 , n t} respectively;

[0019] When the strategic task level of the plan is G x , according to the quota standard for guaranteeing preset equipment, the quantity of equipment types T = {T k , T 1 , …, T 2 , …, T y} that need to be guaranteed at airport a k1 can be calculated as {n k2 , n ky}, and the total space capacity occupied by each type of equipment is C k = {c k1 , c k2 , …, c ky};

[0020] Let the set of all preset points be S = {s 1 , s 2 , …, s r}, the space available for storing guarantee preset equipment at each preset point is V = {v 1 , v 2 , …, v r} cubic meters, the direct path distance between preset point i and airport j is d ij kilometers, the maximum average unit transport capacity of this direct path is f ij cubic meters per hour, the maximum volume that can be accommodated in a single transport is B cubic meters, and the maximum weight that can be transported in a single time is W kilograms;

[0021] When the safeguard task occurs, the time consumption for transporting the preset point i to the airport j is t ij , and the total time limit standard for transporting all maintenance equipment is not more than R hours;

[0022] Let the total number of the safeguard equipment type u at the preset point i be x iu pieces, and the set of storage quantities at each preset point X = {x 1u , x 2u , …, x ru}; after the future safeguard task occurs, the quantity to be sent to the airport j is n ju pieces, and the space occupied by each piece of this equipment is c u , and the weights are w u kilograms;

[0023] For the preset point i, on the premise of not delaying the equipment scheduling, the allowable shortest total response time is

[0024] The objective function is:

[0025] The main constraint conditions to be satisfied are:

[0026] Storage capacity limit:

[0027] Transport capacity limit:

[0028] Transport equipment space limit: c u ≤ B, w u ≤ W;

[0029] When considering more other optimization objectives, the dimension of the objective function will correspondingly increase and become:

[0030] min[F(X)] = [f 1 (x), f 2 (x),..., f n (x)] T , where n is the number of optimization objectives.

[0031] Furthermore, in step S2, the preset indicators are classified into high-level, medium-level, and low-level. During the process of the algorithm, the requirements of high-level indicators are preferentially satisfied, and the low-level indicators are selected or discarded.

[0032] Furthermore, to ensure that the indicators at all levels are processed in order of high and low levels quickly, three fixed weights are assigned to the three types of indicators; when there are multiple indicators at the same level, the average value of each indicator at the same level is used for normalization for the final processing order.

[0033] Furthermore, for the weights assigned to high-level, mid-level, and low-level indicators, with the low-level indicator as the unit 1, the mid-level indicator is at least greater than 10, and the high-level indicator is at least greater than 50.

[0034] Furthermore, the direct associated factors of the preset indicators are the preset location, the type of preset equipment, and the quantity of preset equipment.

[0035] Furthermore, to make full use of the grading of evaluation indicators to optimize the operation of the algorithm, after the data is preprocessed and simplified by the graph algorithm and before the particle swarm algorithm is fully implemented, first sort each indicator in descending order of priority. After successively meeting the preset requirements of the highest-level indicators, the scale of the data to be processed in the problem will be greatly reduced. At this time, on the data with the reduced scale, perform the optimization calculation of ordinary indicators.

[0036] Furthermore, use the graph algorithm to simplify the implementation of the algorithm for this problem. The starting point of the algorithm simplification is based on removing bottlenecks, localizing or approximately localizing the preset storage;

[0037] The process is as follows:

[0038] According to the minimum transportation time of the minimum guarantee equipment from point to point, cancel the connections between some vertices;

[0039] Find the articulation points among the feasible preset points. If there is a path between the articulation points, directly cut it off;

[0040] Remove all the articulation points in the graph, and find the largest connected nodes in each subgraph obtained by segmentation;

[0041] Taking all the largest connected nodes in each subgraph as the center, calculate the maximum flow between the largest connected nodes. If the flow of a certain path between the nodes is less than the preset value, continue to cut off this path;

[0042] Repeat the previous step until it can no longer continue.

