CN105512675A - Memory multi-point crossover gravitational search-based feature selection method - Google Patents

Abstract

The invention discloses a memory multi-point crossover gravitational search-based feature selection method. Each particle is set as the alternative solution of an optimal feature subset; the quality of the alternative solutions are evaluated through a band subset evaluation function; particles are guided to carry out information exchange, and fast convergence can be completed; and solutions corresponding to particles with best quality are optimal spectral feature subsets. According to the method, in order to improve the adaptability of the algorithm, a population evolutionary degree-based information exchange mechanism is put forwards based on a gravitational search algorithm: in an exploration stage, the algorithm fully learns from other particles in a population based on a multi-point crossover strategy so as to carry out extensive search; and in a development stage, the algorithm learns from the optimal experiences of the population and the algorithm itself in a centralized manner so as to ensure fast convergence. With the memory multi-point crossover gravitational search-based feature selection method of the invention adopted, an optimal spectral feature subset which has few bands and can obtain stable classification results can be selected out, and therefore, problems such as complex calculation and low classification accuracy which are caused by high redundancy of hyper-spectral remote sensing image data can be solved.

Description

A kind of feature selection approach based on the search of Memorability multiple-spot detection gravitation

Technical field

The invention belongs to Remote Sensing Image Processing Technology field, particularly relate to a kind of feature selection approach based on the search of Memorability multiple-spot detection gravitation.

Background technology

Along with the development of sensor technology, target in hyperspectral remotely sensed image, after the eighties in 20th century, starts to play an important role in fields such as environmental monitoring, survey of territorial resources assessment, city plannings.In the process, the nicety of grading of remote sensing image directly determines the degree of functioning of its application.Although the spectral signature that target in hyperspectral remotely sensed image enriches can describe covered ground information more accurately, but the spectral information of this magnanimity has very high redundancy usually, Hughes phenomenon can be caused in assorting process, and the storage of at substantial and computer memory.Thus, from high-dimensional spectral band, how to identify the most effective a small amount of wave band, and realize the image classification of degree of precision, become a key issue of Hyperspectral imaging application.

Method for Feature Selection is a kind of directly wave band recognition methods effectively.This method, according to certain objective function or interpretational criteria, selects the least possible wave band to form new character subset, make its to the analysis task of such as data such as Iamge Segmentation, classification can reach with feature selecting before quite or better effect.This back-and-forth method can classify as the optimized algorithm of binary space.Early stage research, exhaustive search algorithm achieves certain success, but the computation complexity of this algorithm, along with the carrying out of iteration exponentially increases.In actual applications, consuming time oversize owing to calculating, be difficult to the requirement meeting target in hyperspectral remotely sensed image.In order to reduce computation complexity, the art teaches branch-and-bound, sequential advancement, sequentially retreat scheduling algorithm, but these algorithms needing the wave band number of artificial specified subset in advance, make the character subset obtained not be optimum subset usually.

Gravitation search algorithm is that the people such as RashediE. inspired by Newton's law of gravitation in 2009, the novel meta-heuristic searching algorithm of one of proposition.This algorithm is thought, with to rely on universal gravitation to attract each other between object among universe the same, can think and be attracted each other by universal gravitation between each particle in population in optimized algorithm.Because gravitational size is proportional to the quality of two objects, be inversely proportional to the distance between object, the object that quality is larger is also larger to the attractive force of other objects.So if give maximum quality by particle best for fitness in optimized algorithm, all the other particles are close to the particle that fitness is best with certain acceleration by following Newton second law, complete searching process.

In the past few years, this algorithm has successfully been applied in numerous optimization problems such as cluster analysis, PID (ProportionIntegrationDifferentiation) parameter optimization, Economic Load Dispatch, pipeline schedule, multi-Level Threshold Image Segmentation, demonstrates it and is easy to series of advantages and wide application prospects such as applying, global optimizing ability is strong.Compared to methods such as traditional exhaustive searchs, utilize gravitation search algorithm to solve the problem of feature selecting, wave band number need not be set, according to the adaptive optimal feature subset that obtains of image feature, the feature selecting of greater efficiency and precision can be realized.

But the learning strategy of gravitation search algorithm and information interchange mode, also there are some problems, such as: mode of learning is single, the mode of all particles and other particle exchange of information is all pass through universal gravitation, this causes the development ability of algorithm not enough, easily there is concussion problem in the later stage, causes speed of convergence slack-off; In addition, particle completes an iteration at every turn, and search information before is all lost, and algorithm does not possess the ability to oneself empirical learning, causes algorithm to be easily absorbed in local optimum, occurs the problems such as Premature Convergence.In order to the problem utilizing gravitation search algorithm to solve band selection more efficiently, need to carry out extension and improvement to algorithm.

