CN113573322B - Multi-target area sensor network coverage optimization method based on improved genetic algorithm - Google Patents

Multi-target area sensor network coverage optimization method based on improved genetic algorithm Download PDF

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CN113573322B
CN113573322B CN202110838171.1A CN202110838171A CN113573322B CN 113573322 B CN113573322 B CN 113573322B CN 202110838171 A CN202110838171 A CN 202110838171A CN 113573322 B CN113573322 B CN 113573322B
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王迪晟
秦会斌
吴建锋
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Huzhou South Taihu Electronic Technology Research Institute
Hangzhou Dianzi University
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Abstract

The invention discloses a multi-target area sensor network coverage optimization method based on an improved genetic algorithm, which comprises the following steps of S1, constructing a coding mode of a decision variable and a mathematical model of a fitness function according to an actual application scene; s2, calculating a fitness function value of each target area according to the position, the monitoring visual angle and the dynamic monitoring target position of the initially distributed sensor network; s3, constructing a reference plane and a reference point required by an algorithm by taking the fitness function as an optimization target and the initial attribute of the sensor network as an input value; and S4, optimizing the established mathematical model according to the provided improved genetic algorithm. The invention optimizes three objective functions of overall coverage, monitoring coverage redundancy and monitoring coverage average redundancy in practical application based on an improved genetic algorithm, so that the overall optimization is in an optimal balance.

Description

Multi-target area sensor network coverage optimization method based on improved genetic algorithm
Technical Field
The invention belongs to the field of sensor network intellectualization, and relates to a multi-target area sensor network coverage optimization method based on an improved genetic algorithm.
Background
The sensor network can improve the capability of human-computer remote interaction. The sensor network can monitor and collect information of various monitoring targets in a network deployment area in real time, and monitoring and tracking of the targets in a specified range are achieved. With the continuous development of embedded technology, distributed information processing technology and narrowband internet of things technology, wireless sensor networks equipped with monitoring equipment have been widely applied to various application scenarios.
When monitoring a set of targets using a vision sensor, it is crucial how to improve the monitoring efficiency. Particularly, in some special applications, such as industrial control and road monitoring management, there are high requirements for monitoring quality, such as overall monitoring coverage and coverage redundancy. A monitoring target is said to be covered if it is sensed by at least one sensor, and a sensor is said to be redundantly covered if it is sensed by two or more sensors. For example, in road monitoring management, it is required that some monitoring target points can be covered redundantly, so as to prevent accidental loss of a single sensor due to faults of hardware, network and the like, and avoid waste of hardware resources caused by excessive redundancy of a certain monitoring target. At present, an optimization algorithm is not applied to solve the problem of optimization of redundant coverage of a sensor network. The invention aims to improve the monitoring coverage rate of the sensor network as much as possible on the premise of keeping the redundancy of the sensor network in a reasonable interval.
The deficiency of the prior art is that,
1. when the multi-objective optimization problem is solved, a plurality of objective functions are generally given weight coefficients and then accumulated to be converted into the optimization problem of a single objective, and finally an optimal solution is solved. This requires a priori estimation of the weighting coefficients, which may be too selective to achieve the desired result. Method for solving redundancy coverage problem by optimization algorithm
2. The intelligent algorithm has strong tendency of individuals in the middle period of iteration and is easy to trap in local optimum in the searching process.
Disclosure of Invention
The invention provides a multi-target area sensor network coverage optimization method based on an improved genetic algorithm for solving the problems, which comprises the following steps:
s1, constructing a coding mode of a decision variable and a mathematical model of a fitness function according to an actual application scene;
s2, calculating a fitness function value of each target area according to the position, the monitoring visual angle and the dynamic monitoring target position of the initially distributed sensor network;
s3, constructing a reference plane and a reference point required by an algorithm by taking the fitness function as an optimization target and the initial attribute of the sensor network as an input value;
and S4, optimizing the established mathematical model according to the provided improved genetic algorithm.
