CN104392412B - Compressed sensing signal recovery method based on evolution orthogonal matching pursuit - Google Patents

Abstract

The invention discloses a kind of signal recovery method based on evolution orthogonal matching pursuit, mainly in solution compressed sensing, traditional tracing algorithm is excessively greedy, and backdating capability is poor and recovers the low problem of accuracy rate.Its technical scheme is：The framework of evolutionary computation is incorporated into compressed sensing signal and recovers central；The problem that atom is selected is converted into the process of the population optimizing based on heuristic search；In conjunction with the dependency of observation error in conventional greedy tracing algorithm and atom, define a kind of activity functions to measure the selected probability of each atom；By activity functions, have devised intersection and the mutation operator of weak greediness, so that more atom is possible to be chosen, increased the reachable tree of atom searching during signal recovers.Experiment shows, the compressed sensing for signal is recovered, and the present invention has higher recovery probability and less restoration errors than traditional greedy tracing algorithm, can be used for the one-dimensional signal and two dimensional image signal recovery problem under low sampling rate random observation.

Description

Compressed sensing signal recovery method based on evolution orthogonal matching pursuit

Technical field

The invention belongs to signal processing technology field, particularly to a kind of compressed sensing signal recovery method.Can be used for one The dimensional signal and two dimensional image signal recovery problem under low sampling rate random observation.

Background technology

Compressed sensing is a kind of efficient signal acquisition means, and it only leads to too small amount of observation and can recover original letter Number.The basic assumption of compressed sensing is：Signal can be organized the sparsely linear expression of base by certain, and that is, most of atomic are Zero, only only a few atomic is non-zero.Under this assumption, by meeting the observation of certain condition, you can extensive exactly Appear again signal.Because compressed sensing is non-convex underdetermined problem, it is difficult to provide a closed solution form.Such issues that solution, is the most frequently used Technology be greedy follow the trail of, classical algorithm has match tracing, orthogonal matching pursuit, subspace is followed the trail of, the orthogonal coupling of segmentation chases after Track and regularization orthogonal matching pursuit.

The basic thought of orthogonal matching pursuit algorithm is：Initialization observation error first is observation vector, in each iteration In, the inner product of each atom in calculating observation error and compressed sensing matrix；Then, select the former of corresponding inner product maximum absolute value Son is in the middle of supported collection, and calculates the coefficient of atom in supported collection with method of least square；Finally, update observation error, enter Next iteration.By this iterative process, so that observation error is gradually reduced, realize primary signal is approached.

Subspace tracing algorithm is improved by orthogonal matching pursuit algorithm, and it introduces back trace technique can not to eliminate The atom of letter, its basic thought is：Assume atom nonzero coefficient number be K, first, initialization observation error be observation to Amount, and calculating observation error and the inner product of each atom in compressed sensing matrix, K atom of inner product maximum absolute value is added To in supported collection, then seek the coefficient of this K atom using method of least square, and update observation error；In each iteration, Again in calculating observation error and compressed sensing matrix each atom inner product, and the K atom by inner product maximum absolute value It is added in supported collection, this results in the supported collection of 2K atom；Then, solve this 2K atom using method of least square Coefficient；Afterwards, by K reservation of 2K atomic maximum absolute value in supported collection, remaining atom is deleted, such Supported collection to a K atom；Method of least square is recycled to solve the coefficient of this K atom；Finally, update observation by mistake Difference, enters next iteration.

Although the innovatory algorithm based on orthogonal matching pursuit for the many obtains very big for signaling protein14-3-3 probability and error Lifting, but due to the limitation such as matching pursuit algorithm itself is excessively greedy and hunting zone is limited, so that search is fallen into Enter local optimum.

Content of the invention

It is an object of the invention to improving, traditional tracing algorithm is excessively greedy, the problem of backdating capability difference, to improve signal Recovery probability and recover precision.It is a kind of compressed sensing signal recovery method based on evolution orthogonal matching pursuit, for right The one-dimensional signal and two dimensional image signal recovery problem under low sampling rate random observation.The present invention is under the framework of evolutionary computation To solve compressed sensing signal recovery problems, gene is introduced according to the dependency size of observation error in greedy algorithm and atom The concept of activity, by the use of gene activity as the heuristic knowledge of whole population, to operate the intersection between Different Individual and change Different, so that whole population being capable of constantly iteration optimizing.

