CN116017285A - Method for joint optimization of deployment position and working state of wireless access point - Google Patents

Abstract

The invention provides a method for jointly optimizing deployment positions and working states of wireless access points, which comprises the steps of obtaining an AP set, position vectors of all APs and working states in a Wireless Local Area Network (WLAN), and dividing areas with a plurality of unit cubes to obtain user density in each subarea; determining target points to be covered by each sub-area to form a target point set, and calculating signals from the AP _i To target point T _j Is a path loss of (a); constructing each sub-cube by taking the total coverage rate of target points in the region of each sub-cube and the association rate of users as constraint conditionsAP _i An objective function associated with TX power of (b); and solving and outputting an optimal solution for the objective function by adopting a single-objective optimization algorithm to obtain the optimal solution for the working states and the positions of all the APs. By implementing the method and the device, on the premise of ensuring the coverage range, the difference of the user densities among different areas and the time fluctuation of the user densities in the WLAN are considered, so that the TX power of the total AP is minimum.

Description

Method for joint optimization of deployment position and working state of wireless access point

Technical Field

The invention relates to the technical field of wireless network access, in particular to a method for jointly optimizing a deployment position and a working state of a wireless access point.

Background

With the increasing demand for broadband internet access and the rapid development of wireless network technology, a large number of Wireless Local Area Networks (WLANs) are deployed and bring great convenience to network access, but also consume a large amount of energy, resulting in a large amount of resource waste.

Currently, two main reasons for energy waste in a WLAN are specifically that on one hand, most APs in the WLAN operate with maximum T X (transmission) power (typically 100mW for indoor APs), and operate continuously for 24 hours a day, which, although maximizing network coverage, also results in energy waste. In addition, too high TX power may also exacerbate signal interference. On the other hand, all WLANs are designed and deployed according to user capacity requirements. In many cases, however, the user capacity will vary over time. For example, for WLAN in a busy shopping mall, the user density tends to exhibit significant periodic fluctuations, especially during shut down, most APs operate at very low loads, even zero load, but still continue to consume energy at maximum power. In view of the above, optimization of AP configuration, i.e., TX power, deployment location, and operating state, has attracted considerable attention in recent years.

In terms of TX power optimization, h.briantoro et al propose a method to determine the AP optimum power by the signal-to-noise ratio of the received signal strength, thereby reducing the overall energy consumption of the WLAN. M.hmila et al propose a two-stage semi-distributed solution to reduce power consumption. In the first stage they use a collaborative league gaming framework for channel allocation. In the second phase, they use fractional programming to determine the TX power of the AP. Guo et al studied in detail the relationship between three key factors in a wireless network, such as energy consumption, sensing quality and connectivity. Whereas w.wu et al discuss the energy effectiveness of WLANs by taking into account congestion avoidance and migration constraints. The method and the device provide an AP joint management framework and channel width selection of active APs in WLAN, so that energy sources can be effectively saved.

In terms of AP deployment location optimization, S.Karimi-Bidhhendi et al propose a heterogeneous two-layer Lloyd-like algorithm to optimize AP deployment in a wireless network. With the overall signal strength of the terminal equipment as an optimization target, J.Du et al propose an AP deployment position automatic optimization deployment mechanism adopting a heuristic algorithm. P.tewari effectively solves the problem of efficient AP placement and frequency allocation by taking into account two important parameters, power adjustment and partially overlapping channel allocation. Wen et al propose a method based on a brute force search algorithm to optimize AP deployment in a communication-based train control system.

Furthermore, some work considers both AP TX power and location optimization. To maximize the overall throughput of the wireless network, x.zhang et al jointly consider power allocation and AP placement. And many researchers have chosen to use the group intelligent optimization algorithm (SIOA) to adjust the AP's location to reduce the total TX power of the network. Liu et al further eliminates redundant APs by traversal checking. While these studies are effective in reducing system power consumption, their optimized scenes are two-dimensional (2D), and the above algorithm may not be applicable to actual three-dimensional optimized scenes (3D). In contrast, q.hu et al propose a new algorithm that optimizes the overall TX power of the network while ensuring effective coverage by jointly optimizing the TX power and location of each AP in the 3D scene.

