Intersection-traffic-flow-forecasting

Intersection traf?c?ow forecasting based onν-GSVR with

a new hybrid evolutionary algorithm

Min-Liang Huang

Department of Industrial Management,Oriental Institute of Technology,58,Section2,Sichuan Road,Panchiao,220Taipei,Taiwan

a r t i c l e i n f o

Article history:

Received7May2014

Received in revised form

19June2014

Accepted20June2014

Communicated by:Wei Chiang Hong

Available online4July2014

Keywords:

Short-term traf?c?ow forecasting

Support vector machine

Gaussian loss function

Genetic algorithm

Chaos map

Cloud model

a b s t r a c t

To deal well with the normally distributed random error existed in the traf?c?ow series,this paper

introduces theν-Support Vector Regression(ν-GSVR)model with the Gaussian loss function to the

prediction?eld of short-term traf?c?ow.A new hybrid evolutionary algorithm(namely CCGA)is

established to search the appropriate parameters of theν-GSVR,coupling the Chaos map,Cloud model

and genetic algorithm.Consequently,a new forecasting approach for short-term traf?c?ow,combining

ν-GSVR model and CCGA algorithm,is proposed.The forecasting process considers the traf?c?ow for the

road during the?rst few time intervals,the traf?c?ow for the upstream road section and weather

conditions.A numerical example from the intersection between Culture Road and Shi-Full Road in

Banqiao is used to verify the forecasting performance of the proposed model.The experiment indicates

that the model yield more accurate results than the compared models in forecasting the short-term

traf?c?ow at the intersection.

1.Introduction

Intersection is a bottleneck in urban road traf?c network and

its passage capacity directly determines the network capacity[1].

The congestion at the intersections wastes time,increases fuel

consumption and environmental pollution.Real-time traf?c?ow

prediction can effectively save travel time,reduce environmental

pollution and save energy,when implemented in real time traf?c

control and guidance.Short-term traf?c?ow prediction is also the

key technology for intelligent transportation systems;therefore

the short-term traf?c?ow prediction at intersections has a great

practical signi?cance.According to different principles,the current

short-term traf?c?ow prediction methods can be classi?ed into

two types.The?rst type is the prediction method based on the

determination of mathematical models,including the early com-

mon autoregressive moving average model(ARMA)[2],the later

more complex ARIMA model[3]with higher accuracy and the

Kalman?lter model[4].The second type is the knowledge-based

intelligent model prediction method,including fuzzy theory[5],

wavelet theory[6],Chaos theory[7]and neural networks[8,9,10].

The traditional calculation method is simple and fast,but does not

re?ect the uncertainty and nonlinearity of the process of traf?c

?ow.Therefore it is ineffective in handling complex traf?c?ow

prediction problems.The neural network algorithm is a typical

representation of the second type method,because the neural

network algorithm cannot overcome de?ciencies in empirical

risk minimization.That is to say,when the sample size of study

is limited,the accuracy is dif?cult to guarantee;but when the

sample size of study is large,it is easy to fall into the trap of over-

?tting,so the neural network algorithm is versatile.

Having overcome the inherent defects in the neural network

[11],the SVR has the advantages of a global optimum,a simple

structure,strong small sample promotion ability and it is based on

structural risk minimization criterion.Therefore,it can solve the

problems such as small sample,nonlinearity,high dimension,local

minimum,and has been successfully applied to short-term traf?c

?ow prediction[11–14].But the standard SVR model cannot

effectively deal with the noise arising from the?ow sequence

due to random factors.Zhu et al.[15]presented the short-term

traf?c?ow prediction model based on wavelet analysis and SVR,

which had better prediction capabilities.Wavelet analysis has an

unparalleled advantage in the handling of noise,but it is complex

process and very time-consuming.Different from other predic-

tions,short-term traf?c prediction is done online in real time,and

has high real-time prediction requirements.That is to say the

computational time is more“expensive”within the accuracy level

required of traf?c?ow prediction.Based on the Gaussian function

which can effectively handle normally distributed random errors,

Wu[16]proposed a Gaussian loss function basedν-support vector

regression(ν-GSVR),which achieved good?ltering results in the

application of predicting product sales.This paper applies the

ν-GSVR model to forecast short-term traf?c?ow at intersections.

