CN105812307A - Probability model based PARR reducing method - Google Patents

Abstract

The invention discloses a probability model based PARR (Peak to Average Power ratio) reducing method. The method includes analyzing variable contained in a preferable group and constructing a probability model meeting the variable distribution; generating a new group which has better quality than the prior group by the probability model; approaching a global optimal solution step by step from the current optimal solution by adopting the above meanings. By adopting a probability model based DE algorithm (DE/EDA algorithm), a differential evolution algorithm and distribution estimation calculation can be combined effectively and local and global information can be utilized effectively, falling into a local optical solution during a PAPR optimization problem solving process can be avoided, so that more powerful PAPR optimization capability can be obtained.

Description

A kind of PAPR based on probabilistic model reduces method

Technical field

The technical field that data signal of the present invention processes, particularly relates to a kind of PAPR (Peak-to-based on probabilistic model Average power ratio, peak-to-average force ratio) reduce method.

Background technology

OFDM (Orthogonal Frequency Division Multiplexing, OFDM) technology by Generally acknowledge as the core transmission technology in 4G mobile communication system.OFDM technology uses multiple mutually orthogonal subcarriers to carry out The transmission of business, in whole transmission band, the frequency spectrum of each subcarrier is overlapped, is so not only able to be greatly improved system Spectrum utilization efficiency, and data stream at a high speed can be assigned to relatively low each of transfer rate by serial to parallel conversion Being transmitted on subcarrier, so transmission data extension on the time domain internal symbol cycle makes OFDM technology be highly resistant to nothing The decline caused of line channel multi-path time delay.It practice, now OFDM technology is in terrestrial wireless broadcast system and wireless Broadband access system is widely used, such as DVB-T (digital video broadcast terrestrial), WLAN (wireless local area Net), DTMB (terrestrial DTV multimedia broadcasting) etc..

OFDM belongs to multi-carrier communication technology.Owing to the time-domain signal through OFDM modulation output is to be believed by multiple subcarriers Number addition, separate between these subcarriers, when the signal phase on these carrier waves is identical, can produce and be much larger than The instantaneous power of average power signal, thus there will be bigger papr.Higher peak-to-average force ratio can reduce to be sent out Penetrate the work efficiency of machine internal power amplifier, increase A/D and the complexity of D/A converter realization；If having relatively high power Signal has exceeded the dynamic range of amplifier, then after amplifier, signal can produce distortion, and destroy between subcarrier is orthogonal Property, cause whole system hydraulic performance decline.

In recent years, more intelligent algorithm have been widely used for PAPR (Peak-to-average power ratio, Peak-to-average force ratio) reduction, such as ant group algorithm, differential evolution algorithm (DE algorithm) etc..Such as document 1:Weng C E, Chang C W, Chen C H, et al.Novel low-complexity partial transmit sequences scheme for PAPR reduction in OFDM systems using adaptive differential evolution Algorithm [J] .Wireless personal communications, 2013,71 (1): 679-694.The technology of document 1 Scheme utilizes differential evolution algorithm to enter traditional PTS (partial transmit sequence) partial transmission sequence method Row improves, and reduces the complexity that its algorithm realizes.The process finding optimum angle weight factor is defined as one by this technical scheme Individual constrained optimization problems, and obtain optimal solution with the differential evolution algorithm improved；Modified hydrothermal process can be with relatively low complexity Realize the reduction of PAPR.But there are the following problems for document 1:

1. this algorithm uses DE algorithm to be optimized PAPR.And DE cannot extract and utilize global search spatial information. Along with the increase of iterations, the probability that this algorithm is absorbed in local extremum is bigger.

2. the program convergence rate and search robustness between clash, it is difficult to obtain simultaneously good robustness and Quickly convergence rate.

Document 2.Wang Y C, Luo Z Q.Optimized iterative clipping and filtering for PAPR reduction of OFDM signals [J] .Communications, IEEE Transactions on, 2011,59 (1): 33-37.Document 2 proposes a constrained optimization problems, using minimum for EVM as optimization aim, and by the PAPR value of signal As constraint.But use the design of convex optimization method to replace each iterative process frequency domain response rectangular filter.By design Optimal Filter can ensure letter with the EVM (Error vector magnitude, error vector magnitude) of minimum signal simultaneously Number PAPR less than specified value.But there are the following problems for document 2:

1. need the process of successive ignition.