In WLAN, energy saving by adjusting the operating state of the AP is also a hot topic. Xu et al propose a resource re-association scheduling algorithm based on Benders decomposition, which reduces system energy consumption by closing part of APs, meets system coverage at the same time, and does not influence user experience. The r.g. garroppo et al propose a method that can reduce the power consumption of a WLAN by turning on only a portion of the APs and associating users with the turned-on APs. Apostono et al combine network clusters and machine learning models to determine the state of the AP throughout the day. In order to ensure load balancing between APs and energy saving of WLAN, m.h. dwijakara et al propose a high-efficiency user association scheme by adjusting the working state of the APs. The goal of r.g. garroppo et al is to minimize the energy consumption of WLAN during periods of low user density by turning off some APs and adjusting the TX power level of each AP.

While the above work has done much in optimizing AP configuration, there are still problems pending. In particular, the above work does not take into account the difference in user density between different areas and the time fluctuations in user density in WLAN.

Disclosure of Invention

The technical problem to be solved by the embodiment of the invention is to provide a method for jointly optimizing the deployment position and the working state of a wireless access point, which can consider the difference of the user density among different areas and the time fluctuation of the user density in a WLAN under the premise of ensuring the coverage area and realize that the TX power of a total AP is minimum.

In order to solve the technical problems, the embodiment of the invention provides a method for jointly optimizing a deployment position and a working state of a wireless access point, which comprises the following steps:

step S1, obtaining the WLAN with the function of wireless local area network

AP set->

Position vector of each AP->

And working state->

And is divided into->

Region of a unit cube->

To obtain the user density in each sub-area +.>

Wherein (1)>

S _i =1 or 0,1 indicates that the AP is in an active state, 0 indicates that the AP is in a sleep state;

Step S2, determining the region D of each subcube _j Middle target point T _j To form a target point set

And is +.>

Calculating a signal from an AP _i To target point T _j Is a path loss of (a);

wherein T is _j Representation area D _j As the target point to be covered, i.e. representing the area D _j And T _j The position of (2) is expressed as

||AP _i ,T _j || ₂ Representing AP _i And T _j A Euclidean distance between them; gamma denotes a path loss factor, which is related to the surrounding environment; x is x _σ A normal random variable representing a standard deviation sigma; d, d _o Representing a reference distance; alpha represents d _o Is a power of reception of (a); beta _o Representing obstacle pairs T _j Is a signal attenuation of (a);

step S3, using the region D of each subcube _j Middle target point T _j Overall coverage of (2)

Association rate with user->

Building up for constraint conditions with each AP _i TX power +.>

The associated objective function is as follows: />

Wherein C1 constrains the full coverage of the target point; c2 ensures the user capacity requirement in the service area;

and->

P _min And P _max Respectively representing the minimum TX power and the maximum TX power of the same AP; r (T) _j ) Representing T _j Whether or not all users in (a) can be associated with the WLAN, and

C(T _j ) Representing T _j Is covered by (a) and

C(AP _i ,T _j ) Representing T _j Whether or not to be covered by AP _i Covering and

representing AP _i TX power, P _0,j Representing T _j The lowest received signal strength that can be covered;

and S4, adopting a single-objective optimization algorithm to solve and output the optimal solution of the objective function, and obtaining the optimal solution of the working states and the positions of all the APs.