Summary of the invention

The deficiency that exists in the demand selected for characteristics of remote sensing image and gravitation search algorithm, the object of the present invention is to provide a kind of feature selection approach based on the search of Memorability multiple-spot detection gravitation, character subset evaluation function is optimized by adaptive equalization exploration and development, and global history optimum is made a variation, effectively improve the problem that gravitation search algorithm development ability is not enough, lack Memorability, easily Premature Convergence, finally obtain wave band number few and the optimum spectral signature subset of stable class result can be obtained.

For solving the problem, the present invention adopts following technical scheme:

A kind of feature selection approach based on the search of Memorability multiple-spot detection gravitation comprises the following steps:

Step S1, select to treat the original remote sensing image HI of feature selecting to determine total wave band number D of remote sensing image HI, simultaneously according to atural object distribution actual original remote sensing image HI on and classification number, determine sample areas and extract sample data SHI;

Step S2, initialization process: setting Population Size, namely setting number of particles is N, and each particle represents character subset to be selected, the position X of each particle in initialization population _ithe speed of (t) and correspondence thereof, 1≤i≤N, and i is positive integer, t is current iteration number of times;

Step S3, beginning iteration: based on support vector machine (SupportVectorMachine, SVM) sorter, utilize each particle X _it character subset that () represents is classified to sample data SHI, obtains the nicety of grading Accuracy=[Acc that N number of particle is corresponding ₁(t), Acc ₂(t) ..., Acc _i(t) ..., Acc _n(t)], wherein, Acc _ithe nicety of grading of (t) i-th character subset;

Step S4, calculate the fitness value fit of each particle _i(t), wherein, ω is the weight of balanced sort precision and wave band number, n _sfor particle i intermediate value is the dimension of 1;

Step S5, fitness value fit based on each particle _it () determines the individual history optimal location Pb of each particle _iglobal history optimal location Gb (t) of (t) and population;

Step S6, based on the fitness value fit of each particle _it () calculates the gravitational acceleration a of each particle _i(t);

Step S7, judge the Evolving State of population, based on the gravitational acceleration a of described each particle _ithe individual history optimal location Pb of (t), described each particle _it global history optimal location Gb (t) of () and population is the most suitable information exchange method of each particle selection according to Evolving State, upgrade particle rapidity and position;

Step S8, according to the position of particle after upgrading, utilize SVM classifier, calculate the nicety of grading Acc of N number of particle characteristic of correspondence subset _i(t+1), then upgrade the fitness value of each particle according to evaluation function, obtain fit _i(t+1);

Step S9, based on fit _i(t+1) the more individual history optimal location of new particle and the global history optimal location of population;

Step S10, make t=t+1, judge whether t is greater than maximum iteration time T _maxif t is not more than T _max, based on the fit obtained in step S8 _i(t+1) and the individual history optimal location of the more new particle obtained in step S9 and the global history optimal location of population carry out the t+1 time interative computation according to step S6 to step S9; If t is greater than T _max, particle best for fitness in current population is exported, exports the global history optimal location of Population Regeneration described in step S9, be the optimal feature subset of sample data SHI;

Step S11, the spectral band comprised according to optimal feature subset, utilize SVM classifier to classify to original remote sensing image HI, obtain its classification results.

As preferably, step S5 is specially: as t=1, the individual history optimal location Pb of each particle of initialization _i(t)=X _it (), then from Pb _it the particle selecting fitness maximum in () is as global history optimal location Gb (t) of population; As t>1, the fitness value before and after first more each particle position upgrades, if new position fitness is larger, then it is optimum that new position becomes individual history; Then from new individual history optimum, the global history optimum before selecting best particle and upgrading is made comparisons, if this particle fitness is comparatively large, then composes the global history optimal location for new population.

