CN109862573B - LTE hybrid networking self-planning method based on multi-target particle swarm - Google Patents

Abstract

The present invention claims to protect a self-planning method for LTE hybrid networking based on multi-target particle swarms. Firstly, the service information of users in the target area is obtained; secondly, combined with the ideal backhaul characteristics of LTE hybrid networking, multiple objective optimization functions are reconstructed; then the user service information is input into the multi-objective optimization function, and the improved discrete multi-objective particle is used. The swarm algorithm is used to optimize the model by selecting the optimal solution from the fuzzy compromise in the Pareto solution set. Finally, the location coordinates of the base station in the LTE hybrid network are obtained. The invention improves the planning efficiency of the LTE hybrid networking.

Description

A self-planning method for LTE hybrid networking based on multi-target particle swarm

technical field

The invention belongs to the technical field of communication LTE hybrid networking, and in particular relates to an LTE hybrid networking self-planning method based on multi-target particle swarms.

Background technique

With the continuous development of mobile communication networks, spectrum resources are becoming more and more scarce, and the independent networking of single-standard base stations is controlled by capacity constraints and cannot meet network requirements. Gradually promote LTE hybrid networking in various regions. LTE hybrid networking is to deploy the existing high-frequency TDD LTE and low-frequency FDD LTE with frequency refarming to a certain area at the same time. The inter-frequency base stations greatly reduce the interference between the same layers through the hybrid networking, and can maximize the Give full play to the advantages of each system, complement each other to make up for deficiencies, reduce investment costs, and provide users with high-quality network services. LTE hybrid networking is attracting more and more attention, and the demand for site selection and self-planning of its hybrid networking base stations is becoming higher and higher.

As an important parameter of base station deployment, base station location planning has a great impact on network coverage and capacity. Nowadays, the complexity of mobile communication networks is getting higher and higher. In many scenarios, multi-standard base stations coexist. It is difficult to find an optimal solution by manual site selection and planning. At the same time, operators are required to reduce costs and improve planning efficiency. The artificial network planning method of measuring information is difficult to adapt to the demand, so the self-planning of communication base station location is particularly important. The existing network self-planning methods often consider incomplete objectives, and the improved algorithm is too complicated and has low practical value, so it cannot be applied to network self-planning under LTE hybrid networking. LTE hybrid network base station self-planning is different from traditional base station network self-planning. Multiple objectives need to be considered at the same time when planning FDD and TDD base stations. At present, it is urgent to develop a LTE hybrid network base station self-planning scheme to provide operators with efficient solutions. Base station deployment plan.

SUMMARY OF THE INVENTION

The present invention aims to solve the above problems of the prior art. A self-planning method for LTE hybrid networking based on multi-objective particle swarms is proposed, which can reduce costs and improve LTE network performance. The technical scheme of the present invention is as follows:

A self-planning method for LTE hybrid networking based on multi-target particle swarm, comprising the following steps:

Step 1: obtain the business information of users in the target area, and obtain the business distribution of the target area;

Step 2: Combined with the ideal backhaul characteristics of the LTE hybrid network, that is, FDD, as a macro base station, mainly provides wide coverage, and TDD, deployed as a small base station, mainly absorbs the characteristics of capacity, and reconstructs the maximum coverage rate, maximum network energy efficiency ratio, and maximum network energy efficiency ratio. Objective optimization function including network load and minimum cost;

Step 3: Using the discrete multi-objective particle swarm algorithm that improves the crowding distance sorting in the Pareto solution set, the optimal solution is selected from the fuzzy compromise in the Pareto solution set to optimize the model, and finally the base station location coordinates of the LTE hybrid network are obtained.

Further, the step 1: obtaining the service information of users in the target area, and obtaining the service distribution of the target area, which specifically includes:

First, the target network P is gridded into N pixel points. According to the business demand forecast, the N test points are divided into N ₁ normal test points and N ₂ hot-spot test points. Any point on P is It can be calibrated in the grid with Cartesian coordinates, any point is denoted as r _i , and the coordinates are (x _i , y _i ).