2. The method for jointly optimizing deployment location and operating state of wireless access point according to claim 1, wherein the specific step of step S4 comprises:

step1: initializing parameters: population N, current iteration number k and maximum iteration number k _max Network parameters; wherein the network parameters include user density

And attenuation of signal by an obstacle beta _o ；

Step2: randomly generating an initial population Y (0) = [ X ] according to the individual coding mode ₁ ,X ₂ ,…,X _N ] ^T And initially solve X _i Uniformly distributed as X over search space _i ＝X _min +r ₁ ·(X _max -X _min ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein X is _i ＝{[s _i,1 ,x _i,1 ,y _i,1 ,z _i,1 ],[s _i,2 ,x _i,2 ,y _i,2 ,z _i,2 ],…,[s _i,n ,x _i,n ,y _i,n ,z _i,n ]-a }; i represents the ith individual in Y (0); n represents the number of APs; s represents the state of the AP; x, y, z denote the position of the AP; x is X _min And X _max Respectively represent solution X _i At the lower boundary of the search spaceAnd an upper bound; r is (r) ₁ Representing a random number between (0, 1);

step3: according to the formula

Calculating the fitness of each individual, and selecting the individual X with the minimum fitness in the population _M And next smallest individual X _FM The method comprises the steps of carrying out a first treatment on the surface of the The sum of the energy consumption of the APs in each individual is the individual fitness;

step4: controlling the exploration and utilization of populations by escaping energy EE and by the formula

Calculating the EE value; if the EE is not less than 1, executing Step5; otherwise, go to Step6; r is (r) ₂ Representing the random number in (0, 1); c ₁ ＝1.5；

Step5: the exploration stage: acquisition of [0,1 ]]Random values within and when the value is greater than 0.5, then the formula is used

Updating the respective positions X _i (k+1); otherwise, use the formula +.>

Sum formula

Updating the respective positions X _i (k+1)；

Wherein r is ₃ ,r ₄ ,r ₅ Respectively representing random numbers between (0, 1); as indicated by the dot product operator, R is calculated _L And Y (k) are the sums of the respective multiplications of the respective components of the two vectors; r is R _L Is an N-dimensional vector in which each element R _L,i I=1, 2, …, N obeys the distribution as

And λ=1.5 and b to N (0, 1), -j>

And is also provided with

Step6: the utilization stage: first, select X _M And X _FM As crossing individuals, the calculation formula is

Wherein (1)>

Representing a crossover operation;

a section representing randomly selected genes from each individual for crossover operation;

then, a [0,1 ] is obtained]Random value in the range, and when the value is greater than 0.5, then the formula X (k+1) =v (k+1) +gs is used ₁ ·||V(k+1),X(k)|| ₂ Updating each position; otherwise, use formula

Updating each position; wherein V (k+1), X (k) | ₂ Representing the Euclidean distance between individuals V and X; GS ₁ N (0,0.333) represents the vector GS ₁ Obeying a gaussian distribution with a mean value of 0 and a standard deviation of 0.333; CL is the center of the search space, and CL, X _M (k)|| ₂ Represents CL and X _M (k) Euclidean distance between them; GS ₂ N (0, 1) represents the vector GS ₂ Obeying a gaussian distribution with a mean value of 0 and a standard deviation of 1;

step7: k=k+1, steps 2 to Step7 are repeated until k=k _max ；

Step8: output of final X _M And obtaining the optimal solutions of all the AP positions and states.

As the target point to be covered; the embodiment of the invention has the following beneficial effects:

the invention constructs each AP with the overall coverage rate of the positions of all users (namely the target points to be covered) in the area of each subcube and the association rate of the users _i And adopts a single-target optimization algorithm to solve the optimal solution so as to obtain the optimal solution of the working states and positions of all the APs, so that the difference of the user densities among different areas and the time fluctuation of the user densities in the WLAN are considered on the premise of ensuring the coverage range, and the TX power of the total AP is minimum.

Drawings

In order to more clearly illustrate the embodiments of the invention or the technical solutions of the prior art, the drawings which are required in the description of the embodiments or the prior art will be briefly described, it being obvious that the drawings in the description below are only some embodiments of the invention, and that it is within the scope of the invention to one skilled in the art to obtain other drawings from these drawings without inventive faculty.