However,the SVR model does not give a method for optimizing

the combination of model parameters,and there is certain

cross-error[17]in the commonly used cross validation.GA[18]

Contents lists available at ScienceDirect

journal homepage:https://www.360docs.net/doc/079779307.html,/locate/neucom

Neurocomputing

https://www.360docs.net/doc/079779307.html,/10.1016/j.neucom.2014.06.054

0925-2312/&2014Elsevier B.V.All rights

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E-mail address:fg002@https://www.360docs.net/doc/079779307.html,.tw

Neurocomputing147(2015)343–349

in the optimization of model parameters has global optimization,robustness and self-adaptability [19,20].But standard GA has some de ?ciencies.While providing an evolution opportunity for the individuals in the population,the random operation inevitably causes degradation in the group,leading to some dependence on the algorithm and the initial population and is prone to “pre-cocious ”or local convergence.The direction of genetic evolution is random and uncontrollable leading to slow searches for the optimal solution or a satisfactory solution.To quickly and accu-rately search for the optimal parameter combinations of ν-GSVR model,the standard GA has been improved through the imple-mentation of Cat map and Cloud models.This paper proposes Chaos Cloud genetic algorithm (CCGA),to optimize the parameter combinations of ν-GSVR model.Finally a new approach for fore-casting short-term traf ?c ?ows at an intersection is established,combining ν-GSVR with CCGA (CCGA –ν-GSVR).The proposed model considers the relationship between the short-term traf ?c ?ow and the real traf ?c ?ow during the ?rst few time intervals,the traf ?c ?ow for the upstream road section and the weather conditions.

The rest of this paper is organized as follows.Section 2describes the ν-GSVR model.Section 3provides CCGA based on Cat Maps,Cloud model and GA algorithm.Section 4introduces the proposed CCGA –ν-GSVR forecasting model.Section 5illustrates a numerical example to reveal the forecasting performance of the proposed forecasting model.The conclusions are given in Section 6.

2.ν-support vector regression model with Gaussian loss

function

2.1.ν-Support vector regression based ε-loss function

Suppose training set T ?{(x 1,y 1),…,(x l ,y l )},where x i is a d -dimen-sional input variable,and y i is the corresponding output value.Through a nonlinear mapping function Ф(x )?{Ф(x 1),Ф(x 2)…Ф(x l )},SVR model maps the sample into a high dimensional feature space R df ,in which the optimal decision function is constructed as follows:f ex T?w T ?ex Ttb ;w A R df ;b A R

e1T

Where,w is weight vector,b is bias value,and ?tting function f

(x )minimizes the following objective function (structural risk):min 12

‖ω‖2

tCR emp

e2T

where e1=2Tjj ωjj 2is the expression for the complexity of the decision function;the second item,empirical risk R emp ,is for the training errors;C is a regulatory factor used to adjust the ratio between the model complexity and the training error R emp .The training error R emp ?e1=l T∑l i ?1j y i àf ex i Tj can be measured with ε,the insensitive loss function de ?ned by c ex i ;y i ;f ex i TT?max f 0;y i àf ex i T àεg .

In the standard support vector regression (ε-SVR)model,εinsensitive factor controls the sparsity of the solutions and the generalization of models.However it is very dif ?cult to reasonably determine the value of εin advance.Therefore Scholkopf et al.[21]presented ν-SVR by introducing a parameter νinto the ε-SVR model.At this point,the ν-SVR model with the ε-insensitive loss function is shown as follows:min

w ;b ;ε;ζen T

τew ;ε;ζen TT?1jj w jj 2tC eνεt1∑l

i ?1

eζi tζn i TTe3T

s :t :

ewx i tb Tày i r εtζi

y i àewx i tb Tr εtζn i ζen TZ 0;εZ 0

8><>:e4T

Where:ζ(n )?(ζ1,ζn 1,…,ζl ,ζn

l )is a slack variable,w is the d-dimen-sional row vector,C (C Z 0)is a penalty coef ?cient,deciding the balance between con ?dence risk and experience risk;νA [0,1]is the upper bound of the proportion of error samples in the total number of training samples and the lower bound of the proportion of support vectors in the total number of training samples;unlike standard SVR,εis present as the variable of optimization problem,and its value will be given as part of the solution.