[0043] Furthermore, when using the particle swarm optimization algorithm to solve the multi-objective optimization preset model of the site, it is necessary to encode the particles, and the information carried by the particles is the solution of the multi-objective optimization preset model. In the multi-objective optimization preset problem of the site, it is necessary to solve the values of each point in the set of site selection points of the guarantee resource site, so as to determine the quantity and location of the guarantee resource site;

[0044] Suppose the position of the i-th particle in the n-dimensional space is S i =(s i1 , s i2 , …, s in ), where i = 1, 2, …, m is the number of particles in the particle swarm, and its best position traveled, that is, the most adaptable value, is S pi =(sp i1 , sp i2 , …, spin ), and the corresponding individual optimal value is denoted as P i ;

[0045] The best position of all particles in the population is denoted as S g =(s g1 , s g2 , …, s gn ), and the corresponding global optimal value is denoted as P g ;

[0046] The velocity of the particle is denoted as V i =(v i1 , v i2 , …, v in );

[0047] At the (t + 1)-th iteration, the velocity of the d-th particle is:

[0048]

[0049] And its position is:

[0050]

[0051] In the formula:

[0052] c 1 and c 2 are learning factors, and c1 = c2 ∈ [1, 2.5];

[0053] r 1 and r 2 are random numbers uniformly distributed in [0, 1];

[0054] γ is the inertia weight, and its value determines how much of the current velocity the particle inherits. Adjusting its size can improve the global and local optimization capabilities of the particle swarm algorithm;

[0055] A large inertia weight is beneficial for global search, while a small inertia weight is beneficial for local search. The calculation formula is as follows:

[0056]

[0057] In the formula:

[0058] γ 0 and γ end are the initial inertia weight and the termination inertia weight respectively;

[0059] t is the current iteration number, and t max is the maximum iteration number.

[0060] Furthermore, the model solving steps based on the particle swarm algorithm are specifically as follows:

[0061] 1. Set the total particle swarm size m, learning factors c 1 and c 2 , the maximum number of evolutionary iterations t max and other calculation parameters;

[0062] 2. Randomly generate the positions s and velocities v of the initial population particles;

[0063] 3. Convert the encoding and determine whether the particles meet the constraints of the optimal pre - setting model for the resource - guarantee sites. For particles that do not meet the constraints, re - initialize them and then calculate the fitness values of the particles;

[0064] 4. After t + 1 iterations, if the current fitness value P i t+1 of the particle is better than the previous fitness value P i t , then the current value is the individual optimal value of the particle, and the position s i t+1 of the current particle is the best position Spi; thus, obtain the individual optimal values of the particles, record the serial numbers and positions P i of the particles with the optimal values;

[0065] 5. Iteratively optimize the velocities and positions of the initialized particles under the constraint conditions. During the iteration, if there is a particle variable in the particle velocity variable greater than the maximum particle velocity υ max , then set If there is a particle variable in the particle velocity variable less than the minimum particle velocity υ min , then set

[0066] 6. Repeat step 4 to search for the positions Pi of other particles under the best fitness value of this particle; then substitute them into the iterative formula, and repeat steps 4, 5, and 6; if the global optimal fitness value of the population particles after iteration is less than the global optimal fitness value after the previous iteration, then update the global optimal fitness value to the minimum fitness value of this time, otherwise do not update; the local optimal update methods and steps of each particle are the same;

[0067] 7. When the iteration result converges and the number of iterations reaches the pre - set maximum number of iterations, stop the iteration, thereby obtaining the optimal pre - setting scheme for the resource - guarantee sites.

[0068] Furthermore, for the evaluation of multi - objective optimization, assume there are n evaluation indicators. For the evaluation of the existing pre - setting scheme, after step 3 is completed, directly enter the output evaluation conclusion link:

[0069] 1. Ignore other objectives and calculate the optimal value OPT of each evaluation indicator separately i;

[0070] 2. Calculate the values VAL of each objective in the optimization plan respectively i ;

[0071] 3. Calculate the relative percentage P of each individual evaluation objective respectively i ;

[0072] 4. Calculate the model score P M ;

[0073] Among them, the normalized score calculation of a single index is as follows:

[0074]

[0075] The model score then aggregates each single index and assigns weights:

[0076]

[0077] Where the w i is the weight assigned to the single score, When the weights of each index are equal, the model score degenerates into the average of the index scores.