Fig. 1 is a flowchart of a method for jointly optimizing a deployment location and an operating state of a wireless access point according to an embodiment of the present invention;

fig. 2 is a flowchart of a method for jointly optimizing a deployment position and a working state of a wireless access point according to an embodiment of the present invention, in which a single-objective optimization algorithm is used to solve an objective function for an optimal solution in step S5;

fig. 3 is a schematic diagram of a user density distribution from 7 am to 11 pm and from 11 pm to 7 pm in the next day in a simulation experiment of a method for jointly optimizing a deployment location and an operating state of a wireless access point according to an embodiment of the present invention.

Fig. 4 is a total TX power comparison chart of different OAC methods based on SIOA (group intelligent optimization algorithm) in a simulation experiment of a method for jointly optimizing deployment positions and working states of wireless access points according to an embodiment of the present invention;

fig. 5 is a coverage ratio comparison chart of different OAC methods based on SIOA in a simulation experiment of a method for jointly optimizing a deployment position and a working state of a wireless access point according to an embodiment of the present invention;

fig. 6 is a comparison chart of AP numbers of different SIOA-based OAC methods in non-working time in a simulation experiment of a method for jointly optimizing a deployment position and a working state of a wireless access point according to an embodiment of the present invention;

fig. 7 is a heat chart of received signal strength at different times in a simulation experiment of a method for jointly optimizing a deployment position and a working state of a wireless access point according to an embodiment of the present invention; wherein, (a) is a heat map of received signal strength from 7 a.m. to 11 a.m. at operating time; (b) For receiving a heat map of signal strength from 11 pm to 7 pm the next day at rest time;

fig. 8 is a graph comparing total TX power under various AP user capacities in a simulation experiment of a method for jointly optimizing a deployment position and an operating state of a wireless access point according to an embodiment of the present invention;

fig. 9 is a coverage ratio comparison chart under various AP user capacities in a simulation experiment of a method for jointly optimizing a deployment position and a working state of a wireless access point according to an embodiment of the present invention;

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings, for the purpose of making the objects, technical solutions and advantages of the present invention more apparent.

As shown in fig. 1, in an embodiment of the present invention, a method for jointly optimizing a deployment location and an operating state of a wireless access point is provided, where the method includes the following steps:

step S1, obtaining the WLAN with the function of wireless local area network

AP set->

Position vector of each AP->

And working state->

And is divided into->

Region of a unit cube->

To obtain the user density in each sub-area +.>

Wherein (1)>

S _i =1 or 0,1 indicates that the AP is in an active state, 0 indicates that the AP is in a sleep state;

Step S2, determining the region D of each subcube _j Middle target point T _j To form a target point set

And is +.>

Calculating a signal from an AP _i To target point T _j Is a path loss of (a);

wherein T is _j Representation area D _j As the target point to be covered, i.e. representing the area D _j And T _j The position of (2) is expressed as

||AP _i ,T _j || ₂ Representing AP _i And T _j A Euclidean distance between them; gamma denotes the path loss factor, which is related to the surroundingsEnvironmental concerns; x is x _σ A normal random variable representing a standard deviation sigma; d, d _o Representing a reference distance; alpha represents d _o Is a power of reception of (a); beta _o Representing obstacle pairs T _j Is a signal attenuation of (a);

step S3, using the region D of each subcube _j Middle target point T _j Overall coverage of (2)

Association rate with user->

Building up for constraint conditions with each AP _i TX power +.>

The associated objective function is as follows:

wherein C1 constrains the full coverage of the target point; c2 ensures the user capacity requirement in the service area;

and->

P _min And P _max Respectively represent the minimum TX power sum of the same APMaximum TX power; r (T) _j ) Representing T _j Whether or not all users in (a) can be associated with the WLAN, and

C(T _j ) Representing T _j Is covered by (a) and

C(AP _i ,T _j ) Representing T _j Whether or not to be covered by AP _i Covering and

representing AP _i TX power, P _0,j Representing T _j The lowest received signal strength that can be covered; as the target point to be covered;

and S4, adopting a preset single-objective optimization algorithm to solve and output an optimal solution for the objective function, and obtaining the optimal solution for the working states and the positions of all the APs.

