CN111542069A - Method for realizing wireless AP deployment optimization based on rapid non-dominated genetic algorithm - Google Patents

Method for realizing wireless AP deployment optimization based on rapid non-dominated genetic algorithm Download PDF

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CN111542069A
CN111542069A CN202010303266.9A CN202010303266A CN111542069A CN 111542069 A CN111542069 A CN 111542069A CN 202010303266 A CN202010303266 A CN 202010303266A CN 111542069 A CN111542069 A CN 111542069A
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唐震洲
支子聪
沈达
孟欣
郭瑞琪
易家欢
应子怡
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Abstract

The invention discloses a method for realizing wireless AP deployment optimization based on a rapid non-dominated genetic algorithm, which comprises the following steps: determining parameters, binary string coding, setting parameters, cross mutation operation, selection operation, judging conditions and screening an optimal solution; the method adopts a non-uniform quantization space model design, more accords with the practical requirement, adjusts the distribution position and the power of the wireless AP through a rapid non-dominated genetic algorithm according to the traditional experience and the classical theory and the data of the power information, the signal intensity decay, the channel interference and the like of the wireless AP, further achieves the aim of optimizing the network topology under the condition of meeting the communication requirement, finally achieves the aim of reducing the number of the wireless APs and the total power, observes the change condition of the signal coincidence rate, greatly reduces the signal coincidence rate and effectively improves the resource utilization.

Description

Method for realizing wireless AP deployment optimization based on rapid non-dominated genetic algorithm
Technical Field
The invention relates to the technical field of wireless local area networks, in particular to a method for realizing wireless AP deployment optimization based on a rapid non-dominated genetic algorithm.
Background
With the rapid development of wireless technology, wlan is widely used in many fields due to its high efficiency, flexibility and low cost;
meanwhile, wireless AP topology optimization in networking is widely researched, which has great significance for improving the performance of a wireless AP network, and in many occasions, wireless APs irregularly and intensively deployed cause resource waste, so that the invention provides a method for realizing wireless AP deployment optimization based on a rapid non-dominated genetic algorithm to solve the problems in the prior art.
Disclosure of Invention
In view of the above problems, the present invention aims to provide a method for optimizing wireless AP deployment based on a fast non-dominated genetic algorithm, which optimizes topology by adjusting the position, power and operating state of an AP, thereby achieving two objectives of reducing the total power of APs and the number of APs under the condition of satisfying the full coverage of a target area.
In order to realize the purpose of the invention, the invention is realized by the following technical scheme: a method for realizing wireless AP deployment optimization based on a rapid non-dominated genetic algorithm comprises the following steps:
the method comprises the following steps: determining parameters
According to the real environment, determining a signal attenuation function and signal attenuation caused by obstacles, setting three types of obstacles and a signal attenuation value corresponding to each type of obstacle, setting partial parameters including reference distance and path attenuation coefficient, establishing a square simulation map in the simulation, carrying out discretization processing on the square simulation map, and setting the three types of obstacles and the signal attenuation value corresponding to each type of obstacle;
step two: binary string coding
According to the first step, N APs which are defaulted to be in working states are initially and uniformly arranged in an area, the position information x, y, the power p and the state k of each wireless AP are set as calculation variables, the calculation variables are x, y, p and k, the calculation variables are coded, after coding, each wireless AP exists in the form of a 25-bit binary string, and the coding mode is as follows: a population has a certain number of individuals, the jth individual rhojExpressed as:
ρj＝(Bj1,Bj2，......BjN) (1)
wherein, Bji＝[ki,xi,yi,αi]|jInformation indicating the ith wireless AP in the jth individual, the wireless AP including a switch state (k)i) Abscissa and ordinate (x)i,yi) And a transmission power (α)i) Information, which is converted to a binary string form, as follows:
Figure BDA0002454808720000021
a set of sizes is ranged in [ U ]l,Uu]The data of (2) is encoded into an h-bit binary string in the following manner:
Figure BDA0002454808720000022
Figure BDA0002454808720000023
Figure BDA0002454808720000024
wherein λ ═ U (U)u-Ul)/(2h-1), the decoding process is the reverse of the encoding process, and the binary string is set to bkbk-1...b1Then, the original value is obtained through decoding:
Figure BDA0002454808720000031
step three: setting parameters
The number of wireless APs and the power variation range are set to [ α ]min,αmax]The number of population iterations is maxgen, and the cross probability in each iteration is PrcThe mutation probability is Prm；
Step four: cross mutation operations
Performing cross operation on the 2M individuals in the parent according to the probability specified in the third step, randomly mating the 2M individuals, specifically selecting a cross point, crossing the binary strings of the two individuals, generating new two individuals after crossing, introducing mutation operation, and realizing by randomly placing the reverse binary strings to finally form a new population;
step five: selection operation
Combining the parent population and the new population to form a temporary population containing 4M individuals, selecting the temporary population, sorting the selection operation according to the quantity and total power of the AP of each individual in NSGA-II to obtain different levels, further ranking the individuals of different levels according to the crowdedness of the individuals, and screening out appropriate 2M sub-generation individuals according to the ranking condition of the selection operation, wherein the 2M sub-generation individuals serve as parents of the next cycle;
step six: judgment of conditions
Judging whether iteration times maxgen of the end loop condition are met or not according to the fifth step, if not, taking the generated filial generation as a parent to continue the loop, returning to the fourth step, and if so, returning to the final generation;
step seven: screening for optimal solutions
And selecting the most appropriate solution set from the last generation of population according to the ranked wireless AP step gradient and the actual demand condition of a producer.