The technical scheme is that：Initialize parent population first, calculate wherein all individual fitness and gene Activity, and record optimum individual.Then the individuality in parent population is matched at random two-by-two, according to gene activity to every a pair Individual enforcement crossover operation, the new individual obtaining is stored in progeny population, and calculates their fitness and gene activity.It Afterwards, row variation is entered to each of progeny population individuality according to overall gene activity, often a variation individual will in time more Its fitness new, gene activity and overall gene activity.Finally, according to fitness quality, select new in parent and filial generation Parent population in next iteration, until iteration stopping.Its concrete steps includes as follows：

(1) input compressed sensing matrix D_csWith observation vector y, initialize one containing S individual parent population P_f= {p_i}_1≤i≤S, put enumerator t=0；

(2) calculate parent populationFitness and gene activity, and to record the maximum individuality of fitness be optimum Body p_best；

(3) to parent populationCarry out crossover operation, obtain progeny population

(4) calculate progeny populationFitness and gene activity；

(5) to progeny populationCarry out mutation operation, update in mutation process each individual fitness, gene activity and Overall gene activity；

(6) from parent populationAnd progeny populationIn select new parent populationAnd update optimum individual p_best, put enumerator t=t+1；

(7) set maximum iteration time as T_maxIf, t<T_max, return to step (3)；Otherwise, export optimal result.

Present invention incorporates evolutionary computation and greedy tracer technique, the solution of sparse coefficient in compressed sensing is converted into weak Greedy heuristic population search procedure, and it is introduced into the dependency of observation error and atom in greedy algorithm as kind of a group hunting Heuristic knowledge, it has the advantage that：

(A), the problem that conventional greedy tracing algorithm is absorbed in local optimum is improved based on the heuristic search of colony；

(B), the recovery probability for one-dimensional signal and recovery precision are significantly improved；

(C), for the recovery of two dimensional image, there is less restoration errors and less blocking effect.

It is demonstrated experimentally that for One-dimensional simulation signaling protein14-3-3, the present invention has higher extensive than traditional greedy tracing algorithm Multiple probability and less restoration errors.For the recovery of two dimensional image, the present invention is higher than traditional greedy tracing algorithm has Y-PSNR PSNR and less restoration errors.

Brief description

Fig. 1 is the overall flowchart of the present invention；

Fig. 2 is the one-dimensional signal recovery effects contrast that the present invention and other methods obey standard just too distribution for coefficient；

Fig. 3 is that the present invention obeys -1 to 1 equally distributed one-dimensional signal recovery effects contrast with other methods for coefficient；

Fig. 4 is that the present invention is contrasted for the recovery effects of two dimensional image Lena with other methods；

Fig. 5 is that the present invention is contrasted for the restoration errors of two dimensional image Lena with other methods；

Specific embodiment

With reference to Fig. 1, the present invention to implement step as follows：

Step 1, initialization one is containing 16 individual parent populations

1.1) input compressed sensing matrix D_csWith observation vector y, putting parent population is empty set

1.2) calculate compressed sensing matrix D_csMiddle atom and the dependency c of observation vector y：

Wherein, | | represent the absolute value seeking vector element；

1.3) by descending for the element in vectorial c sequence：Find a group index sequence { λ₁,λ₂,…,λ_NSo that c [λ₁]≥c[λ₂]≥…≥c[λ_N], wherein c [λ_n] represent the λ of vectorial c_nIndividual element, N is signal dimension；

1.4) generate a full 0 individuality p_i=[0,0 ..., 0], puts p_i[λ_i]=1, wherein p_i[λ_i] represent individual p_i? λ_iIndividual gene；

1.5) by individual p_iIt is added in parent populationPut i=i+1；

1.6) if i≤16, return to step 1.4；Otherwise, export parent population

Step 2, calculates parent populationFitness and gene activity, and to record the maximum individuality of fitness be optimum Individual p_best.

2.1) for parent populationIn each individual p, solve its sparse coefficient vector α, be calculated as follows：

Wherein α_pRepresent the subvector that the position being 1 with gene in individual p is extracted from vectorial α for index,Represent with In individual p, gene is the subvector that 0 position is index extracts from vectorial α,Represent the position being 1 with gene in individual p For index from matrix D_csThe submatrix that the column vector of middle extraction is constituted, subscriptRepresent the pseudoinverse seeking matrix, 0 one element of expression It is all 0 vector；

2.2) seek the fitness value of individual p, be calculated as follows：

Wherein, | | | |₂For calculating 2 norms of vector；

2.3) calculate the gene activity of individual p, be calculated as follows：

Wherein U is normaliztion constant, is equal toThe maximum of middle element；

2.4) individual record maximum for fitness value is optimized individual p_best.