In step S1, the method comprises the steps of obtaining a wireless local area network WLAN having

AP sets, position vectors and operating states of APs, and are divided into +.>

A region of a unit cube to obtain a user density in each sub-region.

In step S2, first, the region D of each subcube is determined _j Middle target point T _j To form a set of target points, i.e. a set of locations of all users to be covered by each sub-area.

Second, calculate the signal from AP _i To target point T _j For subsequent objective function building requirements.

In step S3, the region D of each subcube _j Middle target point T _j Is used as constraint conditions to construct the AP _i TX power of (2)

An associated objective function.

In step S4, as shown in fig. 2, a single-objective optimization algorithm is adopted to solve and output an optimal solution to an objective function, and the specific process is as follows:

step1: initializing parameters: population N, current iteration number k and maximum iteration number k _max Network parameters; wherein the network parameters include user density

And attenuation of signal by an obstacle beta _o ；

Step2: randomly generating an initial population Y (0) = [ X ] according to the individual coding mode ₁ ,X ₂ ,…,X _N ] ^T And initially solve X _i Uniformly distributed as X over search space _i ＝X _min +r ₁ ·(X _max -X _min ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein X is _i ＝{[s _i,1 ,x _i,1 ,y _i,1 ,z _i,1 ],[s _i,2 ,x _i,2 ,y _i,2 ,z _i,2 ],…,[s _i,n ,x _i,n ,y _i,n ,z _i,n ]-a }; i represents the ith individual in Y (0); n represents the number of APs; s represents the state of the AP; x, y, z denote the position of the AP; x is X _min And X _max Respectively represent solution X _i At the lower and upper bounds of the search space; r is (r) ₁ Representing a random number between (0, 1);

step3: according to the formula

Calculating the fitness of each individual, and selecting the individual X with the minimum fitness in the population _M And next smallest individual X _FM The method comprises the steps of carrying out a first treatment on the surface of the The sum of the energy consumption of the APs in each individual is the individual fitness;

step4: controlling the exploration and utilization of populations by escaping energy EE and by the formula

Calculating the EE value; if the EE is not less than 1, executing Step5; otherwise, go to Step6; r is (r) ₂ Representing the random number in (0, 1); c ₁ ＝1.5；

Step5: the exploration stage: acquisition of [0,1 ]]Random values within and when the value is greater than 0.5, then the formula is used

Updating the respective positions X _i (k+1); otherwise, use the formula +.>

Sum formula

Updating the respective positions X _i (k+1)；

Wherein r is ₃ ,r ₄ ,r ₅ Respectively representing random numbers between (0, 1); as indicated by the dot product operator, R is calculated _L And Y (k) is the sum of the products of the respective components of the two vectors; r is R _L Is an N-dimensional vector in which each element R _L,i I=1, 2, …, N obeys the distribution as

And λ=1.5 and b to N (0, 1), -j>

And is also provided with

Step6: first, select X _M And X _FM As crossing individuals, the calculation formula is

Wherein (1)>

Representing a crossover operation;

A section representing randomly selected genes from each individual for crossover operation;

then, a [0,1 ] is obtained]Random value in the range, and when the value is greater than 0.5, then the formula X (k+1) =v (k+1) +gs is used ₁ ·||V(k+1),X(k)|| ₂ Updating each position; otherwise, use formula

Updating each position; wherein V (k+1), X (k) | ₂ Representing the Euclidean distance between individuals V and X; GS ₁ N (0,0.333) represents vector CS ₁ Obeying a gaussian distribution with a mean value of 0 and a standard deviation of 0.333; CL is the center of the search space, and CL, X _M (k)|| ₂ Represents CL and X _M (k) Euclidean distance between them; GS ₂ N (0, 1) represents the vector GS ₂ Obeying a gaussian distribution with a mean value of 0 and a standard deviation of 1;

step7: k=k+1, steps 2 to Step7 are repeated until k=k _max ；

Step8: output of final X _M And obtaining the optimal solutions of all the AP positions and states.