2.2.ν-SVR model based on Gaussian loss function (ν-GSVR)The standard SVR model with ε-insensitive loss function cannot deal with the random error (white noise)in normal distributed prediction sequences;so the standard SVR theoretically does not guarantee the accuracy of time series prediction problems contain-ing white noise.The Gaussian function is in accord with the characteristics of normally distributed noise,thus it can minimize the effects of normally distributed noise as the loss function of SVR to a certain extent.

LSSVR uses the ε-insensitive function as the loss function,uses the sum of the squares of the slack variables and changes the inequality constraints into equality constraints,which aims to simplify the solution of SVR.The ν-GSVR is the establishment of the relationship between slack variables and the loss function and normally distributed noise under the condition that the inequality constraints are not changed,and slack variable is also squared [22].At this point,the ν-GSVR optimization problem is as follows:min

ω;b ;ε;ζen T

τew ;ζen T;εT?12jj w jj 2tC eνεt1l ∑l i ?112

eζ2i tζn 2

i TTe5T

s :t :

ewx i tb Tày i r εtζi

y i àewx i tb Tr εtζn i ζen TZ 0;εZ 0

8><>:e6T

where:ζ(n )?(ζ1,ζn 1,…,ζl ,ζn

l )is the slack variable;w is d -dimen-sional row vector;C (C 40)is the penalty coef ?cient;νvalue range is [0,1];εis the present as optimization variable;its value will be given as part of the solution.Literature [16]makes a detailed proof on the existence and uniqueness of ν-GSVR model solution.

The calculation steps for ν-GSVR model are as follows:

Step 1:Suppose the known training set T ?{(x 1,y 1),…,(x i ,y i ),…,(x l ,y l )},where x i A R d ,y i A R ,i ?1;…;l ;Step 2:Select the appro-priate positive νand C ,and the kernel function K (x i ,y i );Step 3:Construct and solve the optimization problem,and the

basic

Fig.1.The architecture of ν-GSVR.

M.-L.Huang /Neurocomputing 147(2015)343–349

344

structure is shown in Fig.1

min a;a n weα;αnT?

∑l

i;j?1

eαn

àαiTeαn

àαjTKex i;x jTà∑l

i?1

eαn

àαiTy

∑l

i?1

eαn2

tα2

Te7T

s:t:

∑l

i?1

eαn

àαiT?0

∑l

i?1

eαn

tαiTr Cυ

0rαi;αn i r C=l;i?1;…;l

>>>

e8TGet the optimal solutionα(n)?(α1,αl,α1n,…,αl n)Step4:Construct

decision function

fexT?∑

i?1eαn

àαiTKex i;xTtbe9T

where b is calculated as follows;select the two components a j or a k in the open interval(0,C/l),then

b?1

y jty kàe∑

i?1

ea n

àa iTKex i x jTt∑

i?1

ea n

àa iTKex i x kTT

e10T

Parameterεcan be calculated by the following two equations:

ε?∑l

i?1ea n

àa iTKex i x jTtbày

orε?y kà∑

i?1

ea n

àa iTKex i x kTàb

e11T

3.A new hybrid optimization algorithm

The parameter selection in SVR prediction model determines the generalization performance of the model,but there is no effective way to determine the optimal parameter combination,and there is cross error in traditional cross validation[23].In view of this,through the improvement on the standard genetic algorithm(SGA)based on Cat map and Cloud models,this paper presents CCGA to determine the parameter combinations ofν-GSVR model.

3.1.Standard genetic algorithm

By the joint action of reproduction,crossover,mutation and other genetic operators,GA makes the population continuously evolve and eventually arrive at the optimal solution.Due to the self-organization,self-adaptation,self-learning and essential par-allel characteristics of GA,it has been widely used in parameter estimation,pattern recognition,machine learning,neural net-works,industrial control and many other areas;however,the shortcomings of the GA including the slow search for optimal solution or satisfactory solution and the easiness to fall in “prematuration”prevent its use in a wide range of applications. Based on this,the scholars from various countries have conducted in-depth studies on the encoding of GA,the determination of control parameters,the mechanism of action operators and have presented numerous improved methods[24–26],but in the process of application in large-scale complex parameter optimization,there are still defects in search speed and optimiza-tion accuracy.Based on the advantages of Cat map such as good ergodicity and uniformity,resistance to fall into small cycles and ?xed points,as well as the characteristics of cloud droplets of the Cloud models such as randomness and stable orientation,this paper carries out the following improvements on the SGA.