The further improvement lies in that: in the second step, in the process of setting the position information x, y, the power p and the state k of each wireless AP as calculation variables, when k is 0, the AP is in a working state; 0 indicates the off state.
The further improvement lies in that: in the fourth step, the pseudo code of the cross operation is an algorithm:
Figure BDA0002454808720000041
the further improvement lies in that: in the fourth step, the algorithm of the mutation operation is as follows:
Figure BDA0002454808720000042
the further improvement lies in that: in the fifth step, the sorting operation specifically comprises: defining when an individual rho1Is lower than the other individual p simultaneously2Then ρ1Dominating ρ2Recording the individual rhoiSolution set S of dominant other individualsiAnd dominate the individual ρiOf other individuals ViAnd carrying out rapid non-dominant sorting operation on the temporary population, ranking each individual, wherein the operation is shown as an algorithm:
Figure BDA0002454808720000051
the further improvement lies in that: in the fifth step, through rapid non-dominated sorting, each individual is evaluated with a corresponding rank according to the total power and the number of wireless APs, when a certain individual cannot meet the requirement of complete coverage in an area, the individual is ranked at the bottommost, then, the crowding degree of the individuals on the same step is calculated, each individual on the same step is ranked according to the number and the total power of the wireless APs, the crowding degree of the individual having an extreme value in each queue is set to infinity, and the crowding degree of the other individuals is calculated according to the distribution of the adjacent individuals, wherein the specific calculation method is as follows:
Figure BDA0002454808720000061
the further improvement lies in that: in the fifth step, the selecting operation process follows the following principle: sequentially selecting proper individuals until the number of the next generation of population reaches a specified value; preferentially selecting high-order ladder individuals from individuals positioned at different ladders; individuals located at the same step are preferentially selected as those with high crowdedness.
The invention has the beneficial effects that: the method adopts a non-uniform quantization space model design, more accords with the practical requirement, adjusts the distribution position and the power of the wireless AP through a rapid non-dominated genetic algorithm according to the traditional experience and the classical theory and the data of the power information, the signal intensity decay, the channel interference and the like of the wireless AP, further achieves the aim of optimizing the network topology under the condition of meeting the communication requirement, finally achieves the aim of reducing the number of the wireless APs and the total power, observes the change condition of the signal coincidence rate, greatly reduces the signal coincidence rate and effectively improves the resource utilization.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a simulation environment and AP initial distribution diagram of the present invention;
FIG. 3 is a graph of coverage as a function of power increase for a single wireless AP in accordance with the present invention;
FIG. 4 is a graph of total power as a function of iteration number for the present invention;
FIG. 5 is a graph of the number of wireless APs of the present invention as a function of iteration number;
FIG. 6 is a graph of the change in signal coincidence rate during an iteration of the present invention;
FIG. 7 is a schematic cross-over operation of the present invention;
FIG. 8 is a schematic diagram illustrating the variant operation of the present invention;
FIG. 9 is a schematic diagram of screening the new population and the parent population after cross mutation according to the present invention.
Detailed Description
In order to further understand the present invention, the following detailed description will be made with reference to the following examples, which are only used for explaining the present invention and are not to be construed as limiting the scope of the present invention.