[0078] The beneficial effects of the above technical solutions of the present invention are as follows:

[0079] According to the configuration requirements of the maintenance support equipment in the maintenance support plan of the present invention, based on a variety of preset optimization objectives, the maintenance support equipment that is suitable for preset storage is generated under the premise of maximizing the avoidance of delays caused by the temporary lack of support equipment due to unexpected situations. (1) A relatively appropriate plan for each preset location, and (2) A relatively reasonable plan for the type and quantity of detailed equipment to be preset at each preset location, which can improve the rapid response ability of the maintenance support service. When necessary, for the execution efficiency of the optimization algorithm, and moderately considering the influence of climate factors, the quantity of support equipment required for each preset location can be generated according to the shortest (or nearly shortest) response time. Specific implementation manner

[0080] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the described embodiments of the present invention belong to the scope of protection of the present invention.

[0081] Embodiment 1

[0082] This embodiment provides a multi-objective optimization reserve algorithm for support equipment based on the particle swarm algorithm, including the following steps:

[0083] S1. Establish a mathematical model algorithm;

[0084] S2. Quantify the preset indicators by hierarchical weighting;

[0085] S3. Ensure the arrangement of equipment preset points and the distribution of preset quantities, and simplify them using graph algorithms to localize or approximately localize the preset storage;

[0086] S4. Divide the simplified local vertex clusters, which are independent regions, and apply the particle swarm algorithm in each independent region for multi-objective optimization.

[0087] Furthermore, the mathematical model algorithm is as follows:

[0088] Let the input planned task J involve m airports, and the airport set be A = {a 1 , a 2 , …, a m}, where the number of aircraft types P = {p k , p 1 , …, p 2 , …, p t} that need to be guaranteed at airport a p are N 1 = {n 2 , n t} respectively;

[0089] When the strategic task level of the plan is G x , according to the quota standard of guaranteed preset equipment, the number of equipment types T = {T k , T 1 , …, T 2 , …, T y} that need to be guaranteed at airport a k1 can be calculated as {n k2 , n ky , … n k = {c k1 , c k2 , …, c ky} respectively, and the total space capacity occupied by each type of equipment is C

[0090] Let the set of all preset points be S = {s 1 , s 2 , …, s r}, and the space available at each preset point for storing guaranteed preset equipment is V = {v 1 , v 2 , …, v r} cubic meters. The direct path distance from preset point i to airport j is d ij kilometers, and the maximum average unit transportation capacity of this direct path is fij m³ / h, the maximum volume that can be accommodated in a single shipment is B m³, and the maximum weight that can be transported in a single shipment is W kg;

[0091] When a support mission occurs, the time consumption for transporting from pre-positioning point i to airport j is t ij , and the total time limit standard for transporting all maintenance equipment is not more than R hours;

[0092] Let the total number of support equipment types u pre-positioned at pre-positioning point i be x iu pieces, and the set of storage quantities at each pre-positioning point X = {x 1u , x 2u , …, x ru}, and the quantity to be sent to airport j after a future support mission occurs is n ju pieces, and the space occupied by each piece of this equipment is c u , and the weights are w u kg;

[0093] For pre-positioning point i, the shortest total response time allowed without delaying equipment scheduling is

[0094] The objective function is:

[0095] The main constraint conditions to be satisfied are:

[0096] Storage capacity limit:

[0097] Transport capacity limit:

[0098] Transport equipment space limit: c u ≤ B, w u ≤ W;

[0099] When considering more other optimization objectives, the dimension of the objective function will also increase accordingly and become:

[0100] min[F(X)] = [f 1 (x), f 2 (x),..., f n (x)] T , where n is the number of optimization objectives.

[0101] Regarding the individual time optimization objective, obviously, the smaller the total transportation time, the better. If all the preset points are near the mission airport and there is no upper limit to the space for storing support equipment at the preset points, it can be directly concluded that on-site preset is the best. Although this conclusion may not be feasible in reality and is also an important constraint for the optimization objective, this idea can provide some inspiration for the optimization implementation of the algorithm: try to localize each preset requirement and divide it into multiple independent small areas for separate processing.

[0102] To reduce the response time of the preset system, the following simplified processing can be carried out:

[0103] When the single transportation time between a certain preset point and the airport to be transported exceeds a certain preset time limit, directly disconnect the connection between these two points.

[0104] Obviously, except for extreme situations such as resource exhaustion during war, the general situation will not lead to incorrect algorithm conclusions.

[0105] Furthermore, in step S2, the preset indicators are classified into high-level, medium-level, and low-level. During the process of the algorithm, the requirements of high-level indicators are given priority, and the low-level indicators are selected or discarded.