Preferably, said S1 comprises the steps of:
s11, discretizing a target area, wherein the specific precision can be refined according to an actual application scene;
s12, determining the initial position coordinates (x, y) of each sensor, abstracting the attributes of each sensor into (alpha, theta, r), wherein alpha is a rotation angle, theta is a monitoring wide angle, r is a monitoring radius, the attributes of each sensor are the same or different, and the effective monitoring area of each sensor is set to be a fan-shaped area with the vertex being the position of the sensor, the radian being theta and the radius being r;
s13, judging the coordinate to be (x) i ,y i ) Is monitored by i Whether or not it is coordinated as (x) j ,y j ) Monitoring node p j The model of perception is that,
Figure BDA0003177923920000021
wherein
Figure BDA0003177923920000022
For monitoring a target s i To the monitoring node p j Alpha is a rotation angle, theta is a monitoring wide angle, r is a monitoring radius, beta is s i 、p j The angle between the connecting line and the positive direction of the x axis of the coordinate axis.
Preferably, said S2 comprises the steps of:
S21，calculating a fitness function through the perception model constructed in S13
Figure BDA0003177923920000023
Figure BDA0003177923920000031
For sensing a target node s i The number of monitoring nodes of (1), wherein P is a monitoring node set; if f(s) i ,P)>0, then note f union (s i P) =1, and represents a node s i Has been sensed, otherwise f union (s i P) =0; if f(s) i ,P)>1, then note f redundant (s i P) =1, and represents a node s i Has been redundantly covered, otherwise f redundant (s i P) =0, where m is the number of target nodes and N is the number of monitoring nodes;
s22, the integral coverage rate of the sensor network is defined as:
Figure BDA0003177923920000032
s23, the redundant coverage rate of the sensor network is defined as:
Figure BDA0003177923920000033
s24, the sensor network monitoring coverage average redundancy is defined as:
Figure BDA0003177923920000034
preferably, the S3 includes the steps of:
s31, initialization of setting algorithm parameters comprises initial cross probability p start Terminating cross probability p end The population number npop and the maximum iteration number maxiter; using improved genetic algorithms, with f 1 ,f 2 ,f 3 Monitoring according to sensor network as fitness functionCalculating fitness function value (f) of each individual in the initial population by the initial attribute of the node and the current target node position 1 ,f 2 ,f 3 )；
S32, obtaining a fitness function value (f) 1 ,f 2 ,f 3 ) Obtain the ideal point
Figure BDA0003177923920000035
Ideal point
Figure BDA0003177923920000036
Setting as a fitness function value (f) in the population 1 ,f 2 ,f 3 ) According to the obtained ideal point
Figure BDA0003177923920000037
And an objective function f i Obtaining a converted fitness value f' i The structural formula is as follows,
Figure BDA0003177923920000038
s33, constructing an extra point according to the converted fitness value, constructing a formula ASF (x, w) as,
Figure BDA0003177923920000039
wherein x is a member of the group S t A population of individuals;
generating a vector z in a spatial coordinate system from the constructed additional points i,max The structural formula is as follows,
Figure BDA00031779239200000310
wherein
Figure BDA0003177923920000041
Is ASF (x, w) i ) Taking the vector obtained when the minimum value is obtained, and calculatingDe z 1 ,max ,z 2,max ,z 3,max Sequentially calculating three vectors, namely the intercept of a plane and a coordinate axis in a three-dimensional space, and constructing a reference plane;
s34, selecting a reference point according to the obtained reference plane, uniformly dividing the L-dimensional simplex into H equal parts along each direction, calculating to obtain the number of reference points, connecting the space origin with the reference point to obtain a reference line, wherein the number K of the reference points is calculated according to the formula,
Figure BDA0003177923920000042
s35, normalizing the objective function values, calculating the association degree of the individuals in the population according to the reference lines, namely the vertical distance between the individual normalized objective function values and the nearest reference line in the space, wherein the closer the vertical distance is, the higher the association degree is, sorting and screening the population according to the association degree, the normalization formula is,
Figure BDA0003177923920000043
preferably, the S4 includes the steps of:
s41, sorting and screening the parents according to the relevance to generate offspring populations, wherein the population updating formula is as follows,
Figure BDA0003177923920000044
wherein F acc Is a scale factor representing the degree of trust for the parent, controlling the difference between children and parent, p c For cross probability, iter denotes the current iteration number, c parent1 、c parent2 、c parent3 Randomly selecting different individuals from the parent population;
s42, in order to improve the ability of the population to jump out of the local optimum in the iterative process, a linear variation factor is introduced,
Figure BDA0003177923920000045
wherein p is start As initial cross probability, p end For terminating the cross probability, iter represents the current iteration times, and maximer represents the maximum iteration times;
s43, calculating the adaptability value of the offspring population, normalizing by the formula,
Figure BDA0003177923920000046
and S44, calculating the association degree of the individuals according to the fitness value, carrying out non-dominated sorting, and selecting npop individuals to merge into a new population until the maximum iteration number is met.