Further, the second step is to reconstruct the multi-objective optimization model in combination with the ideal backhaul characteristics of the LTE hybrid network, which specifically includes:

First, a k-layer network is deployed on the M candidate subsets. There are 2-layer networks in total, namely the TDD network and the FDD network. k equals 2 to represent the total number of network layers. Each base station has two choices, a _km represents The deployment situation of the base station at the m position of the k-th layer, "1" indicates that the k-layer base station is built at the m position, "0" means that the k-layer base station is not built at the m position, and K×M indicates the size of the location matrix space. Base station address matrix:

Based on the dual-connection feature of LTE hybrid networking, that is, the test point can be connected to TDD and FDD base stations at the same time, and only considering whether the service rate of the test point is satisfied, the base station access indicator function and signal-to-noise ratio are obtained:

和R_k,n,m＝B_k,n×log(1+SINR_k,n,m)

and R _k,n,m =B _k,n ×log(1+SINRk _,n,m )

Among them, Δ _k,n,m represents the situation that the m position of the kth layer covers the test point n, R _k,n,m represents the service rate that the test point n can receive the base station at the m position of the k layer, and the service rate of the hot spot test point The rate is higher than that of ordinary test points. R _min,n indicates the minimum rate that meets the access requirements of test point n. "1" indicates that test point n is covered by position m of layer k. At this time, R _k,n,m ≥R _{min, n} , "0" means that the base station of layer k is not built at the m position, at this time R _k,n,m ≤R _min,n , and B _k,n is the bandwidth of the test point n connected to the base station of layer k;

其中b_nm表示测试点n被m位置基站覆盖情况，m位置上有可能建有TDD基站或 FDD基站，或者未建基站，测试点n被任何一个基站覆盖，则表示测试点n被覆盖；According to the above base station location matrix and the test point access indication function, the final access base station location matrix H of the test point is obtained as:

Among them, b _nm indicates that the test point n is covered by the base station at the m position. There may be a TDD base station or an FDD base station at the m position, or no base station is built. If the test point n is covered by any base station, it means that the test point n is covered;

Finally, the four planning goals of the LTE hybrid network are as follows:

其中N₁表示普通测试点个数，N₂热点测试点个数；1) Maximize coverage

Among them, N ₁ represents the number of common test points, and N ₂ represents the number of hot-spot test points;

其中P_k,m表示为k层m基站的发射功率；2) Maximum network energy efficiency ratio

where P _k,m represents the transmit power of the m base station in the k layer;

其中P_th,m表示为基站 m部署时应达到的负载阻塞门限，用于限制基站接入测试点接入数量。Ψ_k,n,m表示基站m中的负载量占基站需求负载的百分比，实际工程中当此值超过门限P_th,m时，可以用负载限制因素exp(P_th,m-Ψ_k,n,m)来调节降低接入基站m的负载量；3) Maximum network load

Among them, P _th,m represents the load blocking threshold that should be reached when the base station m is deployed, which is used to limit the access quantity of the base station access test point. Ψ _k,n,m represents the percentage of the load in base station m to the demand load of the base station. In actual engineering, when this value exceeds the threshold P _th,m , the load limiting factor exp(P _th,m -Ψ _k,n can be used _{, m} ) to adjust and reduce the load of the access base station m;

其中C_k为第k层基站的成本单价。4) Minimum cost

Wherein C _k is the cost unit price of the base station of the kth layer.