Step 3, to parent populationCarry out crossover operation, obtain progeny population

3.1) set progeny population as empty set：By parent populationIn individuality match two-by-two at random, obtain 8 right Individual (p_i,p_j)；

3.2) to every a pair individual (p_i,p_j), find the different index set Λ of gene under their same positions：

Wherein, p_i[λ] represents individual p_iλ position gene；

3.3) find individual p_iAnd p_jThe position of gene activity maximum in index ΛWith

Wherein, l_i[λ] represents individual p_iThe activity value of λ position gene；

3.4) exchange individual p_iAnd p_jGene position:IfPutObtain new individual p_i', putObtain new individual p '_j；Otherwise, putObtain new individual p_i', put? To new individual p '_j；

3.5) by two new individuals p_i' and p '_jIt is added to progeny populationRepeat step 3.2 to 3.5 Operation, until all individualities complete to intersect.

Step 4, calculates progeny populationFitness and gene activity.

To progeny populationIn all individualities, calculate their fitness and gene activity according to step 2.1 to 2.3.

Step 5, to progeny populationCarry out mutation operation, update each individual fitness in mutation process, gene is lived Property and overall gene activity.

5.1) put i=1；

5.2) calculate progeny populationAverage degree of rarefication K_mean, it is calculated as follows：

Wherein p [j] represents j-th gene of individual p, and N is signal length；

5.3) calculate progeny populationOverall gene activity, be calculated as follows：

Wherein l_jRepresent the gene activity of j-th individuality；

5.4) calculate individual p_iDegree of rarefication K_i：

5.5) judge individual p_iDegree of rarefication K_iWith populationAverage degree of rarefication K_meanSize, and according to magnitude relationship Carry out mutation operation；

5.5.1) if K_i≤K_mean, recording individual p_iMiddle genic value is 0 index set：

Λ=λ | p_i[λ]=0,1≤λ≤N },

Find the position λ of overall gene activity L maximum in index set Λ_max：

Put individual p_iλ_maxIndividual gene is 1, i.e. p_i[λ_max]=1；

5.5.2) if K_i>K_mean, recording individual p_iMiddle genic value is 1 index set：

Λ=λ | p_i[λ]=1,1≤λ≤N },

Find the position λ of overall gene activity L minima in index set Λ_min：

Put individual p_iλ_minIndividual gene is 0, i.e. p_i[λ_min]=0；

5.6) according to step 2.1) to 2.3) more new individual p_iFitness value and gene activity, put i=i+1, if i≤ 16, return to step 5.2)；Otherwise, the progeny population after output variation

Step 6, from parent populationAnd progeny populationIn select new parent populationAnd update optimum Body p_best, put enumerator t=t+1.

In parent populationAnd progeny populationSet in, the new father of the individuality composition that selects 16 fitness values maximum For populationThe maximum individuality of fitness value in new parent population is updated to current optimum individual p_best, and put meter Number device t=t+1.

Step 7, if maximum iteration time is T_max=100, if t<T_max, return to step 3；Otherwise, export optimal result.

The effect of the present invention can be illustrated by emulation experiment：

1. experiment condition

Microcomputer CPU used by experiment is Intel Core22.66GHz internal memory 4GB, and programming platform is Matlab2013.Experiment The view data of middle employing is the Lena image in standard picture test library, and size is 512 × 512.

2. experiment content

The One-dimensional simulation signal that experiment 1 obeys standard normal distribution to nonzero coefficient recovers：

If signal length N=256, observe dimension M=100, the degree of rarefication of sparse coefficient vector α increases to 50 from 10, often Individual degree of rarefication does 1000 independent experiments, and in testing every time, the nonzero coefficient of coefficient vector α is just being distributed very much random producing with standard Raw, compressed sensing matrix D_csElement average be 0, standard deviation be 1/N Gauss distribution produce.Then observation distinct methods exist The correct probability recovering signal and average restoration errors in 1000 experiments.With the present invention and 4 kinds of classical greediness tracing algorithms pair Above-mentioned emulation signal is recovered, and 4 kinds of classical greediness tracing algorithms are respectively：Match tracing MP, orthogonal matching pursuit OMP, point SP is followed the trail of in section orthogonal matching pursuit StOMP and subspace.Experimental result is as shown in Fig. 2 wherein：

Fig. 2 (a), obeys to nonzero coefficient for the present invention and described 4 kinds of classical greediness tracing algorithms under different degree of rarefications The probability correlation curve that the signal of standard normal distribution accurately recovers,

Fig. 2 (b), obeys to nonzero coefficient for the present invention and described 4 kinds of classical greediness tracing algorithms under different degree of rarefications The correlation curve of the signal averaging restoration errors of standard normal distribution.