The beneficial effects of the invention at least comprise:
a multi-target area sensor network coverage optimization method based on an improved genetic algorithm is provided. According to the method, a non-dominated sorting method is introduced in the population screening process, the objective function does not need to be subjected to weighted accumulation to be converted into a single-objective optimization problem, and finally a solution result is a group of optimization solution sets; the differential operator and the self-adaptive cross coefficient are introduced in the process of generating the offspring population, the differential operator increases the number of parent individuals in the cross process, the diversity of the offspring population is increased, the self-adaptive cross coefficient keeps a high value in the initial stage of the algorithm to accelerate the optimization process, the algorithm can be ensured to be gradually converged in the later stage, and then the convergence of the algorithm is ensured and the diversity of solution set is obtained.
Under the application scene that the position of a visual sensor network is fixed and unchanged, a perception model is established, and the coverage performance of a plurality of dynamic targets in a monitoring area is ensured by changing the rotation angle of the visual sensor; according to the method, non-dominated sorting is utilized, weighting accumulation is not needed to be carried out on a plurality of objective functions, and errors of factors considered in prior estimation on an optimization result are effectively avoided; a difference operator and a self-adaptive cross coefficient are introduced, the diversity of a population and the convergence of an algorithm in an iterative process are guaranteed, and three objective functions of overall coverage, monitoring coverage redundancy and monitoring coverage average redundancy in practical application are optimized based on an improved genetic algorithm, so that the overall optimization balance is achieved.
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FIG. 1 is a flowchart illustrating the steps of a method for optimizing the coverage of a multi-target area sensor network based on an improved genetic algorithm according to an embodiment of the present invention;
FIG. 2 is a graph comparing the overall coverage rate of the multi-target area sensor network coverage optimization method based on the improved genetic algorithm of the embodiment of the present invention with the original genetic algorithm of the prior art;
FIG. 3 is a comparison graph of the redundancy coverage of the multi-objective regional sensor network coverage optimization method based on the improved genetic algorithm of the embodiment of the present invention and the original genetic algorithm of the prior art;
FIG. 4 is a comparison graph of the average coverage redundancy of the multi-target area sensor network coverage optimization method based on the improved genetic algorithm and the original genetic algorithm in the prior art according to the embodiment of the present invention;
FIG. 5 is a coverage effect diagram of a set of solutions obtained by the coverage optimization method for a multi-target area sensor network based on the improved genetic algorithm according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
On the contrary, the invention is intended to cover alternatives, modifications, equivalents and alternatives which may be included within the spirit and scope of the invention as defined by the appended claims. Furthermore, in the following detailed description of the present invention, certain specific details are set forth in order to provide a better understanding of the present invention. It will be apparent to one skilled in the art that the present invention may be practiced without these specific details.
Referring to fig. 1, the method comprises the following steps:
s1, constructing a coding mode of a decision variable and a mathematical model of a fitness function according to an actual application scene;
s2, calculating a fitness function value of each target area according to the position, the monitoring visual angle and the dynamic monitoring target position of the initially distributed sensor network;
s3, constructing a reference plane and a reference point required by an algorithm by taking the fitness function as an optimization target and the initial attribute of the sensor network as an input value;
and S4, optimizing the established mathematical model according to the proposed improved genetic algorithm.
In a specific embodiment, each of the steps specifically includes:
s1 comprises the following steps:
s11, discretizing a target area, wherein the specific precision can be refined according to an actual application scene;
s12, determining initial position coordinates (x, y) of each sensor, abstracting attributes of each sensor to be (alpha, theta, r), wherein alpha is a rotation angle, theta is a monitoring wide angle, r is a monitoring radius, the attributes of each sensor are the same or different, and an effective monitoring area of each sensor is set to be a fan-shaped area with the vertex being the position of the sensor, the radian being theta and the radius being r;
s13, judging the coordinate to be (x) i ,y i ) Is monitored by i Whether or not it is coordinated as (x) j ,y j ) Monitoring node p j The model of perception is that,
Figure BDA0003177923920000071
wherein
Figure BDA0003177923920000072
For monitoring a target s i To the monitoring node p j Is a rotation angle, theta is a monitoring wide angle, r is a monitoring radius, beta is s i 、p j The angle between the connecting line and the positive direction of the x axis of the coordinate axis.