As shown in fig. 3 to fig. 9, simulation experiments and results of a method for jointly optimizing a deployment position and an operating state of a wireless access point in an embodiment of the present invention are compared.

In fig. 3, the distribution of user density is schematically shown from 7 am to 11 pm and 11 pm to 7 am the next day.

FIG. 4 is a graph comparing total TX power for different SIOA-based OAC methods; FIG. 5 is a graph comparing coverage of different SIOA-based OAC methods; fig. 6 is a graph comparing the number of APs during a holiday for different SIOA-based OAC methods.

FIG. 7 is a thermal diagram of received signal strength at various times, from a top view at an X-Y angle; wherein, (a) is a heat map of received signal strength from 7 a.m. to 11 a.m. at operating time; (b) For receiving a heat map of signal strength from 11 pm to 7 pm the next day at rest time.

Fig. 8 is a graph of total TX power versus various AP user capacities.

Fig. 9 is a graph comparing coverage at various AP user capacities.

From the above experimental and results comparison graphs, it can be seen that the proposed IEGJO-OAC method is very efficient. It can significantly reduce the total AP TX power of the WLAN while still ensuring full effective coverage of the service area.

The embodiment of the invention has the following beneficial effects:

the invention constructs each AP with the overall coverage rate of the positions of all users (namely the target points to be covered) in the area of each subcube and the association rate of the users _i And adopts a single-target optimization algorithm to solve the optimal solution so as to obtain the optimal solution of the working states and positions of all the APs, so that the difference of the user densities among different areas and the time fluctuation of the user densities in the WLAN are considered on the premise of ensuring the coverage range, and the TX power of the total AP is minimum.

Those of ordinary skill in the art will appreciate that all or a portion of the steps in implementing the methods of the above embodiments may be implemented by a program to instruct related hardware, where the program may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc.

The above disclosure is only a preferred embodiment of the present invention, and it is needless to say that the scope of the invention is not limited thereto, and therefore, the equivalent changes according to the claims of the present invention still fall within the scope of the present invention.

Claims (2)

1. A method for joint optimization of wireless access point deployment location and operating state, the method comprising the steps of:

step S1, obtaining the WLAN with the function of wireless local area network

AP set->

Position vector of each AP->

And working state->

And is divided into

Region of a unit cube->

To obtain the user density in each sub-area

Wherein (1)>

S _i =1 or 0,1 indicates that the AP is in an active state, 0 indicates that the AP is in a sleep state; j=d ₁ ,D ₂ ,…,

Step S2, determining eachRegion D of the subcube _j Middle target point T _j To form a target point set

And is +.>

Calculating a signal from an AP _i To target point T _j Is a path loss of (a);

wherein T is _j Representation area D _j As the target point to be covered, i.e. representing the area D _j And T _j The position of (2) is expressed as

||AP _i ,T _j || ₂ Representing AP _i And T _j A Euclidean distance between them; gamma denotes a path loss factor, which is related to the surrounding environment; x is x _σ A normal random variable representing a standard deviation sigma; d, d _o Representing a reference distance; alpha represents d _o Is a power of reception of (a); beta _o Representing obstacle pairs T _j Is a signal attenuation of (a);

step S3, using the region D of each subcube _j Middle target point T _j Overall coverage of (2)

Association rate with user->

Building up for constraint conditions with each AP _i TX power +.>

The associated objective function is as follows:

wherein C1 constrains the full coverage of the target point; c2 ensures the user capacity requirement in the service area;

and P is _j ^APi ＝min{max{β _i,j +P _0,j ,P _min },P _max }，P _min And P _max Respectively representing the minimum TX power and the maximum TX power of the same AP; r (T) _j ) Representing T _j Whether or not all users in (a) can be associated with the WLAN, and

C(T _j ) Representing T _j Is covered by (a) and

C(AP _i ,T _j ) Representing T _j Whether or not to be covered by AP _i Covering and

representing AP _i TX power, P _0,j Representing T _j The lowest received signal strength that can be covered;

and S4, adopting a single-objective optimization algorithm to solve and output the optimal solution of the objective function, and obtaining the optimal solution of the working states and the positions of all the APs.