Experiment 2 is obeyed -1 to 1 equally distributed One-dimensional simulation signal to nonzero coefficient and is recovered：

If signal length N=256, observe dimension M=100, the degree of rarefication of sparse coefficient vector α increases to 50 from 10, often Individual degree of rarefication does 1000 independent experiments, in testing every time, the nonzero coefficient of coefficient vector α with -1 to 1 be uniformly distributed with Machine produces, compressed sensing matrix D_csElement average be 0, standard deviation be 1/N Gauss distribution produce.Then observe not Tongfang The method correct probability recovering signal and average restoration errors in 1000 experiments.Calculated with classical greedy tracking of the present invention and 4 kinds Method is recovered to above-mentioned emulation signal, and 4 kinds of classical greediness tracing algorithms are respectively：Match tracing MP, orthogonal matching pursuit SP is followed the trail of in OMP, segmentation orthogonal matching pursuit StOMP and subspace.Experimental result is as shown in figure 3, wherein：

Fig. 3 (a) be the present invention and described 4 kinds of classical greediness tracing algorithms under different degree of rarefications, nonzero coefficient is obeyed- The probability correlation curve that 1 to 1 equally distributed signal accurately recovers,

Fig. 3 (b) be the present invention and described 4 kinds of classical greediness tracing algorithms under different degree of rarefications, nonzero coefficient is obeyed- The correlation curve of 1 to 1 equally distributed signal averaging restoration errors.

As can be seen that for one-dimensional emulation signal, greedy follow the trail of classical compared to other 4 kinds is calculated from Fig. 2 and Fig. 3 Method, the present invention has higher recovery probability and less restoration errors.

Experiment 3 carries out splits' positions perception and recovers to two dimensional image Lena, compares the Y-PSNR PSNR of algorithms of different：

Lena image is divided into 8 × 8 fritter, setting observation dimension M=32, maximum iteration time is 16.Observing matrix Element average in Φ is 0, and standard deviation is that the Gauss distribution of 1/N produces, and base dictionary Ψ adopts DCT dictionary, compressed sensing square Battle array D_cs=Φ Ψ.Observe the restoration result of distinct methods, and compare their Y-PSNR PSNR.With the present invention and existing Match tracing MP is recovered to image Lena with orthogonal matching pursuit OMP algorithm.Experimental result is as shown in figure 4, wherein：

Fig. 4 (a) is original Lena topography,

Fig. 4 (b) is the restoration result to Lena topography for the present invention, Y-PSNR PSNR=31.3dB,

Fig. 4 (c) is the restoration result to Lena topography for the MP algorithm, Y-PSNR PSNR=29.2dB,

Fig. 4 (d) is the restoration result to Lena topography for the OMP algorithm, Y-PSNR PSNR=29.6dB.

From fig. 4, it can be seen that for two dimensional image signaling protein14-3-3, the border of restoration result of the present invention closest to artwork, Y-PSNR PSNR highest, and artificial blocking effect is minimum.

Experiment 4 carries out splits' positions perception and recovers to two dimensional image Lena, compares the restoration errors of algorithms of different：

Lena image is divided into 8 × 8 fritter, setting observation dimension M=32, maximum iteration time is 16.Observing matrix Element average in Φ is 0, and standard deviation is that the Gauss distribution of 1/N produces, and base dictionary Ψ adopts DCT dictionary, compressed sensing square Battle array D_cs=Φ Ψ.Observe the restoration errors figure of distinct methods.Relatively the present invention and subspace follow the trail of SP, match tracing MP with orthogonal The restoration errors of match tracing OMP algorithm.Experimental result is as shown in figure 5, wherein：

Fig. 5 (a) is the restoration errors figure to Lena topography for the SP algorithm,

Fig. 5 (b) is the restoration errors figure to Lena topography for the present invention,

Fig. 5 (c) is the restoration errors figure to Lena topography for the MP algorithm,

Fig. 5 (d) is the restoration errors figure to Lena topography for the OMP algorithm.

From the point of view of Error Graph from Fig. 5, the error span of restoration result of the present invention is minimum.