As preferably, step S7 is specially:

In more current population, whether the standard deviation std (fit) of particle fitness value meets std (fit) <rand with random number rand and compares crossing-over rate p _cbe multiplied by t/T _maxvalue and random number rand whether meet p _c× t/T _max>rand,

If two conditions all do not meet, then think that search procedure is in the exploration stage, particle i renewal speed is:

${v_i}^d(t+1)=rand\&CenterDot;{v_i}^d\left(t\right)+{a_i}^d\left(t\right)$

Wherein, be in the t time iteration particle i in the renewal speed of d dimension, be the speed of particle in the t time iteration, for particle i is at the gravitational acceleration of d dimension;

If two conditions have one or two to be met, then think that search procedure enters the development phase, for each dimension d, first will will judge aberration rate p _mwhether p is met with random number rand _m>rand, if do not met, Gb (t) remains unchanged; If met, then to the d dimension Gb of Gb (t) ^dt () carries out Gaussian mutation, namely

Then based on the speed of each dimension of multiple-spot detection policy update particle of Memorability:

$v_i^d(t+1)=rand\&CenterDot;(\frac{c^{\&prime;}}{2}{\mathrm{Gb}}^d{\left(t\right)}^{\&prime;}-{\mathrm{Pb}}_i^d(t)-x_i^d(t\left)\right)$

Wherein, be in the t time iteration particle i in the renewal speed of d dimension, the history being particle i in the t time iteration is optimum in the position of d dimension, be in the t time iteration particle i in the position of d dimension, c '=c+2t/T _max, maximum iteration time T _max.

Upgrade particle position based on new speed, particle i updated space is set to:

$x_i^d(t+1)=x_i^d\left(t\right)+v_i^d(t+1)$

Wherein, be in the t time iteration particle i in the renewal position of d dimension.

Beneficial effect of the present invention: the present invention is directed to target in hyperspectral remotely sensed image data redudancy high, process the problems such as consuming time, based on Memorability multiple-spot detection gravitation search algorithm, each particle is set as the alternative solution of an optimal feature subset, the quality of alternative solution is assessed by band subset evaluation function, and guide particle to carry out information interchange, complete Fast Convergent.The disaggregation that top-quality particle is corresponding is optimum spectral signature subset.It is few and can obtain the optimum spectral signature subset of stable class result that the present invention can select wave band number, thus solve the problems such as high calculation of complex, the nicety of grading caused of target in hyperspectral remotely sensed image data redudancy is low.

Accompanying drawing explanation

Fig. 1 is the overall construction drawing of the multiple-spot detection gravitation searching method that the present invention is based on Memorability;

Fig. 2 is the schematic flow sheet of the multiple-spot detection gravitation searching method based on Memorability;

Fig. 3 is image feature and binary-coded schematic diagram.

Embodiment

Be described further below in conjunction with the embodiment of accompanying drawing to the inventive method.

Feature selection approach based on the search of Memorability multiple-spot detection gravitation provided by the invention, is applicable to the process to the IndianPine area target in hyperspectral remotely sensed image that AVIRIS (AirborneVisibleInfraredImagingSpectrometer) sensor obtains.The spatial resolution of original AVIRIS data and spectral resolution are respectively 10m (rice) and 10nm (nanometer), and spectral range covers 400-2400nm, has 224 spectral coverages.Because the value of wherein 4 wave bands is 0, so by filtering.In addition, on IndianPine image, have 20 wave bands, comprise wave band [104-108], [150-163] and 220 value easily by water suction wave band impact, in present case, these wave bands are also by filtering.So, the wave band that the IndianPine image that present case adopts adopts altogether has 200, image size is 145 × 145 (pixels), and type of ground objects comprises 16 class identifiable design atural objects (mainly different crops), and rest of pixels is considered to background.

As shown in Figure 1, 2, the invention provides a kind of feature selection approach based on the search of Memorability multiple-spot detection gravitation to comprise the following steps:

Step S1, select to treat the original remote sensing image HI of feature selecting, determine total wave band number D of remote sensing image HI, wave band is (b ¹, b ², b ³..., b ^d... b ^d), 1≤d≤D, and d is positive integer, D=200, simultaneously according to atural object distribution actual on original remote sensing image HI and classification number, determines sample areas and extracts sample data SHI, wherein, the every class of random selection 5% pixel be sample data SHI, remaining data are as test set.