J为自规划目标总数，f_j(i+1)和f_j(i-1)为粒子i的前后粒子的第j个目标值；f_jmax和f_jmin为外部文档中所有粒子的第j个目标函数的最大值和最小值；Further, using the improved discrete multi-objective particle swarm algorithm in the third step, the optimal solution is selected from the fuzzy compromise in the Pareto solution set to optimize the model, and finally the base station location coordinates of the LTE hybrid networking are obtained, including: first, Improved dynamic crowding distance

J is the total number of self-planning targets, f _j (i+1) and f _j (i-1) are the j-th target values of particles before and after particle i; f _jmax and f _jmin are the j-th target values of all particles in the external document the maximum and minimum values of the objective function;

计算粒子i 的标准隶属度函数，其中u_ij表示标准隶属度函数；Calculate the crowding degree between the individual and the adjacent individuals in the external file, and then sort the new crowded distance and remove the solution with the smallest dense distance, and then calculate the dense distance of the remaining Pareto solutions, and repeat the calculation until the number of remaining Pareto solutions is the expected set. The fixed external capacity S; finally according to the formula

Calculate the standard membership function of particle i, where u _ij represents the standard membership function;

In the iterative formula of discrete particle swarm, the iterative formulas of velocity and position are:

和

分别表示粒子i在t+1代的第d维空间的速度和位置；

和

分别是粒子i在t代的个体极值和全局极值；r₁和r₂是一个0与1之间的随机数；c₁与 c₁是学习因子，通常同时取2；ω是惯性权重，本文采用自适应变换的惯性权重，ω表示为：

t为当前迭代的次数，t_max是最大的迭代次数，ω_max和ω_min分别是ω最大和最小的惯性权重，通常取ω_max＝0.9，ω_min＝0.4。

and

respectively represent the velocity and position of particle i in the d-dimensional space of generation t+1;

and

are the individual extremum and the global extremum of particle i in the t generation, respectively; r ₁ and r ₂ are random numbers between 0 and 1; c ₁ and c ₁ are learning factors, usually taking 2 at the same time; ω is the inertia weight , this paper adopts the inertia weight of adaptive transformation, and ω is expressed as:

t is the number of current iterations, t _max is the maximum number of iterations, ω _max and ω _min are the inertia weights of the maximum and minimum ω, respectively, usually ω _max =0.9, ω _min =0.4.

Further, in the third step, the specific calculation steps of the improved discrete multi-objective particle swarm algorithm include:

Step 1. Input data, input the number of candidate base stations, test point information, access rate, function boundary, and dimension;

和0时刻的初始速度

计算每一个粒子的目标函数，粒子的局部最优化位置初始化为

外部档案为空，设置边界最大拥挤距离为d；Step 2. Initialize the particle population: set the population number and the maximum number of iterations, and randomly generate the initial position at time 0 according to the constraint relationship

and the initial velocity at time 0

Calculate the objective function of each particle, and the local optimal position of the particle is initialized as

The external file is empty, and the maximum crowding distance of the boundary is set to d;

一次加入其中并保留支配解，表示为外部档案中的初始解；Step 3. Initialize external files:

Add it once and keep the dominant solution, expressed as the initial solution in the external file;

计算外部档案中所有个体的拥挤度，并采用前面介绍的轮盘赌的方法，从中选择一个个体作为全局最优解

Step 4, the iteration starts, t=1; according to the above formula

Calculate the crowding degree of all individuals in the external file, and use the roulette method introduced earlier to select an individual as the global optimal solution

Step 5. According to the particle swarm iteration formula introduced above, update the position x and velocity v of the particle, and recalculate the fitness of the individual;

Step 6. Update the external file: Add the updated particles to the external file in turn and judge the dominance relationship according to the crowding distance. If the newly added individual dominates the individual in the external file, add the new individual and delete the dominant individual; If the individual does not dominate the individual in the external file, it will not join; if it cannot be compared, then compare the current external capacity S' with the expected external capacity S, if S'≤S, then the new individual will join the external file, and S is incremented by 1, When the solution in the external file is larger than the specified value, use the above circular deletion method to update the non-inferior solution set;

Step 7. Update the P _best of the particle. If the maximum number of iterations is satisfied, stop the search, output the Pareto optimal frontier according to the external elite solution set, and use the above fuzzy decision-making method to find a compromise solution, otherwise t=t+1, go to step 4.