To sum up, no matter in One-dimensional simulation signal or two dimensional image signaling protein14-3-3, the recovery effects of the present invention are all excellent Classical greedy tracing algorithm in other 4.

Claims (5)

1. a kind of compressed sensing signal recovery method based on evolution orthogonal matching pursuit, its flow process is as follows：

(1) input compressed sensing matrix D_csWith observation vector y, initialize one containing S individual parent populationPut enumerator t=0；

(2) calculate parent populationFitness and gene activity, and to record the maximum individuality of fitness be optimum individual p_best, calculate gene activity formula as follows：

$l=\frac{\left|D_{cs}^T(y-D_{cs}\mathrm{\&alpha;})\right|}{U}$

Wherein U is normaliztion constant, is equal toThe maximum of middle element, y represents observation vector, D_csRepresent compression Perception matrix, α represents sparse coefficient vector；

(3) to parent populationCarry out crossover operation, obtain progeny population

(4) calculate progeny populationFitness and gene activity；

(5) to progeny populationCarry out mutation operation, in mutation process, update each individual fitness, gene activity and entirety Gene activity, the formula calculating overall gene activity is as follows：

$L=\underset{j=1}{\overset{S}{\&Sigma;}}{l}_j$

Wherein l_jRepresent the gene activity of j-th individuality, S represents the quantity containing individuality in population；

(6) from parent populationAnd progeny populationIn select new parent populationAnd update optimum individual p_best, put Enumerator t=t+1；

(7) set maximum iteration time as T_maxIf, t ＜ T_max, return to step (3)；Otherwise, export optimal result.

2. the compressed sensing signal recovery method based on evolution orthogonal matching pursuit according to claim 1, its step (1) Described input compressed sensing matrix D_csWith observation vector y, initialize one containing S individual parent populationPut enumerator t=0 to comprise the following steps that：

(1.1) input compressed sensing matrix D_csWith observation vector y；

(1.2) putting parent population is empty setPut i=1；

(1.3) calculate compressed sensing matrix D_csMiddle atom and the dependency c of observation vector y:

$c=\left|D_{cs}^{T}y\right|$

Wherein, | | represent the absolute value seeking vector element；

(1.4) by descending for the element in vectorial c sequence：Find a group index { λ₁,λ₂,...λ_n...,λ_NSo that c [λ₁]≥c[λ₂]≥...c[λ_n]...≥c[λ_N], wherein c [λ_n] represent the λ of vectorial c_nIndividual element, N is signal dimension；

(1.5) generate a full 0 individuality p_i=[0,0 ..., 0], puts p_i[λ_i]=1, wherein p_i[λ_i] represent individual p_iλ_iIndividual Element；

(1.6) by individual p_iIt is added in parent populationPut i=i+1；

(1.7) set S as parent populationIn individual amount, if i≤S, return (1.5)；Otherwise, export parent populationPut meter Number device t=0.

3. the compressed sensing signal recovery method based on evolution orthogonal matching pursuit according to claim 1, its step (2) Described calculating parent populationFitness and gene activity, and to record the maximum individuality of fitness be optimum individual p_best Concretely comprise the following steps：

(2.1) for parent populationIn each individual p, solve its sparse coefficient vector α：

Wherein α_pRepresent the subvector that the position being 1 with element in individual p is extracted from vectorial α for index,Represent with individual p Middle element be 0 position be index from vectorial α extract subvector,Represent with element in individual p be 1 position as rope Draw from matrix D_csThe submatrix that the column vector of middle extraction is constituted, subscriptRepresent the pseudoinverse seeking matrix, 0 one element of expression is all 0 vector；

(2.2) seek the fitness value of individual p：

$f=\frac{1}{\left|\right|y-D_{cs}\mathrm{\&alpha;}|{|}_2}$

Wherein, | | | |₂For calculating 2 norms of vector；

(2.3) calculate the gene activity of individual p：

$l=\frac{\left|D_{cs}^T(y-D_{cs}\mathrm{\&alpha;})\right|}{U}$

Wherein U is normaliztion constant, is equal toThe maximum of middle element.