2. program interior point method solves the convex optimization problem of Optimal Filter design.Convex optimization problem is to try to achieve the overall situation Optimal solution, the time complexity of system is too high, reaches O (N³), it is impossible to realize in needing the real system processed in real time.

3. these problems do not consider the distribution statistics of signal PAPR.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of PAPR (Peak-to-average based on probabilistic model Power ratio, peak-to-average force ratio) reduce method.

For solving the problems referred to above, the present invention adopts the following technical scheme that:

A kind of PAPR based on probabilistic model reduces method and comprises the following steps:

Step S1, randomly generate initial population

Randomly generate N number of solutionForm initial population X⁰If, evolutionary generation K=0；

Step S2, according to DE/EDA algorithm both candidate nodes produce algorithm generate next generation solution population be:Comprise the following steps:

Step S21, structure probabilistic model

From current population X^kIn select best M solution and build probabilistic model and be

Wherein,

P_{J, n}The value of nth elements of the jth sequence for producing；

Step S22, intersection and mutation operation

Mutation operation:

By the equation of differential variation, obtaining variation individuality is:

Wherein,Randomly generate three sample vectors in representative sample space, r1j, r2j, r3j generation The sequence number that table randomly chooses,For variation individuality, F is zoom factor, and expression difference vector affects journey to individuality of future generation Degree,

Intersect and operate: utilize the different information of population and the distributed intelligence that population advantage is individual, produce candidate's population at individual,

Intersect and operate You Liangge branch, wherein,

One branch utilizes DE variation formula to produce candidate's descendant nodes, is expressed as follows:

Wherein,Represent the vector after intersecting and operating,For object vector, rand () is between [0,1] Uniform random number, j=1,2 ... m represents jth variable (gene), and m is the dimension of variable, and CR is the crossover probability factor,

Another branch utilizes the probability Distribution Model of EDA algorithm to produce candidate's descendant nodes

Step S23, replacement operation

It is chosen as determining trial vector U_{I, t}Whether can become the member in the next generation, according to greedy criterion by trial vector With the object vector E in current population_{I, t}Comparing, computing formula is as follows:

Wherein,

E_{I, t+1}For follow-on object vector；

Step S3, iteration

If given termination condition is not up to, k=k+1 continues executing with step S22, and the termination condition set is as current Population optimal objective function reaches maximum iteration time less than given numerical value or iterations.

The present invention having the beneficial effect that compared to existing technology:

1, the probabilistic model of PAPR signal optimum population is set up, based on this probabilistic model improved differential evolution algorithm, permissible Avoid the problem that conventional differential evolution is easily trapped into local optimum.

2, can effectively describe Evolutionary direction by probabilistic model, overall PAPR signal performance is carried out " macroscopical " aspect Simulation, thus there is good search capability.

3, PAPR can be reduced to 5.5dB, than can reduce 1dB with DE algorithm merely.

In sum, merge two kinds of algorithms of DE and EDA and PAPR optimization problem is solved, both make use of current population Distance and directional information, make use of again the distributed intelligence of whole search volume optimal solution.

Accompanying drawing explanation

Fig. 1 is the flow chart that PAPR of the present invention reduces method.

Detailed description of the invention

Below in conjunction with embodiment and accompanying drawing, technical scheme is further elaborated.

In ofdm system, a multi-carrier signal is the superposition of multiple independent sub-carriers signal.Assume on each subcarrier The data symbol of transmission is discrete-time signal, and discrete-time signal x (n) is expressed as:

Wherein, X (k) is 16-QAM modulated signal, L be over-sampling because of Son.Generally, it is considered that oversample factor L=4 can obtain the effect being similar to continuous time signal.For discrete-time signal x (n), PAPR value can be defined as:Wherein, E [] represents mathematic expectaion.