[0106] Furthermore, to ensure that the indicators at all levels are processed in order of high and low levels quickly, three fixed weights are assigned to the three indicators; when there are multiple indicators at the same level, the average value of each indicator at the same level is used for normalization for the final processing order.

[0107] Furthermore, the weights assigned to high-level, medium-level, and low-level indicators are calculated with the low-level indicator as the unit 1. The medium-level indicator is at least greater than 10, and the high-level indicator is at least greater than 50.

[0108] Furthermore, the direct associated factors of the preset indicators are the preset location, the type of preset equipment, and the quantity of preset equipment.

[0109] Furthermore, to make full use of the classification of evaluation indicators to optimize the operation of the algorithm, after the data is preprocessed and simplified by the graph algorithm and before the particle swarm algorithm is fully implemented, the indicators are sorted in descending order of priority. After the preset requirements of the highest-level indicators are sequentially met, the scale of the data to be processed in the problem will be greatly reduced. At this time, on the data with the reduced scale, the optimization calculation of ordinary indicators is carried out.

[0110] Furthermore, use the graph algorithm to simplify the implementation of the algorithm for this problem. The starting point of the algorithm simplification is based on removing bottlenecks, localizing or approximately localizing the preset storage; therefore, it is carried out from aspects such as articulation points, minimum cost maximum flow of the network, and hub points.

[0111] 1. Articulation points

[0112] Articulation points are also known as cut points. Removing an articulation point from a graph will disconnect the graph, and the material transportation through an articulation point will cause congestion. If there is a path between two articulation points, this path is generally called a bridge.

[0113] 2. Maximum flow in a network

[0114] The maximum flow in a network is the maximum feasible flow from the source node to the sink node. By calculating the cut capacity of a subgraph, the maximum feasible material transportation volume between regions on the graph can be determined.

[0115] 3. Hub points

[0116] Just like the central cities in life, to reduce the total cost of material transportation, except for some super-large and overweight equipment that is directly pre-positioned at the using airport due to transportation difficulties, it is considered to concentrate the pre-positioned equipment as much as possible in the central city or the surrounding areas within the close radiation of the central city, which can ensure timely response when needed.

[0117] The process is as follows:

[0118] Cancel the connections between some vertices according to the minimum guaranteed equipment transportation time from point to point;

[0119] Find articulation points among the feasible pre-positioning points. If there is a path between the articulation points, cut it directly;

[0120] Remove all articulation points from the graph and find the largest connected nodes in each of the divided subgraphs;

[0121] Taking all the largest connected nodes in each subgraph as the center, calculate the maximum flow between the largest connected nodes. If the flow of a certain path between the nodes is less than the preset value, continue to cut this path;

[0122] Repeat the previous step until it can no longer continue.

[0123] Furthermore, when using the particle swarm optimization algorithm to solve the multi-objective optimization pre-positioning model of stations, it is necessary to encode the particles, and the information carried by the particles is the solution of the multi-objective optimization pre-positioning model. In the multi-objective optimization pre-positioning problem of stations, it is necessary to solve the values of each point in the set of site selection points of the guarantee resource stations, so as to determine the number and location of the guarantee resource stations;

[0124] Suppose the position of the i-th particle in the n-dimensional space is S i =(s i1 , s i2 , …, s in ), where i = 1, 2, …, m is the number of particles in the particle swarm. The best position it has traveled, that is, the most adaptable value, is S pi =(sp i1 , sp i2 , …, sp in ), and the corresponding individual optimal value is denoted as Pi ;

[0125] The best position of all particles in the population is denoted as S g =(s g1 , s g2 , …, s gn ), and the corresponding global optimal value is denoted as P g ;

[0126] The velocity of the particle is denoted as V i =(v i1 , v i2 , …, v in );

[0127] At the (t + 1)-th iteration, the velocity of the d-th particle is:

[0128]

[0129] And its position is:

[0130]

[0131] In the formula:

[0132] c 1 and c 2 are learning factors, and c1 = c2 ∈ [1, 2.5];

[0133] r 1 and r 2 are random numbers uniformly distributed in [0, 1];

[0134] γ is the inertia weight, and its value determines how much of the current velocity the particle inherits. Adjusting its size can improve the global and local optimization capabilities of the particle swarm algorithm;

[0135] A large inertia weight is beneficial for global search, while a small inertia weight is beneficial for local search. The calculation formula is as follows:

[0136]

[0137] In the formula:

[0138] γ 0 and γ end are the initial inertia weight and the termination inertia weight, respectively;

[0139] t is the current iteration number, and t max is the maximum iteration number.