According to fig. 1, 2, 3, 4, 5, 6, 7, 8, and 9, the present embodiment provides a method for implementing wireless AP deployment optimization based on a fast non-dominated genetic algorithm, including the following steps:
the method comprises the following steps: determining parameters
According to the real environment, determining a signal attenuation function and signal attenuation caused by obstacles, setting three types of obstacles and a signal attenuation value corresponding to each type of obstacle, setting partial parameters including reference distance and path attenuation coefficient, establishing a square simulation map in the simulation, carrying out discretization processing on the square simulation map, and setting the three types of obstacles and the signal attenuation value corresponding to each type of obstacle;
step two: binary string coding
According to the first step, N APs which are defaulted to be in working states are initially and uniformly distributed in an area, the position information x, y, the power p and the state k of each wireless AP are set as calculation variables, and when k is 0, the AP is shown to be in the working state; and if the value is 0, the state is closed, then the wireless AP is coded according to the calculation variables x, y, p and k, and after the coding, each wireless AP exists in the form of a 25-bit binary string in the following coding mode: a population has a certain number of individuals, the jth individual rhojExpressed as:
ρj＝(Bj1,Bj2，......BjN) (1)
wherein, Bji＝[ki,xi,yi,αi]|jInformation indicating the ith wireless AP in the jth individual, the wireless AP including a switch state (k)i) Abscissa and ordinate (x)i,yi) And a transmission power (α)i) Information, which is converted to a binary string form, as follows:
Figure BDA0002454808720000081
a set of sizes is ranged in [ U ]l,Uu]The data of (2) is encoded into an h-bit binary string in the following manner:
Figure BDA0002454808720000091
Figure BDA0002454808720000092
Figure BDA0002454808720000093
wherein λ ═ U (U)u-Ul)/(2h-1), the decoding process is the reverse of the encoding process, and the binary string is set to bkbk-1...b1Then, the original value is obtained through decoding:
Figure BDA0002454808720000094
step three: setting parameters
The number of wireless APs and the power variation range are set to [ α ]min,αmax]The number of population iterations is maxgen, and the cross probability in each iteration is PrcThe mutation probability is Prm；
Step four: cross mutation operations
And (3) performing crossing operation on the 2M individuals in the parent according to the probability specified in the step three, randomly mating the 2M individuals, wherein the specific operation is to select a crossing point, cross the binary strings of the two individuals, and generate new two individuals after crossing, as shown in fig. 7, and the pseudo code of the crossing operation is an algorithm:
Figure BDA0002454808720000095
then, introducing mutation operation is realized by randomly placing inverse binary strings, and finally forming a new population, as shown in fig. 8, the algorithm of the mutation operation is as follows:
Figure BDA0002454808720000101
step five: selection operation
Combining the parent population and the new population to form a temporary population containing 4M individuals, carrying out selection operation on the temporary population, sorting the selection operation according to the quantity and total power of the AP of each individual in NSGA-II, distinguishing to different levels, further ranking the individuals of different levels according to the crowdedness, screening out appropriate 2M sub-generation individuals according to the ranking condition of the selection operation, wherein the 2M sub-generation individuals serve as parents of the next cycle, and in the traditional genetic algorithm, the children of the individual with higher fitness are more distributed in the next generation according to the arrangement of the fitness of each individual from high to low, so that the situation that the individual is easy to fall into the local optimal solution is caused; in the improved NSGA-II, different from the traditional genetic algorithm, the filial generation generated by the parent is directly selected, in the process of selecting the NSGA-II, the parent is combined with the filial generation undergoing crossing and mutation to form a temporary population, and the selection operation is carried out on the temporary population, as shown in figure 9, so that the condition that excellent personality is filtered out due to the crossing mutation operation in the early stage can be avoided,
here, the current individual ρ is specified1Is lower than the other individual p simultaneously2Then ρ1Dominating ρ2Recording the individual rhoiSolution set S of dominant other individualsiAnd dominate the individual ρiOf other individuals ViAnd carrying out rapid non-dominant sorting operation on the temporary population, ranking each individual, wherein the operation is shown as an algorithm:
Figure BDA0002454808720000111
through rapid non-dominated sorting, each individual is evaluated with a corresponding rank according to the total power and the number of wireless APs, when a certain individual cannot meet the requirement of complete coverage in an area, the individual is ranked at the bottommost, then the crowding degree of the individuals on the same step is calculated, each individual on the same step is ranked according to the number and the total power of the wireless APs, the crowding degree of the individual with an extreme value in each queue is set to be infinite, and the crowding degree of the other individuals is calculated according to the distribution of the adjacent individuals, wherein the specific calculation method comprises the following steps:
Figure BDA0002454808720000121
wherein, the process of the selection operation follows the following principle: sequentially selecting proper individuals until the number of the next generation of population reaches a specified value; preferentially selecting high-order ladder individuals from individuals positioned at different ladders; individuals located at the same step, preferably with high crowdedness
Step six: judgment of conditions
Judging whether iteration times maxgen of the end loop condition are met or not according to the fifth step, if not, taking the generated filial generation as a parent to continue the loop, returning to the fourth step, and if so, returning to the final generation;
step seven: screening for optimal solutions
And selecting the most appropriate solution set from the last generation of population according to the ranked wireless AP step gradient and the actual demand condition of a producer.