3.2.Initialization of parent population with Cat map

Chaos optimization approach is a global optimization technique [27–30],using the nature of chaos such as ergodicity and initial value sensitivity.The current existing chaos optimization approaches have mostly used the logistic map as a chaotic sequence generator. The probability density of the chaotic sequence generated by the logistic map obeys the Chebyshev distribution similar to the‘bath tub’curve,and such a distribution hinders the global search capa-bility and ef?ciency of the algorithm.To overcome the shortcomings of the logistic map,the Cat map with the advantages of good ergodicity and uniformity,its resistance to fall into small cycles and ?xed points,is used in the initialization of the parent population of GA.

3.2.1.Cat map

The two-dimensional Cat map[31]equation is as follows:

x nt1?ex nty nTmod1

y nt1?ex nt2y nTmod1

(

e12T

Where:x mod1?xà[x];now,the two Lyapunov indices of Cat map are L1?lnee3t

???

T=2T40and L2?lnee3à

???

T=2To0,indi-cating that Cat map has chaotic characteristics.

3.2.2.Analysis of chaotic characteristics of Cat map and logistic map

Logistic map equation:

x nt1?ux ne1àx nTe13TWhere x n is the n th iteration value of variable x and u is a control parameter.When u?4,the system completely is in a chaotic state[32,33].Furthermore x0can take any initial values except for0.25,0.5and0.75within the interval of(0,1).

To analyze the chaotic characteristics of Cat map and logistic map,suppose the initial values of logistic map are0.2,0.4,0.6and 0.8whilst the initial values of Cat map are0,0.2,0.4,0.6,0.8and1. After50,000iterations the distribution graph for the two maps within the range of[0,1]was obtained.The statistics for the values with the maximum and minimum number of occurrences were carried out and the results obtained are shown in Table1.

The statistics in Table1show the maximum frequency of the logistic map within(0;0.01)and(0.99;1)exceeds3000times, while the average value frequency within(0.01,0.99)interval is only about500times.So,when the optimal solution is in the midrange,the application of the logistic map in the generation of the parent population makes it dif?cult to ensure an ef?cient search for the optimal solution.Meanwhile the maximum fre-quency of occurrence for the Cat map is E560times and the minimum frequency is E440times,this indicates that the Cat map is more evenly distributed.Secondly the initial values of Cat map can range between0and1,which is not permissible for the

Table1

Comparison on chaotic distribution of logistic map and Cat map.

Logistic map Cat map

Initial value0.20.40.60.800.20.40.60.81 Max frequency3222324132393284559563547556546559 Min frequency283290289291450440452437458450

M.-L.Huang/Neurocomputing147(2015)343–349345

logistic map.Therefore the Cat map has better chaotic distribution characteristics,and its application in the initialization of parent population for GA is able to better able to maintain the population diversity for an ergodic search theoretically.

3.3.Crossover and mutation based on Cloud model

Cloud models have the characteristics of random and bias stability[34].The random property avoids a local minimum solution,and the bias stability aids the positioning of the global optimum.Thus,introduction of Cloud models into the GA can reduce optimization time-consuming and improve the ability to avoid falling into local minimums when used with both the basic cloud generated algorithm and the Y-condition cloud generated algorithm which perform the mutation operation and the cross-over operation respectively.

Suppose T is the language value in the domain u,map C T(x):u-[0,1],8x A u,x-C T(x),then the distribution of C T(x)on u is called the membership cloud under T.In the case of obeying the normal distribution,C T(x)is known as the normal Cloud models[35].The overall characteristics of the Cloud models can be represented by the three digital features including desired E,entropy S and hyperentropy H.

E is the expectation of spatial distribution of cloud droplet in the domain as well as the point that is the most able to represent the qualitative concept.S represents the measurable granularity of the qualitative concept,and the greater the entropy S the larger the concept.H is the uncertain measurement of entropy and is jointly determined by the randomness and fuzziness of the entropy.