[0140] Furthermore, the model solving steps based on the particle swarm algorithm are specifically as follows:

[0141] 1. Set the total number of particles m, learning factors c 1 and c 2 in the particle swarm algorithm, the maximum number of evolutionary iterations t max and other calculation parameters;

[0142] 2. Randomly generate the positions s and velocities v of the particles in the initial population;

[0143] 3. Convert the encoding and determine whether the particles meet the constraints of the optimal preset model for the resource guarantee site. For particles that do not meet the constraints, after re-initialization, calculate the fitness value of the particles;

[0144] 4. After t + 1 iterations, if the current fitness value P i t+1 of the particle is better than the previous fitness value P i t , then the current value is the individual optimal value of the particle, and the position of the current particle is the best position Spi; thus, obtain the individual optimal value of the particle, record the particle number and position P i of the optimal value;

[0145] 5. Iteratively optimize the velocities and positions of the initialized particles under the constraint conditions. During the iteration process, if there is a particle variable in the particle velocity variable that is greater than the maximum particle velocity υ max , then set If there is a particle variable in the particle velocity variable that is less than the minimum particle velocity υ min , then set

[0146] 6. Repeat step 4 to search for the positions Pi of other particles under the best fitness value of the particle; then substitute it into the iterative formula, and repeat steps 4, 5, and 6; if the global optimal fitness value of the population particles after iteration is less than the global optimal fitness value after the previous iteration, then update the global optimal fitness value to the minimum fitness value of this time, otherwise do not update; the local optimal update methods and steps of each particle are the same;

[0147] 7. When the iteration result converges and the number of iterations reaches the preset maximum number of iterations, the iteration stops, thereby obtaining the optimal preset scheme for the guaranteed resource sites. Compared with the single-objective optimization problem, where the superiority or inferiority of any two feasible solutions is directly determined by comparing the values of the objective function, the biggest difference in the multi-objective optimization problem is that the objective function is a multi-dimensional vector. In principle, it is necessary to determine the superiority or inferiority by comparing the magnitudes of the components of the vector, or to compare the modulus in the multi-dimensional space by discarding the characteristics of the components as in mathematics. However, due to the multi-dimensionality of the objective function in the multi-objective optimization problem, even the simplest dimensional units of each optimization objective are generally not consistent. Therefore, these theoretical methods are difficult to implement in actual use, and it is also difficult to balance all optimization objectives. It is not convenient to directly compare the superiority or inferiority of each feasible solution, or even the local optimal solution.

[0148] The solution that theoretically makes each objective of the multi-objective optimization problem optimal is generally called the absolute optimal solution, but it often does not exist in practical problems. There are more or less contradictions among multiple objectives. Commonly, the better of one objective may lead to the worse of another objective, and there may even be contradictions and oppositions between optimization objectives. For example, the pursuit of the shortest response time generally leads to a relatively large and redundant local preset storage capacity, etc. Finally, the evaluation of the multi-objective optimization problem is balanced.

[0149] The present invention evaluates the multi-objective optimization. Suppose there are n evaluation indicators. For the evaluation of the existing preset scheme, after step 3 is completed, it directly enters the link of outputting the evaluation conclusion:

[0150] 1. Ignore other objectives and calculate the optimal value OPT of each evaluation indicator separately i ;

[0151] 2. Calculate the values VAL of each objective in the optimization scheme separately i ;

[0152] 3. Calculate the relative percentage P of each individual evaluation objective separately i ;

[0153] 4. Calculate the model score P M ;

[0154] Among them, the normalized score calculation of a single indicator is as follows:

[0155]

[0156] The model score then aggregates each single indicator and assigns weights:

[0157]

[0158] Among them, w i is the weight assigned to the single score, When the weights of all indicators are equal, the model score degenerates into the average of the indicator scores.