且 P(x₁)+P(x₂)+…+P(x_N)＝1,则累计分布概率为：

具体操作步骤：按照上式计算各个个体的选择概率和累计分布概率，用rand()产生一个[0,1]之间的随机数r，若r≤q₁，则个体x₁被选中。若q_k-1＜r＜q_k(2≤k≤N),则个体x_k被选中。Further, the roulette method in the step 4 specifically includes: the basic idea is: the probability of each individual being selected is proportional to the value of its fitness function, and the group size is set as N, and the fitness of the individual x _i is f( x _i ), then the probability of individual x _i 's choice is:

And P(x ₁ )+P(x ₂ )+…+P(x _N )=1, then the cumulative distribution probability is:

Specific operation steps: Calculate the selection probability and cumulative distribution probability of each individual according to the above formula, and use rand() to generate a random number r between [0,1]. If r≤q ₁ , then the individual x ₁ is selected. If q _k-1 < r < q _k (2≤k≤N), then the individual x _k is selected.

The advantages and beneficial effects of the present invention are as follows:

The present invention proposes an LTE hybrid networking self-planning method, and its innovations include the following points;

1. Establish an LTE hybrid networking optimization model. The invention constructs and reconstructs the LTE hybrid networking hierarchical multi-objective base station planning model with coverage rate, load rate, energy efficiency ratio and cost as optimization objectives. The model comprehensively considers the characteristics of LTE hybrid networking from four aspects. Compared with the previous planning model, only considering the cost and coverage of networking, the present invention has certain advantages for establishing a model.

2. The crowding distance sorting method in the multi-objective granular algorithm is improved. The traditional crowding sorting only uses the geometric distance between particles to sort, which will cause the particles with excellent moderate values to be deleted at the back. The invention improves the particle crowding distance sorting method, adopts the dynamic particle crowding distance sorting, and is beneficial to the excellent particles being selected in the front.

On the whole, the present invention fully considers the characteristics of LTE hybrid networking, establishes a more perfect model, adopts an improved discrete multi-objective particle swarm algorithm, and tries to search for high coverage, low cost, large load and low energy efficiency ratio as much as possible. The combination of base station site selection improves the site selection efficiency and has certain value.

Description of drawings

1 is a schematic flowchart of a self-planning method for LTE hybrid networking based on multi-target particle swarms according to a preferred embodiment of the present invention;

FIG. 2 is an overall frame diagram of a preferred embodiment provided by the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be described clearly and in detail below with reference to the accompanying drawings in the embodiments of the present invention. The described embodiments are only some of the embodiments of the invention.

The technical scheme that the present invention solves the above-mentioned technical problems is:

As shown in Figures 1 and 2: First, forecast the business in the area to obtain the capacity of the hotspot area and the general area. In addition, the obtained area is represented by the central test point of an area square, and the coverage and capacity of the test point are represented by The coverage and capacity of the block in this area; secondly, combined with the ideal backhaul characteristics of the LTE hybrid network, multiple objective optimization functions are reconstructed; then the user service information is input into the multi-objective optimization function, and the improved discrete multi-objective particles are used. The swarm algorithm is used to optimize the model by selecting the optimal solution from the fuzzy compromise in the Pareto solution set. Finally, the location coordinates of the base station in the LTE hybrid network are obtained.

Step 1: Obtain the business information of users in the target area, and obtain the business distribution of the target area:

First, the target network P is gridded into N pixel points. According to the business requirement prediction, the N test points can be further divided into N ₁ normal test points and N ₂ hot area test points. Any point on P can be calibrated in the grid with Cartesian coordinates, any point is denoted as r _i , and the coordinates are (x _i , y _i ).

Step 2: Reconstruct multiple objective optimization functions based on the ideal backhaul characteristics of LTE hybrid networking.

First, deploy a k-layer network on the M candidate subsets, each base station has two choices, and the base station address matrix of the hybrid network is obtained by analysis:

Based on the dual-connection feature of LTE hybrid networking, the test point can be connected to any layer of the network, and there is no need to limit the number and type of base stations that the test point can access. and the signal-to-noise ratio.