Step S2, initialization process: setting Population Size, namely setting number of particles is N, preferred N=30, and each particle represents an alternative features subset, each particle adopts position and speed two attribute to represent, by the position of each particle in binary-coded method random initializtion population $X_i\left(t\right)=\&lsqb;x_i^1\left(t\right),x_i^2\left(t\right),...,x_i^d\left(t\right),...x_i^D\left(t\right)\&rsqb;$ And the speed of correspondence $V_i\left(t\right)=\&lsqb;v_i^1\left(t\right),v_i^2\left(t\right),...,v_i^d\left(t\right),...v_i^D\left(t\right)\&rsqb;,$ 1≤d≤D, 1≤i≤N, and d, i are positive integer, t is iterations, 1≤t≤T _max, and t is positive integer, each particle position initial value is each particle rapidity initial value is V _i(1)=0; As shown in Figure 2, each particle is in the position of d dimension initial value be set as 0 or 1 at random, if 0 represents that the d wave band of sample data SHI is not selected, if 1 represents that d wave band is selected, selected d wave band is called d dimension; Setting maximum iteration time T _maxbe 200, crossing-over rate p _cbe 0.05, aberration rate p _mbe 0.5, initialization coordinating factor c is 0.5.

Step S3, beginning iteration: based on support vector machine (SupportVectorMachine, SVM) sorter, utilize each particle X _it character subset that () represents is classified to sample data SHI, obtains the nicety of grading Accuracy=[Acc that N number of particle is corresponding ₁(t), Acc ₂(t) ..., Acc _i(t) ..., Acc _n(t)], wherein, Acc _ithe nicety of grading of i-th character subset.

Step S4, calculate the fitness value fit of each particle _i(t), this fitness value fit _it () is the evaluation function of evaluating characteristic subset quality, wherein, ω is the weight of a balanced sort precision and wave band number, and preferred ω is 0.5, n _sfor particle i intermediate value is the dimension of 1, namely selected wave band number.

Step S5, determine the individual history optimal location Pb of each particle _iglobal history optimal location Gb (t) of (t) and population.As t=1, the individual history optimal location Pb of each particle of initialization _i(t)=X _it (), then from Pb _it the particle selecting fitness maximum in () is as global history optimal location Gb (t) of population.As t>1, the fitness value before and after first more each particle position upgrades, if new position fitness is larger, then it is optimum that new position becomes individual history; Then from new individual history optimum, the global history optimum before selecting best particle and upgrading is made comparisons, if this particle fitness is comparatively large, then composes the global history optimal location for new population.

Step S6, calculate the gravitational acceleration of each particle, according to gravitation search algorithm, the computing formula of gravitational acceleration is:

$a_i^d\left(t\right)=\frac{F_i^d\left(t\right)}{M_i\left(t\right)},$

Wherein, be that in the t time iteration, particle i is subject to making a concerted effort of other all particle sucking action in d dimension (selected wave band), M _it () is the quality of particle i in the t time iteration, be in the t time iteration particle i at the gravitational acceleration of d dimension, wherein,

$F_i^d\left(t\right)=\underset{j=1,j\&NotEqual;i}{\overset{N}{\mathrm{\&Sigma;}}}rand\&CenterDot;G\left(t\right)\frac{M_i\left(t\right)\&times;M_j\left(t\right)}{R_{ij}\left(t\right)+\mathrm{\&epsiv;}}\left(x_j^d\left(t\right)-x_i^d\left(t\right)\right)$

$M_i\left(t\right)=\frac{m_i\left(t\right)}{{\mathrm{\&Sigma;}}_{j=1}^N{m}_j\left(t\right)}$

Wherein, G (t) is gravitational constant G (t)=100 × exp (-20 × t/T in the t time iteration _max), R _ijt () is the Euclidean distance in the t time iteration between particle i and particle j, ε is a minimum constant being greater than 0, can be set to ε=10 ^-6, m _jt () is the particle fitness value in the t time iteration after particle j normalization, M _jt () is the quality of particle j in the t time iteration, m _it () is the particle fitness value in the t time iteration after particle i normalization.

Step S7, according to the adaptive selection Information exchange mechanism of the Evolving State of population.First judge that the Evolving State of population is in exploration or development phase, be then the most suitable information exchange method of each particle selection according to Evolving State, particle rapidity and position upgraded, realizes the adaptive equalization to exploration and development.Further, in order to prevent Premature Convergence, with certain probability, mutation operation is performed to the position of global history optimal particle.

Judge that the method for Evolving State is: in (1) more current population, whether the standard deviation std (fit) of particle fitness value meets std (fit) <rand with random number rand and (2) compare crossing-over rate p _cbe multiplied by t/T _maxvalue and random number rand whether meet p _c× t/T _max>rand.

If two conditions all do not meet, then think that search procedure is in the exploration stage, particle should be allowed to carry out information interchange fully, explore region widely, so particle i renewal speed is:

$v_i^d(t+1)=\mathrm{rand}\&CenterDot;v_i^d\left(t\right)+a_i^d\left(t\right)$

Wherein, be in the t time iteration particle i in the renewal speed of d dimension, be in the t time iteration particle i in the speed of d dimension.