[0159] The above are the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A multi-objective optimization based on particle swarm algorithm for guaranteeing equipment reservation algorithm, Characterized in that: It includes the following steps: S1. Establish a mathematical model algorithm; S2. Quantify the preset indicators by hierarchical weighting; S3. Arrange the preset points of guarantee equipment and allocate the preset quantity, and use graph algorithm to simplify it, so that the preset storage is localized or approximately localized; S4. Divide the simplified local vertex clusters, which are some independent regions, and the algorithm uses particle swarm algorithm to perform multi-objective optimization in each independent region; The mathematical model algorithm is as follows: Suppose the input scheduled task J involves m airports, and the set of airports is A = {a 1 , a 2 , …, a m}, where for airport a k , the quantities of each type of aircraft P = {p 1 , p 2 , …, p t} to be guaranteed are respectively N p = {n 1 , n 2 , …, n t}; When the strategic mission level of the plan is G x When the airport a is calculated according to the quota standard for pre-placed equipment k Equipment type to be protected T = {T 1 ,T 2 ,…,T y The number of} is {n k1 ,n k2 ,…n ky }, the total space occupied by various devices is C k ={c k1 ,c k2 ,…,c ky }; Let the set of all preset points be \(S = \{s 1 , s 2 , \cdots, s r \}\), and the spaces that each preset point can be used to store the guarantee preset equipment are \(V=\{v 1 , v 2 , \cdots, v r \}\) cubic meters. The direct path distance from preset point \(i\) to airport \(j\) is \(d ij \) kilometers, and the maximum average unit transportation capacity of this direct path is \(f ij \) cubic meters per hour. The maximum volume that can be accommodated in a single delivery is \(B\) cubic meters, and the maximum weight that can be transported in a single delivery is \(W\) kilograms; When the safeguard task occurs, the time consumption for transporting the preset point i to the airport j is t ij , and the total time limit standard for transporting all maintenance equipment is not more than R hours; Let the total number of pre-set points for pre-setting support equipment type u be x iu pieces, and the set of storage quantities at each pre-set point is X = {x 1u , x 2u , …, x ru}. After a future support mission occurs, the quantity to be sent to airport j is n ju pieces. The space occupied by each piece of this equipment is c u , and the weights are w u kilograms; For preset point i, the shortest total response time allowed without delaying equipment scheduling is, and the objective function is: The main constraints to be satisfied are: Storage capacity limit: Transportation capacity limit: Space limitation of transportation equipment: c u ≤B,w u ≤W; When considering more other optimization objectives, the dimension of the objective function will also increase accordingly, becoming: min[F(X)] = [f 1 (x), f 2 (x),..., f n (x)] T , where n is the number of optimization objectives; Use graph algorithm to simplify the implementation of this problem algorithm. The starting point of algorithm simplification is based on removing bottlenecks, and the preset storage is localized or approximately localized; The process is as follows: According to the minimum transportation time of guarantee equipment from point to point, cancel the connection between some vertices; Find articulation points among the feasible preset points. If there is a path between the articulation points, cut it directly; Remove all articulation points in the graph, and find the largest connected nodes in each subgraph segmented; Taking all the largest connected nodes of each subgraph as the center, calculate the maximum flow between the largest connected nodes. If the flow of a certain path between the nodes is less than the preset value, continue to cut this path; Repeat the previous step until it can no longer continue.

2. The multi-objective optimization based on particle swarm algorithm for guaranteeing equipment reservation algorithm according to claim 1, Characterized in that: In step S2, the preset indicators are classified into high level, middle level and low level. During the process of the algorithm, the requirements of high-level indicators are preferentially satisfied, and the low-level indicators are selected or discarded.

3. The multi-objective optimization based on particle swarm algorithm for guaranteeing equipment reservation algorithm according to claim 2, Characterized in that: In order to ensure that the indicators at all levels are processed in order of high and low levels quickly, three fixed weights are assigned to the three indicators; when there are multiple indicators at the same level, the average value of each indicator at the same level is used for normalization for the final processing order.

4. The multi-objective optimization based on particle swarm algorithm for guaranteeing equipment reservation algorithm according to claim 3, Characterized in that: The weights assigned to high-level, middle-level and low-level indicators are calculated with the low-level indicator as the unit 1. The middle-level indicator is at least greater than 10, and the high-level indicator is at least greater than 50.