The basic thought of margining amplitude technique is predetermined amplitude limit thresholding, and the part that ofdm signal envelope exceedes thresholding is carried out directly Eliminate.Margining amplitude technique can effectively suppress signal peak-to-average ratio, and, owing to its complexity is low, effect substantially becomes application at present One of most commonly used peak-to-average force ratio Restrain measurement.Traditional slicing algorithm is exactly the peak value of input signal when exceeding a certain thresholding, Just signal is limited on setting thresholding, if lower than this threshold value, the most directly passes through.Signal after amplitude limit can be expressed as:

But, owing to amplitude limit is a non-linear process, also result in inband distortion and out-of-band radiation, thus reduce whole The bit error rate performance of individual system and spectrum efficiency.Amplitude limit post filtering can reduce out of band spectrum interference, but this will cause again peak value Regeneration.In order to avoid this situation, first with longer IFFT, input data vector is transformed into time domain from frequency domain over-sampling.Right In given oversample factor J, between frequency domain data vector, add N (J-1) individual 0 expand original data vector, The interpolation of time-domain signal is realized after IFFT conversion.Then the signal after interpolation is carried out amplitude limit.Owing to amplitude limit is non-linear process, Therefore it can bring in-band noise and out-of-band interference.In order to eliminate out-of-band interference, it is necessary to the signal after amplitude limit is filtered.Although Filtering can cause peak regeneration, but more much smaller than the signal peak before amplitude limit.In order to amplitude limit repeatedly can be passed through as far as possible Filtering reduces the peak value of signal further.During successive ignition limit filtration, can cause signal band attenuation and Radiation outside band, so signal is retrained by definition Error Vector Magnitude EVM.

For an OFDM symbol, its EVM can be defined as:If transmission signal meets EVM retrains, then receiving terminal can correctly recover data.

The probability statistical analysis of PAPR is as follows:

1, the definition of PAPR

Wherein,X (t) represents one Comprise the OFDM symbol Equivalent Base-Band complex representation of N number of subcarrier.

2, OFDM statistical property

It is the ofdm system of N for subcarrier number

According to central limit theorem, when N is sufficiently large, it is 0 that the real part of x (t) and imaginary part meet average respectively, and variance is 1/2 Gauss distribution；The power of ofdm signal is respectively accounted for half by real part and imaginary part；The envelope r of signal meets rayleigh distributed, its probability Density functionIt is 0 that power meets average, and variance is the χ that degree of freedom is 2 of 1²Distribution；Its probability density Function is: P_power(y)=e^-y。

3, the probability description of PAPR

Cumulative distribution function CDF, complementary Cumulative Distribution Function CCDF is used to be described；CDF is that PAPR value is less than In the probability of a certain threshold value, CCDF is the probability that PAPR value exceedes a certain threshold value.

CDF:

Assuming that each sampled value in ofdm signal symbol period is incoherent, and average power signal normalizing Change, then

CDF:P{power≤Z}=(1-e^-Z)^N

CCDF:P{power ＞ Z}=1-(1-e^-Z)^N

4, for characteristics of signals, a probability statistics model is built, it may be preferred to go out the preferable signal of PAPR characteristic.? In ofdm system, a road high-speed data-flow is divided into N road low rate data streams, and N is the number of subcarrier；Each subcarriers uses PSK or qam mode；Final utilization inverse fast Fourier transform (IDFT) generates the ofdm signal being ready for sending.

Assume that input signal is: X=[X₀..., X_N-1]^T, N subcarriers is mutually orthogonal.

In a symbol period, the ofdm signal of transmission is:In sequence Each element be considered a stochastic variable, belong to Bernoulli Jacob distribution.

Its probability Distribution Model is:

Wherein, P is a stochastic variable, and U is probability distribution parameters.

N number of element of sequence is tested generation by the Bernoulli Jacob of n times independence, and each of which element belongs to above probability distribution Function；Experiment is by distributed constant every timeControlling, U is parameter vector；Un represent nth elements in sequence be 1 general Rate, 1-Un represents that in sequence, nth elements is the probability of 0；Since each element of sequence is independent generation, so system The probability that fixed sequence is generated is:So, after length N of sequence determines, this Random sequence J just creates.

Initial probability density functionIterations is T, and the value of initial p APR is

The sequence generated uses QPSK modulation.

The time-domain signal of transmitting terminal is produced after subsequent passing through IFFT conversion.

Finally we can obtain the PAPR value of signal.

The PAPR value of this group sequence is carried out ascending order arrangement.

Simultaneously by the thresholding of the 40th PAPR value formation sequence the most.

Go successively to iteration next time.

The formation sequence of next iteration updates iterative parameter Un. by following criterion

Wherein,It is indicator function, as F (P_j)≤γ, then haveIt is otherwise 0, P_{J, n}It it is the value of j-th sequence n-th element.