S2 comprises the following steps:
s21, sense of construction in S13The known model further calculates a fitness function and records the fitness function
Figure BDA0003177923920000073
Figure BDA0003177923920000074
For sensing a target node s i The number of monitoring nodes of (1), wherein P is a monitoring node set; if f(s) i ,P)>0, then note f union (s i P) =1, and represents a node s i Has been sensed, otherwise f union (s i P) =0; if f(s) i ,P)>1, then, note f redundant (s i P) =1, and represents a node s i Has been redundantly covered, otherwise f redundant (s i P) =0, where m is the number of target nodes and N is the number of monitoring nodes;
s22, the integral coverage rate of the sensor network is defined as:
Figure BDA0003177923920000075
s23, the redundant coverage rate of the sensor network is defined as follows:
Figure BDA0003177923920000076
s24, the sensor network monitoring coverage average redundancy is defined as:
Figure BDA0003177923920000077
s3 comprises the following steps:
s31, initialization of setting algorithm parameters comprises initial cross probability p start Terminating cross probability p end The population number npop and the maximum iteration number maxiter; using improved genetic algorithms, with f 1 ,f 2 ,f 3 As a fitness function, monitoring the initial attribute of the node and the current target node according to the sensor networkThe fitness function value (f) of each individual in the initial population is calculated by position 1 ,f 2 ,f 3 )；
S32, obtaining a fitness function value (f) 1 ,f 2 ,f 3 ) Obtain the ideal point
Figure BDA0003177923920000078
Ideal point
Figure BDA0003177923920000079
Set as fitness function value (f) in population 1 ,f 2 ,f 3 ) According to the obtained ideal point
Figure BDA00031779239200000710
And an objective function f i To obtain a converted fitness value f' i The structural formula is as follows,
Figure BDA0003177923920000081
s33, constructing an extra point according to the converted fitness value, constructing a formula ASF (x, w) as,
Figure BDA0003177923920000082
wherein x is an individual, S t A population of individuals;
generation of a vector z in a spatial coordinate system from constructed additional points i,max The structural formula is as follows,
Figure BDA0003177923920000083
wherein
Figure BDA0003177923920000084
Is ASF (x, w) i ) Taking the vector taken when the minimum value is taken, and calculating the obtained z 1 ,max ,z 2,max ,z 3,max Sequentially calculating three vectors, namely intercept of a plane and a coordinate axis in a three-dimensional space, and constructing a reference plane;
s34, selecting a reference point according to the obtained reference plane, uniformly dividing the L-dimensional simplex into H equal parts along each direction, calculating to obtain the number of reference points, connecting the space origin with the reference point to obtain a reference line, wherein the number K of the reference points is calculated according to the formula,
Figure BDA0003177923920000085
s35, normalizing the objective function values, calculating the association degree of the individuals in the population according to the reference lines, namely the vertical distance between the individual normalized objective function values and the nearest reference line in the space, wherein the closer the vertical distance is, the higher the association degree is, sorting and screening the population according to the association degree, the normalization formula is,
Figure BDA0003177923920000086
s4 comprises the following steps:
s41, sorting and screening parent generations according to the relevance to generate offspring populations, wherein the population updating formula is as follows,
Figure BDA0003177923920000087
wherein F acc Is a scale factor representing the degree of trust for the parent, controlling the difference between children and parent, p c For cross probability, iter denotes the current iteration number, c parent1 、c parent2 、c parent3 Randomly selecting different individuals from the parent population;
s42, introducing linear variation factors for improving the ability of the population to jump out of the local optimum in the iterative process,
Figure BDA0003177923920000091
wherein p is start To initial cross probability, p end For terminating the cross probability, iter represents the current iteration times, and maxim represents the maximum iteration times;
s43, calculating the fitness value of the offspring population, normalizing the fitness value by the normalized formula,
Figure BDA0003177923920000092
and S44, calculating the association degree of the individuals according to the fitness value, carrying out non-dominated sorting, and selecting npop individuals to merge into a new population until the maximum iteration number is met.