Verification example:
fig. 2 is a 100m by 100m simulation map, which is discretized into a 20 × 20 grid with three types of obstacles. In the initial situation, there are 36 wireless APs with power of 10-35 dbm in the simulation environment, and each wireless AP is in the working state by default (i.e. k is 1). The position and power of each wireless AP are adjusted, so that the sum of power is minimized when the signal coverage rate is 1.
For the sake of close reality, the model is considered from multiple angles such as signal strength, channel interference, coverage area, space environment and the like. The following assumptions are made:
1. when the deployment result meets the requirement that the coverage rate of the target area reaches C0, the area can be effectively covered;
2. n wireless APs are deployed in the network to operate, and the maximum transmission power of each wireless AP is αmaxThe minimum transmission power is αm i n。
3. Propagation loss β is divided into indoor propagation loss β1And attenuation β caused by obstacles2。
4. The minimum power capable of ensuring normal communication quality of the terminal is α0。
5. The area to be covered is a two-dimensional plane S with the area of m, and the area is discretized into m2And in each grid to be covered, the geometric center position of each grid point is a covering target position, and the set is P (x, y). The wireless APs are deployed in a plane S, denoted G ═ AP1,AP2...APN}。
If the jth overlay target Pj(xj,yj),j＝1,2,3....m2The signal received from any wireless AP is greater than or equal to α0Then the grid is considered to be covered by the network.
Indoor wireless propagation model path loss β1The formula is as follows:
Figure BDA0002454808720000141
in formula (1), γ is a path loss exponent, which represents the rate of increase in path loss with distance, and depends on the surrounding environment and the type of building; xσIs a normal random variable of standard deviation σ; d0Is a reference distance; di,jIs the distance between the wireless AP and the test point.
From the ith AP node to the coverage target point PjIs a distance of
Figure BDA0002454808720000142
Wherein, the specific initialized parameters of the wireless AP are shown in table 1
TABLE 1
Figure BDA0002454808720000143
Wherein, considering that some factors obstructing propagation exist in the floor, typical attenuation values of a part of obstacles are introduced as shown in the following table 2:
TABLE 2
Figure BDA0002454808720000151
Attenuation β during transmission is divided into two parts, attenuation β caused by obstacle2And attenuation β of indoor radio propagation itself1。
β＝β1+β2(3)
To sum up, the ith AP is aligned with the target point PjThe coverage probability of (j ∈ M) is expressed by a Boolean type, as shown in the following formula (4):
Figure BDA0002454808720000152
any one of the target positions Pj(j ∈ M) can be covered by multiple wireless APs simultaneously, and the joint coverage probability for the target point is expressed as the following formula (5):
Figure BDA0002454808720000153
the coverage of this region is COV (M, G) as shown in the following formula (6):
Figure BDA0002454808720000154
in order to investigate its redundancy, the coincidence is introduced here. Defining a certain position Pj(j ∈ M), which is a coincidence point if covered by two or more wireless APs at the same timejIs:
Figure BDA0002454808720000161
the calculated coincidence ratio is calculated as shown in the following formula (8):
Figure BDA0002454808720000162
traditionally, wireless APs that are not optimized are always evenly distributed. In this case, power is allocated to the wireless APs, as shown in fig. 3, the 36 wireless APs in the map are uniformly arranged according to the conventional situation, and the area can reach full coverage only when the power allocated to each wireless AP reaches 23.1dbm, and the signal coincidence rate reaches 76.8%. We consider this as the optimum case when the APs are uniformly arranged.