4. the compressed sensing signal recovery method based on evolution orthogonal matching pursuit according to claim 1, its step (3) Described to parent populationThe method carrying out crossover operation is as follows：

(3.1) putting progeny population is empty setBy parent populationIn individuality match two-by-two, obtain S/2 to individuality；

(3.2) to every a pair individual (p_i,p_j), find the different index set Λ of gene under their same positions, that is,：

$\mathrm{\&Lambda;}=\left\{\mathrm{\&lambda;}\right|p_i\&lsqb;\mathrm{\&lambda;}\&rsqb;-p_j\&lsqb;\mathrm{\&lambda;}\&rsqb;\&NotEqual;0,\&ForAll;1\&le;\mathrm{\&lambda;}\&le;N\}$

(3.3) find individual p_iAnd p_jThe position of gene activity maximum in index ΛWithI.e.:

$\begin{array}{cc}{l}_i\&lsqb;{\mathrm{\&lambda;}}_i^{max}\&rsqb;\&GreaterEqual;l_i\&lsqb;\mathrm{\&lambda;}\&rsqb;& \&ForAll;{\mathrm{\&lambda;}}_i^{max},\mathrm{\&lambda;}\&Element;\mathrm{\&Lambda;}\end{array}$

$\begin{array}{cc}{l}_j\&lsqb;{\mathrm{\&lambda;}}_j^{max}\&rsqb;\&GreaterEqual;l_j\&lsqb;\mathrm{\&lambda;}\&rsqb;& \&ForAll;{\mathrm{\&lambda;}}_j^{\max },\mathrm{\&lambda;}\&Element;\mathrm{\&Lambda;}\end{array}$

Wherein l_i[λ] represents individual p_iThe gene activity value of λ position；

(3.4) exchange individual p_iAnd p_jGene position：IfPutObtain new individual p '_i, PutObtain new individual p '_j；Otherwise, putObtain new individual p '_i, putObtain new Individual p '_j；

(3.5) by two new individual p '_iWith p '_jIt is added to progeny populationRepeat step (3.2) arrives (3.5) Operation, until all individualities complete to intersect.

5. the compressed sensing signal recovery method based on evolution orthogonal matching pursuit according to claim 1, its step (5) Described to progeny populationCarry out mutation operation, process is as follows：

(5.1) put i=1；

(5.2) calculate progeny populationAverage degree of rarefication K_mean：

$K_{mean}=\frac{1}{S\&times;N}\underset{p\&Element;P_s}{\&Sigma;}\underset{j=1}{\overset{N}{\&Sigma;}}p\&lsqb;j\&rsqb;$

Wherein p [j] represents j-th gene of individual p, and N is signal length；

(5.3) calculate progeny populationOverall gene activity, formula is as follows：

$L=\underset{j=1}{\overset{S}{\&Sigma;}}{l}_j$

Wherein l_jRepresent the gene activity of j-th individuality；

(5.4) calculate individual p_iDegree of rarefication K_i, formula is as follows：

$K_i=\underset{j=1}{\overset{N}{\&Sigma;}}{p}_i\&lsqb;j\&rsqb;$

(5.5) judge individual p_iDegree of rarefication K_iWith populationAverage degree of rarefication K_meanSize, and carried out according to magnitude relationship Mutation operation；

If (5.5.1) K_i≤K_mean, recording individual p_iMiddle genic value is 0 index set：

Λ=λ | p_i[λ]=0,1≤λ≤N },

Find the position λ of overall gene activity L maximum in index set Λ_max：

$\begin{array}{cc}L\&lsqb;{\mathrm{\&lambda;}}_{max}\&rsqb;\&GreaterEqual;L\&lsqb;\mathrm{\&lambda;}\&rsqb;& \&ForAll;{\mathrm{\&lambda;}}_{max},\mathrm{\&lambda;}\&Element;\mathrm{\&Lambda;},\end{array}$

Put individual p_iλ_maxIndividual gene is 1, i.e. p_i[λ_max]=1；

If (5.5.2) K_i＞ K_mean, recording individual p_iMiddle genic value is 1 index set：

Λ=λ | p_i[λ]=1,1≤λ≤N },

Find the position λ of overall gene activity L minima in index set Λ_min：

$\begin{array}{cc}L\&lsqb;{\mathrm{\&lambda;}}_{\min }\&rsqb;\&le;L\&lsqb;\mathrm{\&lambda;}\&rsqb;& \&ForAll;{\mathrm{\&lambda;}}_{min},\mathrm{\&lambda;}\&Element;\mathrm{\&Lambda;},\end{array}$

Put individual p_iλ_minIndividual gene is 0, i.e. p_i[λ_min]=0；

(5.6) more new individual p_iFitness value, gene activity, put i=i+1, if i≤S, return (5.2)；Otherwise, output variation Progeny population afterwards