5. The multi-objective optimization based on particle swarm algorithm for guaranteeing equipment reservation algorithm according to claim 4, Characterized in that: The direct associated factors of the preset indicators are the preset location, the type of preset equipment and the quantity of preset equipment.

6. The multi-objective optimization based on particle swarm algorithm for guaranteeing equipment reservation algorithm according to claim 5, Characterized in that: In order to make full use of the hierarchical evaluation indicators to optimize the operation of the algorithm, after the data is preprocessed and simplified by the graph algorithm and before the particle swarm algorithm is fully implemented, the indicators are sorted in descending order of priority. After the preset requirements of the highest-level indicators are sequentially satisfied, the scale of the data to be processed in the problem will be greatly reduced. At this time, on the data with the reduced scale, the optimization calculation of ordinary indicators is carried out.

7. The multi-objective optimization based on particle swarm algorithm for guaranteeing equipment reservation algorithm according to claim 1, It is characterized in that: When the particle swarm optimization algorithm is used to solve the multi-objective optimization preset model of the site, it is necessary to encode the particles, and the information carried by the particles is the solution of the multi-objective optimization preset model. In the multi-objective optimization preset problem of the site, it is necessary to solve the values of each point in the set of location points of the guarantee resource site, so as to determine the number and location of the guarantee resource site; Suppose the position of the \(i\) -th particle in the \(n\) -dimensional space is \(\mathbf{S}\) i =(s i1 ,s i2 ,…,s in ), \(i = 1,2,\cdots,m\) is the number of particles in the particle swarm, and the best position it has traveled, that is, the most adaptable value is \(\mathbf{S}\) pi =(sp i1 ,sp i2 ,…,sp in ), and the corresponding individual optimal value is denoted as \(\mathbf{P}\) i ; The best position of all particles in the population is denoted as S g =(s g1 , s g2 , …, s gn ), and the corresponding global optimal value is denoted as P g ; The velocity of the particle is denoted as V i =(v i1 , v i2 , …, v in ); At the (t + 1)-th iteration, the velocity of the d-th particle is: Its position is: In the formula: c 1 and c 2 are learning factors, and c1 = c2 ∈ [1, 2.5]; r 1 and r 2 are random numbers uniformly distributed in [0, 1]; γ is the inertia weight, and its value determines how much of the current velocity the particle inherits. Adjusting its size can improve the global and local optimization capabilities of the particle swarm algorithm; A large inertia weight is beneficial to global search, and a small inertia weight is beneficial to local search. The calculation formula is as follows: In the formula: γ 0 and γ end are the initial inertia weight and the terminal inertia weight, respectively; t is the current iteration number, t max is the maximum number of iterations.

8. The multi-objective optimization guarantee equipment reservation algorithm based on the particle swarm algorithm as claimed in claim 7, It is characterized in that: The model solving steps based on the particle swarm algorithm are specifically as follows: (1) Set the total particle swarm size m, learning factors c 1 and c 2 , maximum number of evolutionary iterations t max and other calculation parameters; (2), Randomly generate the positions s and velocities v of the initial population particles; (3), Convert the encoding and determine whether the particles meet the constraints of the multi-objective optimization preset model of the guarantee resource site. For the particles that do not meet the constraints, after re-initialization, calculate the fitness value of the particles; (4) After t+1 iterations, if the current fitness value P of the particle i t+1 is better than the previous fitness value P i t , then the current value is the individual optimal value of the particle, and the position of the current particle is the best position Spi; furthermore, the individual optimal value of the particle is obtained, and the particle number and position P of the optimal value are recorded i ; (5) Iteratively optimize the velocities and positions of the initialized particles under the constraint conditions. During the iterative process, if there is a certain particle variable in the particle velocity variable greater than the maximum particle velocity υ max , then set If there is a certain particle variable in the particle velocity variable less than the minimum particle velocity υ min , then set (6), Repeat step 4 to search for the positions Pi of other particles under the best fitness value of this particle; then substitute them into the iterative formula, and repeat steps (4), (5), and (6); if the global optimal fitness value of the population particles after iteration is less than the global optimal fitness value after the previous iteration, the global optimal fitness value is updated to the minimum fitness value of this time, otherwise it is not updated; the local optimal update methods and steps of each particle are the same; (7), When the iteration result converges and the number of iterations reaches the preset maximum number of iterations, stop the iteration, so as to obtain the best preset scheme of the guarantee resource site.

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