Use iterations as judging the condition of iteration ends, or can also be by twice grey iterative generation before and after judgement In sequence, the difference absolute value of minimum PAPR value is less than the condition of convergence condition as iteration ends of a certain threshold value；Through the most repeatedly In generation, probability-distribution function just has greater probability to produce the PAPR sequence of PAPR more excellent performance；So this probability can be passed through Model, continues to optimize the PAPR characteristic of sequence.

5, PAPR optimization problem based on probability Distribution Model definition

In OFDM real system, we it is generally desirable to the signal of transmitting terminal and do not exceed the PAPR thresholding specified.Some grind The person of studying carefully is established as constrained optimization problems, using minimum for EVM value as optimization aim.Wang and Luo [1] proposes one Constrained optimization problems, using minimum for EVM as optimization aim, and using the PAPR value of signal as constraint.Meanwhile, Alok [2] definition One PAPR optimization problem, using minimum for PAPR as optimization aim, and using EVM value as retraining.Above problem has two kinds The constraint of type and two kinds of optimization aim, be PAPR and EVM respectively.Then, these problems do not consider signal The distribution statistics of PAPR.So, we can consider the PAPR characteristic using probability Distribution Model to carry out Filled function signal. According to this, we define a new PAPR optimization problem based on probability constraints.

[1] Wang Y C, Luo Z Q.Optimized iterative clipping and filtering for PAPR reduction of OFDM signals [J] .Communications, IEEE Transactions on, 2011,59 (1): 33-37.

[2] Aggarwal A, Meng T H.Minimizing The Peak-To-Average Power Ratio Of Ofdm Signals Using ConveX Optimization[J].IEEE Transactions on Signal Processing, 2006,54 (8): 3099-3110.

Define new problem: probability constraints PAPR optimizes:

Input: original time-domain signal x (n), threshold value PA that PAPR sets_max, threshold value E of EVM setting_max。

Output: prepare time-domain signal x ' (n) launched after optimization.

Constraint:

1)

2)

Optimization aim: PAPR is minimum.

This problem proposes motivation and is: uses probabilistic model based on outstanding population as constraints, is selected by iteration Select the signal of PAPR characteristic good, the PAPR characteristic of signal can be effectively improved.Asking of traditional PAPR constrained optimization problems Solve, use interior point method.Then in the enforcement of actual ofdm system, it would be desirable to real-time signal processing, interior point method efficiency The highest, it is impossible to be enough suitable for the needs that Real-time hardware processes.It follows that we are by the problem for new definition, design one effectively Algorithm for Solving.The optimality that new algorithm will consider that efficiency is conciliate simultaneously.

6, the solving of new problem: combine Estimation of Distribution Algorithm with differential evolution algorithm and solve.The DEEDA algorithm pair i.e. designed The new problem proposed solves.

Differential evolution algorithm (differential evolution, DE) is a kind of random search algorithm based on population, It utilizes the different information between current population to carry out guiding search.Along with the increase of evolutionary generation, the diversity between individuality will More and more less, and simple differential evolution algorithm lacks the global information that effective mechanism utilizes and produces in search volume, because of And usually converge on local optimization solution.Estimation of Distribution Algorithm utilizes the global information of population to set up probabilistic model, from " macroscopical " Control algolithm is searched for.Thus combine differential evolution algorithm and Estimation of Distribution Algorithm can effectively utilize local message and overall situation letter Breath, forms the hybrid algorithm that function is more powerful.

DE-EDA filial generation generates scheme: the more excellent solution of selected part from current population, and utilizes these more excellent solutions to go to estimate Meter and the distributed model of study population；Then this distributed model of sampling obtains new more excellent population；Successive iteration, final approach is Excellent solution；The direction of advance of conducting evolution search can be carried out, it is to avoid traditional genetic algorithm is handed over by the probability distribution of excellent disaggregation Fork operator and the blindness brought of mutation operator and randomness, be effectively improved evolutionary search efficiency.

As it is shown in figure 1, the embodiment of the present invention provides a kind of PAPR based on probabilistic model to reduce method, including following step Rapid:

Step S1, randomly generate initial population

If population is N-dimensional noise vector, initial noisc vector uses random method to produce from whole spatial noise.

First definition N-dimensional noise vector e (n)

E (n)=x (n)-x ' (n),

E (n) is the skew introduced due to various methods in filtering.Noise can produce identical purpose, but phase Ratio primary signal, can effectively reduce the search volume of signal；X (n) is original time-domain signal, and x ' (n) is filtered letter Number.