和R_k,n,m＝B_k,n×log(1+SINR_k,n,m)

and R _k,n,m =B _k,n ×log(1+SINRk _,n,m )

According to the above base station location matrix and the test point access indication function, the final access base station location matrix H of the test point is obtained as:

Finally, the four finalized goals of the LTE hybrid network are:

1) Maximize coverage

2) Maximum network energy efficiency ratio

3) Maximum network load

4) Minimum cost

Finally, the LTE hybrid networking self-planning model is obtained:

计算个体与外部档案中相邻个体的拥挤程度，然后跟新拥挤距离排序后去除密集距离最小的解，再计算剩余的Pareto解的密集距离，循环计算，直至剩余Pareto解的个数为预期设定的外部容量S。最后根据式子

计算粒子i的标准隶属度函数。求解过程如下：3. Step 3: Using the improved discrete multi-objective particle swarm algorithm, the optimal solution is selected from the fuzzy compromise in the Pareto solution set to optimize the model, and finally the base station location coordinates of the LTE hybrid network are obtained. Further, in step 2, the characteristics of the ideal backhaul of the LTE hybrid networking are used to reconstruct multiple objective optimization functions, which specifically includes: selecting a better solution from the Pareto solution set by fuzzy compromise to optimize the model, and finally obtaining the LTE hybrid networking. The location coordinates of the base station of the network. First, improve the dynamic crowding distance

Calculate the crowding degree between the individual and the adjacent individuals in the external file, and then sort the new crowded distance and remove the solution with the smallest dense distance, and then calculate the dense distance of the remaining Pareto solutions, and repeat the calculation until the number of remaining Pareto solutions is the expected set. The specified external capacity S. Finally according to the formula

Compute the standard membership function for particle i. The solution process is as follows:

Step 1. Input data, input the number of candidate base stations, test point information, access rate, function boundary, and dimension;

和0时刻的初始速度

计算每一个粒子的目标函数，粒子的局部最优化位置初始化为

外部档案为空，设置边界最大拥挤距离为d；Step 2. Initialize the particle population: set the population number and the maximum number of iterations, and randomly generate the initial position at time 0 according to the constraint relationship

and the initial velocity at time 0

Calculate the objective function of each particle, and the local optimal position of the particle is initialized as

The external file is empty, and the maximum crowding distance of the boundary is set to d;

一次加入其中并保留支配解，表示为外部档案中的初始解；Step 3. Initialize external files:

Add it once and keep the dominant solution, expressed as the initial solution in the external file;

计算外部档案中所有个体的拥挤度，并采用前面介绍的轮盘赌的方法，从中选择一个个体作为全局最优解

Step 4, the iteration starts, t=1; according to the above formula

Calculate the crowding degree of all individuals in the external file, and use the roulette method introduced earlier to select an individual as the global optimal solution

Step 5. According to the particle swarm iteration formula introduced above, update the position x and velocity v of the particle, and recalculate the fitness of the individual;

Step 6. Update the external file: Add the updated particles to the external file in turn and judge the dominance relationship according to the crowding distance. If the newly added individual dominates the individual in the external file, add the new individual and delete the dominant individual; If the individual does not dominate the individual in the external file, it will not join; if it cannot be compared, then compare the current external capacity S' with the expected external capacity S, if S'≤S, then the new individual will join the external file, and S is incremented by 1, When the solution in the external file is larger than the specified value, use the above circular deletion method to update the non-inferior solution set;

Step 7. Update the P _best of the particle. If the maximum number of iterations is satisfied, stop the search, output the Pareto optimal frontier according to the external elite solution set, and use the above fuzzy decision-making method to find a compromise solution, otherwise t=t+1, go to step 4.