2. The method for jointly optimizing deployment location and operating state of wireless access point according to claim 1, wherein the specific step of step S4 comprises:

step1: initializing parameters: population N, current iteration number k and maximum iteration number k _max Network parameters; wherein the network parameters include user density

And attenuation of signal by an obstacle beta _o ；

Step2: randomly generating an initial population Y (0) = [ X ] according to the individual coding mode ₁ ,X ₂ ,…,X _N ] ^T And initially solve X _i Uniformly distributed as X over search space _i ＝X _min +r ₁ ·(X _max -X _min ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein X is _i ＝{[s _i,1 ,x _i,1 ,y _i,1 ,z _i,1 ],[s _i,2 ,x _i,2 ,y _i,2 ,z _i,2 ],…,[s _i,n ,x _i,n ,y _i,n ,z _i,n ]-a }; i represents the ith individual in Y (0); n represents the number of APs; s represents the state of the AP; x, y, z denote the position of the AP; x is X _min And X _max Respectively represent solution X _i At the lower and upper bounds of the search space; r is (r) ₁ Representing a random number between (0, 1);

step3: according to the formula

Calculating the fitness of each individual, and selecting the individual X with the minimum fitness in the population _M And the next smallest individual X _FM The method comprises the steps of carrying out a first treatment on the surface of the The sum of the energy consumption of the APs in each individual is the individual fitness;

step4: controlling the exploration and utilization of populations by escaping energy EE and by the formula

Calculating the EE value; if the EE is not less than 1, executing Step5; otherwise, go to Step6; r is (r) ₂ Representing the random number in (0, 1); c ₁ ＝1.5；

Step5: the exploration stage: acquisition of [0,1 ]]Random values within and when the value is greater than 0.5, then the formula is used

Updating the respective positions X _i (k+1); otherwise, use the formula +.>

Sum formula

Updating the respective positions X _i (k+1)；

Wherein r is ₃ ,r ₄ ,r ₅ Respectively representing random numbers between (0, 1); as indicated by the dot product operator, R is calculated _L And Y (k) are the sums of the respective multiplications of the respective components of the two vectors; r is R _L Is an N-dimensional vector in which each element R _L,i I=1, 2, …, N obeys the distribution as

And λ=1.5 and b to N (0, 1), -j>

And is also provided with

Step6: the utilization stage: first, select X _M And X _FM As crossing individuals, the calculation formula is

Wherein (1)>

Representing a crossover operation;

a section representing randomly selected genes from each individual for crossover operation;

then, a [0,1 ] is obtained]Random value in the range, and when the value is greater than 0.5, then the formula X (k+1) =v (k+1) +gs is used ₁ ·||V(k+1),X(k)|| ₂ Updating each position; otherwise, use formula

Updating each position; wherein V (k+1), X (k) | ₂ Representing the Euclidean distance between individuals V and X; GS ₁ N (0,0.333) represents the vector GS ₁ Obeying a gaussian distribution with a mean value of 0 and a standard deviation of 0.333; CL is the center of the search space, and CL, X _M (k)|| ₂ Represents CL and X _M (k) Euclidean distance between them; GS ₂ N (0, 1) represents the vector GS ₂ Obeying a gaussian distribution with a mean value of 0 and a standard deviation of 1;

step7: k=k+1, steps 2 to Step7 are repeated until k=k _max ；

Step8: output of final X _M And obtaining the optimal solutions of all the AP positions and states.

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