X ' (K)=DFT [x ' (n)]

=DFT (x (n)-e (n))_LN

=X (k)-DFT (e (n))_LN

=X (k)-E (k).

E (k) is the frequency domain vectors that e (n) is corresponding, is also the error vector of primary signal and filtered signal.It is directly determined Determine the size of EVM.In this problem, it would be desirable to search for a most suitable E (k), thus meet the requirement of system.We can It is called that PAPR reduces vector with E (k).

Initial noisc vector is produced by random method according to the upper and lower bound of spatial noise.First generation initial noisc Population can be expressed as:

I=1,2 ..., N；J=1,2 ..., D

Wherein,It is the upper bound and the lower bound of noise vector respectively.rand_j(0,1) is equally distributed random change Amount, and rand_j(0,1) ∈ [0,1].The scope of noise vector is chosen as (-0.5-0.5)

If Population Size is N, kth is defined as set for population member

Randomly generate N number of solutionForm initial population X⁰If, evolutionary generation K=0.

Step S2, according to DE/EDA algorithm both candidate nodes produce algorithm generate next generation solution population be:Comprise the following steps:

Step S21, structure probabilistic model

Advantage individuality according to current population sets up the overall distribution of more excellent solution, ranked selects M best solution party Case, wherein, M=0.4*N.

From current population X^kIn select best M solution and build probabilistic model and be

Wherein, P_{J, n}The value of nth elements of the jth sequence for producing

Step S22, intersection and mutation operation

Mutation operation:

By the equation of following differential variation, obtaining variation individuality is:

Wherein,Randomly generate three sample vectors in representative sample space, r1j, r2j, r3j Representing the sequence number randomly choosed, r1, r2, r3 are different,For variation individuality, F is zoom factor, represents difference vector pair Individual influence degree of future generation.F value size has material impact to algorithm performance.Value is excessive, and algorithm the convergence speed becomes Slowly；Value is too small, and population diversity reduces, and algorithm is easily absorbed in local optimum.

Intersect and operate, for increasing individual the dividing of the multiformity of population, its different information utilizing population and population advantage Cloth information, produces candidate's population at individual.

Intersect and operate You Liangge branch.

One branch utilizes DE variation formula to produce candidate's descendant nodes

Can be expressed as follows

Wherein,Represent the vector after intersecting and operating,For object vector, rand () is between [0,1] Uniform random number；J=1,2 ... m represents jth variable (gene), and m is the dimension of variable.CR is the crossover probability factor, CR It is the biggest,RightContribution the biggest, algorithm evolution speed is the fastest, is the most more easily trapped into local optimum；CR is the least,RightContribution the biggest, be more beneficial to keep the multiformity of population, improve the ability of searching optimum of algorithm.

Another branch utilizes the probability Distribution Model of EDA algorithm to produce candidate's descendant nodes.

So, this evolutionary process both make use of the difference information of population member, make use of again the general of whole population optimal solution Rate distributed intelligence.

Step S23, replacement operation

It is chosen as determining trial vector U_{I, t}Whether can become the member in the next generation, DEPR will test according to greedy criterion Vectorial with current population in object vector E_{I, t}Compare.If object function to be minimized, then have relatively Small object The vector of function will win a position on the ground in population of future generation.All individualities in the next generation all ratios corresponding of current population Body is more preferably or the best.

Wherein, E_{I, t+1}For follow-on object vector；

Value obtained by object function is signal calculated PAPR in above-mentioned formula, can calculate according to following formula.

Step S3, iteration

If given termination condition is not up to, k=k+1 continues executing with step S22；The termination condition set is as current Population optimal objective function reaches maximum iteration time less than given numerical value or iterations.

The process of boundary condition

The present invention needs to meet the constraint of EVM, it is ensured that the feasible zone that the new individual parameter value of generation is positioned at problem is necessary 's.Regenerating trial vector by not meeting the new individual of boundary constraint according to step 2, then carrying out intersecting operating, until producing Till raw new individuality meets boundary constraint.

The constraints of EVM is as follows:

Terminate iteration: if population meets end condition and (i.e. produces an acceptable solution or reach greatest iteration time Number), then export, otherwise forward step 2. to

The calculating of complexity

If the complexity that population scale is Np, EDA algorithm is:

It is O (Np) that the first step first step randomly generates the complexity of initial population, and best population foundation based on NP/5 is general The complexity of rate model is O (Np).From the population of 4Np/5, the new individual complexity of sampling is O (4Np/5).