The above embodiments should be understood as only for illustrating the present invention and not for limiting the protection scope of the present invention. After reading the contents of the description of the present invention, the skilled person can make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims (1)

1. An LTE hybrid networking self-planning method based on multi-target particle swarm is characterized by comprising the following steps:

the method comprises the following steps: acquiring service information of a target area user to obtain service distribution of a target area;

step two: combining the characteristics of ideal backhaul of LTE hybrid networking, namely FDD is used as a macro base station to mainly provide wide coverage, TDD is used as a small base station to be deployed to mainly absorb capacity, and a target optimization function including the maximized coverage rate, the maximum network energy efficiency ratio, the maximum network load and the minimum cost is reconstructed;

step three: selecting a better solution from Pareto solution centralized fuzzy compromise to optimize a model by utilizing a discrete multi-target particle swarm algorithm for improving Pareto solution centralized congestion distance sequencing, and finally obtaining a base station site selection coordinate of the LTE hybrid networking;

the first step is as follows: acquiring service information of a target area user to obtain service distribution of a target area, specifically comprising:

firstly, gridding a target network P into N pixel points, and dividing N test points into common tests according to service demand predictionPoint N₁Individual sum hot spot area test point N₂Any point on P can be calibrated in a grid by Cartesian coordinates, and any point is represented as r_iThe coordinate is (x)_i，y_i)；

The second step combines the characteristics of the ideal backhaul of the LTE hybrid networking to reconstruct a multi-objective optimization model, and specifically comprises the following steps:

firstly, deploying k-layer networks on M candidate subsets, wherein the total number of the k-layer networks is 2, namely a TDD network and an FDD network, k is equal to 2 and represents the total number of the network layers, each base station has two choices, a_kmRepresenting the deployment situation of the base station at the position of the K layer M, wherein '1' represents that the base station at the K layer is built at the position of the M, and '0' represents that the base station at the K layer is not built at the position of the M, and K multiplied by M represents the size of an address selection matrix space, so that the address selection matrix of the base station of the hybrid networking can be obtained:

based on the characteristics of dual connection of the LTE hybrid networking, namely, a test point can be simultaneously connected with a TDD base station and an FDD base station, and only whether the service rate of the test point is met or not is considered, so that a base station access indication function and a signal-to-noise ratio are respectively obtained;

and R_k,n,m＝B_k,n×log(1+SINR_k,n,m)

Wherein Δ_k,n,mRepresents the situation that the k layer m position covers the test point n, R_k,n,mThe service rate that the base station at the position of k layers m can reach when the test point n receives the test point n is represented, the service rate of the hot test point is higher than the requirement of the common test point, R_min,nRepresenting the minimum rate for meeting the access requirement of the test point n, and '1' representing that the test point n is covered by the position of k layers m, and R is at the moment_k,n,m≥R_min,nAnd 0 indicates that no k-layer base station is built at the m position, and R is in the time_k,n,m≤R_min,n，B_k,nThe bandwidth of a test point n connected with a k-layer base station;

obtaining the test point according to the base station site selection matrix and the test point access indication functionAnd the final access base station site selection matrix H is as follows:

wherein b is_nmThe situation that the test point n is covered by the base station at the position m is represented, a TDD base station or an FDD base station may be built at the position m, or the base station is not built, and the test point n is covered by any base station, so that the test point n is represented to be covered;

finally, the four planning targets of the LTE hybrid networking are respectively as follows:

1) maximizing coverage

Wherein N is₁Number of common test points, N₂The number of hot spot test points is determined;

2) maximum network energy efficiency ratio

Wherein P is_k,mExpressed as the transmit power of a k-tier m base station;

3) maximum network load

Wherein P is_th,mExpressed as the load blocking threshold to be reached at the time of deployment of base station m, for limiting the number of access test points, Ψ, of base stations_k,n,mRepresenting the percentage of the load in the base station m to the base station demand load, when the value exceeds the threshold P in the practical engineering_th,mThen, the load limiting factor exp (P) may be used_th,m-Ψ_k,n,m) The load of the access base station m is adjusted and reduced;

4) minimum cost

Wherein C is_kThe cost unit price of the kth base station;

in the third step, an improved discrete multi-target particle swarm algorithm is utilized, and a better solution is selected from a Pareto solution set fuzzy compromise to optimize the modelFinally, obtaining a base station site selection coordinate of the LTE hybrid networking, comprising: first, dynamic crowding distance is improved