If two conditions have one or two to be met, then think that search procedure enters the development phase.In the development phase, should carry out preparing and separate fine search around, better be separated.In order to prevent the generation of Premature Convergence, for each dimension d, first aberration rate p to be judged _mwhether p is met with random number rand _m>rand, if do not met, Gb ^dt () remains unchanged, if met, then to Gb ^dt () carries out Gaussian mutation:

Wherein, Gb ^d(t) ' be in the t time iteration through the global history optimal particle of Gaussian mutation in the position of d dimension.

If the new position obtained is better than original position, then replace original position with new position, then perform the speed of each dimension of multiple-spot detection policy update particle based on Memorability:

$v_i^d(t+1)=rand\&CenterDot;\left(\frac{c^{\&prime;}}{2}{\mathrm{Gb}}^d{\left(t\right)}^{\&prime;}-{\mathrm{Pb}}_i^d\left(t\right)-x_i^d\left(t\right)\right)$

Wherein, be in the t time iteration particle i in the renewal speed of d dimension, the history being particle i in the t time iteration is optimum in the position of d dimension, be in the t time iteration particle i in the position of d dimension, c '=c+2t/T _max, namely along with the carrying out of iteration, c ' is worth increasing, makes interlace operation tend to Gb ^dt () position, is conducive to convergence speedup.

Step S8, renewal particle position: after the speed that completes upgrades, upgrade particle position based on new speed, particle i updated space is set to:

$x_i^d(t+1)=x_i^d\left(t\right)+v_i^d(t+1)$

Wherein, be in the t time iteration particle i in the renewal position of d dimension.

Step S9, according to the position of particle after upgrading, utilize SVM classifier, calculate the nicety of grading Acc of N number of particle characteristic of correspondence subset _i(t+1), then upgrade the fitness value of each particle according to evaluation function, obtain fit _i(t+1).

Step S10, based on fit _i(t+1) according to the more individual history optimal location of new particle and the global history optimal location of population of the method in step S5.

Step S11, make t=t+1, judge whether t is greater than maximum iteration time T _max; If t is not more than T _max, based on the fit obtained in step S9 _i(t+1) and step the S10 individual history optimal location of more new particle, the global history optimal location of Population Regeneration that obtain carry out the t+1 time interative computation according to step S6 to step S10; If t is greater than T _max, particle best for fitness in current population is exported, exports the global history optimal location of Population Regeneration described in step S10, be the optimal feature subset of sample data SHI.At this moment, think that this character subset has that wave band number is few and classification results is excellent.

Step S12, the spectral band comprised according to optimal feature subset, utilize SVM classifier to classify to original remote sensing image HI, obtain its classification results.

In order to verify the classifying quality of band selection, the average nicety of grading after the band selection under 10 random training sets and test and wave band number have been added up in this enforcement.Table 1 gives the wave band number that obtains after gravitation search algorithm GGSA (Adaptivegbest-guidedgravitationalsearchalgorithm), PSOGSA (Hybridparticleswarmoptimizationandgravitationalsearchalg orithm) that the inventive method and two kinds improve carry out levying selection for IndianPine image spy and the general classification through svm classifier.As shown in table 1, compared to GGSA algorithm and PSOGSA algorithm, the inventive method can obtain more excellent, more stable nicety of grading, and required wave band number is also much smaller than two kinds of contrast algorithms.

Table 1 feature selecting and classification results

Should be noted that; specific embodiment described herein is only for explaining the present invention; the enforcement be not intended to limit the present invention and interest field, all technical schemes identical or equivalent with content described in the claims in the present invention, all should be included in scope.

Claims (3)

1., based on a feature selection approach for Memorability multiple-spot detection gravitation search, it is characterized in that, comprise the following steps:

Step S1, select to treat the original remote sensing image HI of feature selecting to determine total wave band number D of remote sensing image HI, simultaneously according to atural object distribution actual original remote sensing image HI on and classification number, determine sample areas and extract sample data SHI;

Step S2, initialization process: setting Population Size, namely setting number of particles is N, and each particle represents an alternative features subset, the position X of each particle in initialization population _ithe speed V of (t) and correspondence thereof _i(t), 1≤i≤N, and i is positive integer, t is current iteration number of times;