The complexity of the most total EDA algorithm is:

O (Np)+O (Np)+O (4Np/5)=O (Np)

The complexity of DE algorithm:

Then the first step randomly generates the complexity of initial population is O (Np), and the complexity of second step variation is O (Np), the Three complexities intersected are O (Np), and the complexity that the 4th step selects is O (Np*Nlog2N). therefore, total complexity is

O(Np)+O(Np)+O(Np)+O(Np*Nlog₂N)=O (Np*N log₂N)

In the present invention, take Population Size Np=100 and be obtained with a good optimum results.And the size of Np is far away Less than actual sub-carrier number N, because it is maximum iteration time that N=1024. sets G, DEEDA algorithm finds answering of optimal solution Miscellaneous degree is: O (GNlog₂N), this time complexity is well below additive method.

The present invention proposes a new PAPR optimization problem based on probabilistic model constraint, including: analyze institute of more excellent colony The variable comprised, builds the probabilistic model meeting the distribution of these variablees；This probabilistic model produces new population again；The matter of new population Amount is better than original population；Finally according to this kind of form, current optimal solution is approached globally optimal solution length by length.The present invention Use DE algorithm (DE-EDA algorithm) based on probabilistic model, differential evolution algorithm can be effectively combined and distribution estimating is calculated, Effectively utilize local and global information, it is to avoid be absorbed in locally optimal solution when solving PAPR optimization problem, thus obtain more Powerful PAPR optimization ability.

Last it is noted that above example is only in order to illustrate technical scheme, it is not intended to limit；Although With reference to previous embodiment, the present invention is described in detail, it will be understood by those within the art that: it still may be used So that the technical scheme described in foregoing embodiments to be modified, or wherein portion of techniques feature is carried out equivalent； And these amendment or replace, do not make appropriate technical solution essence depart from various embodiments of the present invention technical scheme spirit and Scope.

Claims (1)

1. a PAPR based on probabilistic model reduces method, it is characterised in that comprise the following steps:

Step S1, randomly generate initial population

Randomly generate N number of solutionForm initial population X⁰If, evolutionary generation K=0；

Step S2, according to DE/EDA algorithm both candidate nodes produce algorithm generate next generation solution population be:Comprise the following steps:

Step S21, structure probabilistic model

From current population X^kIn select best M solution and build probabilistic model and be

Wherein,

P_{J, n}The value of nth elements of the jth sequence for producing；

Step S22, intersection and mutation operation

Mutation operation:

By the equation of differential variation, obtaining variation individuality is:

$V_{ij}^{(t+1)}=E_{r3j}^{\left(t\right)}+F\×(E_{r1j}^{\left(t\right)}-E_{r2j}^{\left(t\right)})$

Wherein,Randomly generate three sample vectors in representative sample space, r1j, r2j, r3j represent with The sequence number that machine selects,For variation individuality, F is zoom factor, represents the difference vector influence degree to individuality of future generation,

Intersect and operate: utilize the different information of population and the distributed intelligence that population advantage is individual, produce candidate's population at individual,

Intersect and operate You Liangge branch, wherein,

One branch utilizes DE variation formula to produce candidate's descendant nodes, is expressed as follows:

$U_{ij}^{(t+1)}=\left\{\begin{array}{ccccc}{V}_{ij}^{(t+1)}& {\mathrm{rand}}_j(0,1)\≤CR& or& j=j_{rand}& j=1,2...,D\\ E_{ij}^{\left(t\right)}& {\mathrm{rand}}_j(0,1)>CR& & & \end{array}\right.$

Wherein,Represent the vector after intersecting and operating,For object vector, rand () is uniform between [0,1] Random number, j=1,2 ... m represents jth variable (gene), and m is the dimension of variable, and CR is the crossover probability factor,

Another branch utilizes the probability Distribution Model of EDA algorithm to produce candidate's descendant nodes

Step S23, replacement operation

It is chosen as determining trial vector U_{I, t}Whether can become the member in the next generation, by trial vector and work as according to greedy criterion Object vector E in front population_{I, t}Comparing, computing formula is as follows:

Wherein,

E_{I, t+1}For follow-on object vector；

Step S3, iteration

If given termination condition is not up to, k=k+1 continues executing with step S22, and the termination condition set is as current population Optimal objective function reaches maximum iteration time less than given numerical value or iterations.