The method comprises the steps of establishing a perception model according to an actual application scene; compared with the traditional method for weighting and accumulating multiple targets, the non-dominated sorting is introduced, so that errors caused by the introduction of human factors in the setting link of weight coefficients of the optimization results are avoided; a difference operator is introduced in the iterative process, so that the individual tendency in the iterative process is reduced, and the diversity of the population is improved; and self-adaptive cross coefficients are introduced to ensure the convergence of the algorithm.
To illustrate the technical effects of the present invention, fig. 2 is a comparison of the overall coverage optimized by the original genetic algorithm of the prior art and the genetic algorithm after the improvement of the present invention, fig. 3 is a comparison of the redundant coverage optimized by the original genetic algorithm of the prior art and the genetic algorithm after the improvement of the present invention, fig. 4 is a comparison of the average coverage redundancy optimized by the original genetic algorithm of the prior art and the genetic algorithm after the improvement of the present invention, and fig. 5 is a coverage effect map of a set of solutions obtained after the optimization of the genetic algorithm after the improvement of the present invention.
The method provided by the invention can improve the overall redundant coverage rate and the average coverage redundancy rate of the sensor network on the premise of keeping the overall coverage rate. The method optimizes three objective functions of overall coverage, monitoring coverage redundancy and monitoring coverage average redundancy in practical application by using the improved genetic algorithm, so that the overall coverage of the sensor network is optimally balanced, and the coverage performance and robustness of the sensor network are further improved.
The overall coverage of the original genetic algorithm and the improved genetic algorithm of the invention is compared by FIG. 2, and the objective function f 1 The monitoring coverage rate of the monitoring node to the target node is shown, the larger the numerical value is, the better the coverage optimization effect of the sensor network is, and f 1 The expression is given in S22.
FIG. 3 compares the redundancy coverage of the original genetic algorithm and the improved genetic algorithm of the present invention, the objective function f 2 Representing the proportion of the target nodes covered by the redundancy monitoring to the whole target set, the larger the numerical value is, the better the redundancy coverage optimization effect of the sensor network is, and f 2 The expression is given in S23.
FIG. 4 is a comparison of the average coverage redundancy optimized by the original genetic algorithm and the improved genetic algorithm of the present invention, with the objective function f 3 The average value of the number of the monitoring nodes sensing each target node is shown, the higher the value is, the better the optimization effect is shown, f 3 The expression is given in S24.
Fig. 5 is a coverage effect graph of a group of solutions obtained after genetic algorithm optimization is improved, an asterisk indicates a target node, a sector area is a sensing range of a monitoring node, and it can be seen that, except for target nodes with coordinates (25, 51), (45, 25) which are all located in the sensing range of the monitoring node, other target nodes are monitored and covered. The convergence curves of fig. 3 and fig. 4 show that the method provided by the present invention can significantly improve the overall redundant coverage and the average coverage redundancy of the sensor network while maintaining the overall coverage. The method optimizes three objective functions of overall coverage, redundant coverage and monitoring coverage average redundancy in practical application based on the improved genetic algorithm, so that the overall coverage of the sensor network is optimally balanced, and the coverage performance and robustness of the sensor network are further improved.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (1)

1. The multi-target area sensor network coverage optimization method based on the improved genetic algorithm is characterized by comprising the following steps of:
s1, constructing a coding mode of a decision variable and a mathematical model of a fitness function according to an actual application scene;
s2, calculating a fitness function value of each target area according to the position, the monitoring visual angle and the dynamic monitoring target position of the sensor network which is initially distributed;
s3, constructing a reference plane and a reference point required by an algorithm by taking the fitness function as an optimization target and the initial attribute of the sensor network as an input value;
s4, optimizing the established mathematical model according to the proposed improved genetic algorithm;
the S1 comprises the following steps:
s11, discretizing a target area, wherein the specific precision can be refined according to an actual application scene;
s12, determining initial position coordinates (x, y) of each sensor, abstracting attributes of each sensor to be (alpha, theta, r), wherein alpha is a rotation angle, theta is a monitoring wide angle, r is a monitoring radius, the attributes of each sensor are the same or different, and an effective monitoring area of each sensor is set to be a fan-shaped area with the vertex being the position of the sensor, the radian being theta and the radius being r;