And after the virtual model is built, applying NSGA-II substitution and calculation.
As shown in fig. 4, in the iterative process, the sum of the transmission powers of the first-step individuals always decreases with the iterative process. After 2600 iterations, the maturation was reached. The signal overlapping rate of the optimal batch of individuals changes as shown in fig. 6, and the signal overlapping rate is reduced from 80.8% in the initial state to 32.0% in the final state. The utilization rate of resources is effectively improved.
As shown in fig. 5, the initial number of wireless APs is 36, and all the wireless APs are in an open state. Wherein the red line represents the variation of the number of APs in operation for each individual (feasible solution) in a population during the optimization process, and the blue line represents the variation of the number of APs in operation in the first step (both using the average). After 3400 iterations, the number of wireless APs of the first ladder individual is kept at 26, which indicates that 26 wireless APs are the minimum number of APs that can be used in the case of keeping the area completely covered, and is far lower than the initial 36 wireless APs.
Several top-ranked feasible solutions are analyzed at this time, and as shown in table 3, 7 feasible solutions are located in 3 steps, respectively. The 2 individuals at the first step are all pareto optimal solutions. The feasible solution a can be interpreted as a pareto optimal solution with the minimum number of nodes in the convergence layer, and the feasible solution b is the pareto optimal solution with the minimum total power.
Table 3 partial working examples
Figure BDA0002454808720000171
In the simulation, the power sum of all wireless APs is obviously reduced after the NSGA-II is used, and the aim of reducing energy consumption is fulfilled. In real life, the wireless AP network topology can be optimized through a genetic algorithm by only acquiring power information and environmental conditions of the wireless AP and substituting the power information and the environmental conditions into the model.
According to the table 3, taking the feasible solution a as an example, it is compared with the optimal case when the APs are uniformly arranged, as shown in table 4: the total power of the system is reduced from 7350.3mW before optimization to 4230.3mW, and the energy consumption is saved by 42.4%; the number of the nodes is reduced from the original 36 to 25, and is reduced by 30.6 percent; coverage overlap was also reduced from the initial 76.75% to 32.0%. The optimization effect is more obvious.
TABLE 4 comparison of parameters before and after optimization
Figure BDA0002454808720000172
Figure BDA0002454808720000181
FIG. 6 is a graph showing the variation of the coincidence rate of the signals of the individual in the first step in the iterative process. It can be seen that through the NSGA-II algorithm, the coincidence rate of signals is reduced, and the resource utilization rate is improved.
The method adopts a non-uniform quantization space model design, more accords with the practical requirement, adjusts the distribution position and the power of the wireless AP through a rapid non-dominated genetic algorithm according to the traditional experience and the classical theory and the data of the power information, the signal intensity decay, the channel interference and the like of the wireless AP, further achieves the aim of optimizing the network topology under the condition of meeting the communication requirement, finally achieves the aim of reducing the number of the wireless APs and the total power, observes the change condition of the signal coincidence rate, greatly reduces the signal coincidence rate and effectively improves the resource utilization.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (7)

1. A method for realizing wireless AP deployment optimization based on a rapid non-dominated genetic algorithm is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: determining parameters
According to the real environment, determining a signal attenuation function and signal attenuation caused by obstacles, setting three types of obstacles and a signal attenuation value corresponding to each type of obstacle, setting partial parameters including reference distance and path attenuation coefficient, establishing a square simulation map in the simulation, carrying out discretization processing on the square simulation map, and setting the three types of obstacles and the signal attenuation value corresponding to each type of obstacle;
step two: binary string coding
According to the first step, N APs which are defaulted to be in working states are initially and uniformly arranged in an area, the position information x, y, the power p and the state k of each wireless AP are set as calculation variables, the calculation variables are x, y, p and k, the calculation variables are coded, after coding, each wireless AP exists in the form of a 25-bit binary string, and the coding mode is as follows: a population has a certain number of individuals, the jth individual rhojExpressed as:
ρj＝(Bj1,Bj2，……BjN) (1)
wherein, Bji＝[ki,xi,yi,αi]|jInformation indicating the ith wireless AP in the jth individual, the wireless AP including a switch state (k)i) Abscissa and ordinate (x)i,yi) And a transmission power (α)i) Information, which is converted to a binary string form, as follows:
Figure FDA0002454808710000011
a set of sizes is ranged in [ U ]l,Uu]The data of (2) is encoded into an h-bit binary string in the following manner:
Figure FDA0002454808710000021
Figure FDA0002454808710000022
Figure FDA0002454808710000023
wherein λ ═ U (U)u-Ul)/(2h-1), the decoding process is the reverse of the encoding process, and the binary string is set to bkbk-1...b1Then, the original value is obtained through decoding:
Figure FDA0002454808710000024
step three: setting parameters
The number of wireless APs and the power variation range are set to [ α ]min,αmax]The number of population iterations is maxgen, and the cross probability in each iteration is PrcThe mutation probability is Prm；
Step four: cross mutation operations
Performing cross operation on the 2M individuals in the parent according to the probability specified in the third step, randomly mating the 2M individuals, specifically selecting a cross point, crossing the binary strings of the two individuals, generating new two individuals after crossing, introducing mutation operation, and realizing by randomly placing the reverse binary strings to finally form a new population;
step five: selection operation
Combining the parent population and the new population to form a temporary population containing 4M individuals, selecting the temporary population, sorting the selection operation according to the quantity and total power of the AP of each individual in NSGA-II to obtain different levels, further ranking the individuals of different levels according to the crowdedness of the individuals, and screening out appropriate 2M sub-generation individuals according to the ranking condition of the selection operation, wherein the 2M sub-generation individuals serve as parents of the next cycle;
step six: judgment of conditions
Judging whether iteration times maxgen of the end loop condition are met or not according to the fifth step, if not, taking the generated filial generation as a parent to continue the loop, returning to the fourth step, and if so, returning to the final generation;
step seven: screening for optimal solutions
And selecting the most appropriate solution set from the last generation of population according to the ranked wireless AP step gradient and the actual demand condition of a producer.
2. The method according to claim 1, wherein the method for optimizing the deployment of the wireless AP based on the fast non-dominated genetic algorithm comprises: in the second step, in the process of setting the position information x, y, the power p and the state k of each wireless AP as calculation variables, when k is 0, the AP is in a working state; 0 indicates the off state.
3. The method according to claim 1, wherein the method for optimizing the deployment of the wireless AP based on the fast non-dominated genetic algorithm comprises: in the fourth step, the pseudo code of the cross operation is an algorithm:
Figure FDA0002454808710000031
4. the method according to claim 1, wherein the method for optimizing the deployment of the wireless AP based on the fast non-dominated genetic algorithm comprises: in the fourth step, the algorithm of the mutation operation is as follows:
Figure FDA0002454808710000041
5. the method according to claim 1, wherein the method for optimizing the deployment of the wireless AP based on the fast non-dominated genetic algorithm comprises: in the fifth step, the sorting operation specifically comprises: defining when an individual rho1Is lower than the other individual p simultaneously2Then ρ1Dominating ρ2Recording the individual rhoiSolution set S of dominant other individualsiAnd dominate the individual ρiOf other individuals ViAnd carrying out rapid non-dominant sorting operation on the temporary population, ranking each individual, wherein the operation is shown as an algorithm:
Figure FDA0002454808710000042
Figure FDA0002454808710000051
6. the method according to claim 5, wherein the method for optimizing the deployment of the wireless AP based on the fast non-dominated genetic algorithm comprises: in the fifth step, through rapid non-dominated sorting, each individual is evaluated with a corresponding rank according to the total power and the number of wireless APs, when a certain individual cannot meet the requirement of complete coverage in an area, the individual is ranked at the bottommost, then, the crowding degree of the individuals on the same step is calculated, each individual on the same step is ranked according to the number and the total power of the wireless APs, the crowding degree of the individual having an extreme value in each queue is set to infinity, and the crowding degree of the other individuals is calculated according to the distribution of the adjacent individuals, wherein the specific calculation method is as follows:
Figure FDA0002454808710000052
Figure FDA0002454808710000061
7. the method according to claim 1, wherein the method for optimizing the deployment of the wireless AP based on the fast non-dominated genetic algorithm comprises: in the fifth step, the selecting operation process follows the following principle: sequentially selecting proper individuals until the number of the next generation of population reaches a specified value; preferentially selecting high-order ladder individuals from individuals positioned at different ladders; individuals located at the same step are preferentially selected as those with high crowdedness.
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