J is the total number of self-planned targets, f_j(i +1) and f_j(i-1) j' th target value of the particle before and after the particle i; f. of_jmaxAnd f_jminMaximum and minimum values of the jth objective function for all particles in the external document;

calculating the crowding degree of the individual and the adjacent individual in the external file, then removing the solution with the minimum dense distance after sorting the crowding degree with the new crowding distance, then calculating the dense distance of the remaining Pareto solutions, and circularly calculating until the number of the remaining Pareto solutions is the external capacity S expected to be set; finally according to the formula

Calculating a standard membership function for particle i, wherein u_ijRepresenting a standard membership function;

in the iterative formula of the discrete particle swarm, the iterative formulas of the speed and the position are respectively as follows:

and

respectively representing the speed and the position of the particle i in the d-dimensional space of the t +1 generation;

and

the individual extreme value and the global extreme value of the particle i in the generation t are respectively; r is₁And r₂Is a random number between 0 and 1; c. C₁And c₁Is a learning factor, usually taken 2 at the same time; ω is the inertial weight, using the inertial weight of the adaptive transform, and ω is expressed as:

t is the number of current iterations, t_maxIs the maximum number of iterations, ω_maxAnd ω_minThe inertial weights, ω max and min, respectively, are usually taken to be ω_max＝0.9，ω_min＝0.4；

In the third step, the improved discrete multi-target particle swarm algorithm specifically comprises the following steps:

step 1, inputting data, and inputting the number of candidate base stations, test point information, access rate, function boundary and dimensionality;

step 2, initializing a particle population: setting the population number and the maximum iteration number, and randomly generating the initial position of 0 moment according to the constraint relation

And initial velocity at time 0

Calculating an objective function for each particle, initializing the local optimum position of the particle to

Setting the maximum crowding distance of the boundary as d when the external file is empty;

step 3, initializing an external file: will be provided with

Adding the dominant solution into the external archive at one time and retaining the dominant solution, wherein the dominant solution is represented as an initial solution in the external archive;

step 4, starting iteration, wherein t is 1; according to the above formula

Calculating the crowdedness of all individuals in the external file, and selecting one individual as a global optimal solution by adopting a roulette method

Step 5, updating the position x and the speed v of the particles according to the particle swarm iterative formula and recalculating the fitness of the individual;

step 6, updating an external file: sequentially adding the particles subjected to position updating into an external file, judging a domination relationship according to the crowding distance, and if the newly added individuals dominate the individuals in the external file, adding the new individuals and deleting the domination individuals; if the new individual does not dominate the individuals in the external file, not adding; if the comparison is impossible, comparing the current external capacity S 'with the expected set external capacity S, if S' is less than or equal to S, adding a new individual into an external file, and adding 1 to S, and when the solution in the external file is greater than a specified value, updating a non-inferior solution set by using a cyclic deletion method;

step 7, updating P of the particle_best(ii) a If the maximum iteration times are met, stopping searching, outputting a Pareto optimal front edge according to an external elite solution set, finding a compromise solution by using a fuzzy decision method, otherwise, turning to the step 4 if t is t + 1;

the roulette method in the step 4 specifically includes: the probability of each individual being selected is in direct proportion to the fitness function value, the group size is set to be N, and the individual x_iHas a fitness of f (x)_i) Then the individual x_iThe probability of selection of (a) is:

and P (x)₁)+P(x₂)+…+P(x_N) When 1, the cumulative distribution probability is:

the method comprises the following specific operation steps: calculating the selection probability and cumulative distribution probability of each individual according to the above formula, and generating a probability by using rand ()[0,1]R is a random number r between, if r is less than or equal to q₁Then the individual x₁Selecting the selected plants; if q is_k-1＜r＜q_k(2. ltoreq. k. ltoreq.N), then the individual x_kAnd (6) selecting.

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