Step S3, beginning iteration: based on support vector machine (SupportVectorMachine, SVM) sorter, utilize each particle X _it character subset that () represents is classified to sample data SHI, obtains the nicety of grading Accuracy=[Acc that N number of particle is corresponding ₁(t), Acc ₂(t) ..., Acc _i(t) ..., Acc _n(t)], wherein, Acc _it () represents the nicety of grading of i-th character subset;

Step S4, calculate the fitness value fit of each particle _i(t), wherein, ω is the weight of balanced sort precision and wave band number, n _sfor X _it () intermediate value is the dimension of 1;

Step S5, fitness value fit based on each particle _it () determines the individual history optimal location Pb of each particle _iglobal history optimal location Gb (t) of (t) and population;

Step S6, based on the fitness value fit of each particle _it () calculates the gravitational acceleration a of each particle _i(t);

Step S7, judge the Evolving State of population, based on the gravitational acceleration a of described each particle _ithe individual history optimal location Pb of (t), described each particle _it global history optimal location Gb (t) of () and population is the most suitable information exchange method of each particle selection according to Evolving State, upgrade particle rapidity and position;

Step S8, according to the position of particle after upgrading, utilize SVM classifier, calculate the nicety of grading Acc of N number of particle characteristic of correspondence subset _i(t+1), then upgrade the fitness value of each particle according to evaluation function, obtain fit _i(t+1);

Step S9, based on fit _i(t+1) the more individual history optimal location of new particle and the global history optimal location of population;

Step S10, make t=t+1, judge whether t is greater than maximum iteration time T _maxif t is not more than T _max, based on the fit obtained in step S8 _i(t+1) the individual history optimal location of the particle and after the renewal obtained in step S9 and the global history optimal location of population carry out the t+1 time interative computation according to step S6 to step S9; If t is greater than T _max, exported by particle best for fitness in current population, export the global history optimal location of the population after upgrading described in step S9, be the optimal feature subset of sample data SHI, be also the optimal feature subset of original remote sensing image HI simultaneously;

Step S11, the spectral band comprised according to optimal feature subset, utilize SVM classifier to classify to original remote sensing image HI, obtain its classification results.

2. as claimed in claim 1 a kind of based on Memorability multiple-spot detection gravitation search feature selection approach, it is characterized in that, step S5 is specially: as t=1, the individual history optimal location Pb of each particle of initialization _i(t)=X _it (), then from Pb _it the particle selecting fitness maximum in () is as global history optimal location Gb (t) of population; As t>1, the fitness value before and after first more each particle position upgrades, if new position fitness is larger, then it is optimum that new position becomes individual history; Then from new individual history optimum, the global history optimum before selecting best particle and upgrading is made comparisons, if this particle fitness is comparatively large, then composes the global history optimal location for new population.

3. as claimed in claim 1 a kind of based on Memorability multiple-spot detection gravitation search feature selection approach, it is characterized in that, step S7 is specially:

In more current population, whether the standard deviation std (fit) of particle fitness value meets std (fit) <rand with random number rand and compares crossing-over rate p _cbe multiplied by t/T _maxvalue and random number rand whether meet p _c× t/T _max>rand.

If two conditions all do not meet, then think that search procedure is in the exploration stage, particle i renewal speed is:

v _i ^d(t+1)＝rand·v _i ^d(t)+a _i ^d(t)

Wherein, be in the t time iteration particle i in the renewal speed of d dimension, be the speed of particle in the t time iteration, a _i ^dt () is for particle i is at the gravitational acceleration of d dimension;

If two conditions have one or two to be met, then think that search procedure enters the development phase, for each dimension d, first will will judge aberration rate p _mwhether p is met with random number rand _m>rand, if do not met, Gb (t) remains unchanged; If met, then to the d dimension Gb of Gb (t) ^dt () carries out Gaussian mutation, that is:

Then based on the speed of each dimension of multiple-spot detection policy update particle of Memorability:

$v_i^d(t+1)=rand\&CenterDot;(\frac{c^{\&prime;}}{2}{\mathrm{Gb}}^d{\left(t\right)}^{\&prime;}-{\mathrm{Pb}}_i^d(t)-x_i^d(t\left)\right)$

Wherein, be in the t time iteration particle i in the renewal speed of d dimension, the history being particle i in the t time iteration is optimum in the position of d dimension, be in the t time iteration particle i in the position of d dimension, c '=c+2t/T _max, maximum iteration time T _max.

Upgrade particle position based on new speed, particle i updated space is set to:

$x_i^d(t+1)=x_i^d\left(t\right)+v_i^d(t+1)$

Wherein, be in the t time iteration particle i in the renewal position of d dimension.