s13, judging the coordinate to be (x) i ,y i ) Is monitored by i Whether or not it is coordinated as (x) j ,y j ) Monitoring node p j The model of perception is that,
Figure FDA0003846573540000011
wherein
Figure FDA0003846573540000012
For monitoring a target s i To the monitoring node p j Of Euclidean distance, αIs the rotation angle, theta is the monitoring wide angle, r is the monitoring radius, beta is s i 、p j The included angle between the connecting line and the positive direction of the x axis of the coordinate axis;
the S2 comprises the following steps:
s21, calculating a fitness function through the perception model constructed in the S13, and recording the fitness function
Figure FDA0003846573540000013
For sensing a target node s i The number of monitoring nodes of (1), wherein P is a monitoring node set; if f(s) i ,P)>0, then, remember f union (s i P) =1, represents node s i Has been sensed, otherwise f union (s i P) =0; if f(s) i ,P)>1, then note f redundant (s i P) =1, and represents a node s i Has been redundantly covered, otherwise f redunaant (s i P) =0, where m is the number of target nodes and N is the number of monitoring nodes;
s22, the integral coverage rate of the sensor network is defined as:
Figure FDA0003846573540000021
s23, the redundant coverage rate of the sensor network is defined as:
Figure FDA0003846573540000022
s24, the sensor network monitoring coverage average redundancy is defined as:
Figure FDA0003846573540000023
the S3 comprises the following steps:
s31, initialization of setting algorithm parameters comprises initial cross probability p start Terminating cross probability p end Number of populations npop, max stackThe order number maxiter; using improved genetic algorithms, with f 1 ,f 2 ,f 3 Calculating a fitness function value (f) of each individual in the initial population according to the initial attribute of the sensor network monitoring node and the current target node position as a fitness function 1 ,f 2 ,f 3 )；
S32, obtaining a fitness function value (f) 1 ,f 2 ,f 3 ) Obtain the ideal point
Figure FDA0003846573540000024
Ideal point
Figure FDA0003846573540000025
Setting as a fitness function value (f) in the population 1 ,f 2 ,f 3 ) According to the obtained ideal point
Figure FDA0003846573540000026
And an objective function f i To obtain a converted fitness value f' i The structural formula is as follows,
Figure FDA0003846573540000027
s33, constructing an extra point according to the converted fitness value, constructing a formula ASF (x, w) as,
Figure FDA0003846573540000028
wherein x is an individual, S t A population of individuals;
generating a vector z in a spatial coordinate system from the constructed additional points i,max The structural formula is as follows,
Figure FDA0003846573540000029
wherein
Figure FDA00038465735400000210
Is ASF (x, w) i ) Taking the vector taken when the minimum value is obtained, and sequentially calculating three obtained vectors z 1,max ,z 2,max ,z 3,max Namely, the intercept of the plane and a coordinate axis in a three-dimensional space, and constructing a reference plane;
s34, selecting a reference point according to the obtained reference plane, uniformly dividing the L-dimensional simplex into H equal parts along each direction, calculating to obtain the number of reference points, connecting the space origin with the reference point to obtain a reference line, wherein the number K of the reference points is calculated by the formula,
Figure FDA0003846573540000031
s35, normalizing the objective function values, calculating the association degree of the individuals in the population according to the reference lines, namely the vertical distance between the individual normalized objective function values and the nearest reference line in the space, wherein the closer the vertical distance is, the higher the association degree is, sorting and screening the population according to the association degree, the normalization formula is,
Figure FDA0003846573540000032
the S4 comprises the following steps:
s41, sorting and screening the parents according to the relevance to generate offspring populations, wherein the population updating formula is as follows,
Figure FDA0003846573540000033
wherein F acc Is a scale factor representing the degree of trust for the parent, controlling the difference between children and parent, p c For the cross probability, iter denotes the current iteration number, c parent1 、c parent2 、c parent3 For randomization in the parent populationA selection of different individuals;
Figure FDA0003846573540000034
the j dimension variable of parent individual of parent1 of the iter iteration number;
Figure FDA0003846573540000035
the jth dimension variable of the ith population at the iter +1 th time;
s42, in order to improve the ability of the population to jump out of the local optimum in the iterative process, a linear variation factor is introduced,
Figure FDA0003846573540000036
wherein p is start To initial cross probability, p end For terminating the cross probability, iter represents the current iteration times, and maximer represents the maximum iteration times;
s43, calculating the fitness value of the offspring population, normalizing the fitness value by the normalized formula,
Figure FDA0003846573540000037
and S44, calculating the relevance of the individuals according to the fitness value, carrying out non-dominated sorting, and selecting npop individuals to be combined into a new population until the maximum iteration number is met.
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