The Cloud models have the characteristics of the uncertainty with certainty and stability with change,and thus re?ect the basic principle of the evolution of a species in nature.The Cloud models parameter E represents the parent's good individual genetic characteristics and the offspring's inheritance from the parent. The entropy S and hyper-entropy H indicate the uncertainty and fuzziness of the inheritance process,giving the mutation charac-teristics of the species during the evolutionary process.

The algorithm or hardware for the generation of cloud droplets is called the cloud generator[35].The basic cloud generator and Y-condition cloud generator are calculated as follows.

Normal cloud generator:Input the three digital features includ-ing E,S and H,as well as n,the number of cloud droplets;output the quantitative values of n cloud droplets and the certainty of the representative concept.

1.To generate S1,a normal random number with the expectations

of S and the standard deviation of H.

2.To generate x i,the normal random number with the expecta-

tions of E and the standard deviation of S1.

3.Suppose x i should be a speci?c quantitative value of qualitative

concept,called cloud droplets,the calculation m i?eàex iàET=2neS1T2 is conducted.

4.Suppose m i should be the certainty for the qualitative concept

of x i.

5.{x i,m i}completely re?ect the conversion process from qualita-

tive to quantitative.

6.Repeat steps1–5,till the n cloud droplets(x i,m i)are all

generated.

Y-condition cloud generator:input the three digital features including E,S,H,and n,the number of cloud droplets,to randomly generate the certainty of m0;output n cloud droplets.

1.To generate S n,a normal random number with the expectations

of S and the standard deviation of H.

2.Calculate cloud droplet x i,x i?E7S ?????????????????????à2lneμ

.3.Repeat steps1–2,till the n cloud droplets(x i,m0)are all

generated.

https://www.360docs.net/doc/079779307.html,GA

The shortcomings of standard GA are overcome by adopting real-coding,using Cat map for the generation of initial population, using the Y-condition cloud of normal Cloud models to achieve crossover operation and using the basic cloud to achieve mutation operation.The computing process of CCGA is as follows: Step1:Generation of initial population by Cat map:use Eq.(12) to produce the initial population,in order to make it be as uniformly distributed as possible in the solution space,over-come the heterogeneity of the initial population generated by random sequence and improve the diversity of the population.

Step2:Select each individual genes as theν-GSVR model parameters to calculate the individual?tness.

Step3:Selection,copying and migration.

①Copy the best individual to the next generation.

②Select an elite population,and copy it.

③Replace the worst individual by a randomly generated

individual.

Step4:Y-condition cloud crossover.

①Randomly generate membership m0according to the

uniform distribution.

②Ifμ0is less than crossover probability p c,E is be calculated

by:

fitnesseiT

x it

fitnessejT

x je14T

Where:x i and x j respectively are the parent individuals of the crossover operation;?tness(i)and?tness(j)are the ?tnesses of the two parent individuals;

③S?variable search range/c1.

④H?S/c2.

⑤Use the Y-condition cloud generator to produce two off-

spring individuals.

Step5:Mutation of normal cloud.

①Take the original individual as E.

②S?variable search range/c3.

③H?S/c4.

④Activate normal cloud generator to produce cloud

droplets(x i,m i).

⑤If m i is less than the mutation probability p m,x i will be

regarded as the post-mutation individual.

Step6:Go to Step2,till it meets the optimal stopping conditions,where c1–c4is the control parameter.

3.5.Analysis of effects of control parameter value

According to“3δ”rule[36],S value determines the horizontal width of cloud cover,that is,it determines the search range of individual during crossover and mutation operation.The values of c1and c3generally are recommended to be within the interval [6,6P]where P is size of the population.To a certain extent too great a value for H may lead to the loss of“bias stability”in the Cloud models.However too small a value for H may lead to the loss of“randomness”.Therefore the values of c2and c4are recom-mended to be within[1,10].Although S and H are the important parameters for the Cloud models,after several generations,the randomness of E andμconceals the difference in the evolution result due to the difference between the values.That is the

M.-L.Huang/Neurocomputing147(2015)343–349 346

difference in value among the control parameters c1–c4within a certain range do not have a major effect on the?nal evolution https://www.360docs.net/doc/079779307.html,prehensively considering the optimization, speed and accuracy of an algorithm,this experiment takes c1?c3?3P,c1?c4?6.Of course,in the process of practical application the values of parameters c1–c4can be properly determined according to a variable search range,population size and search accuracy.

https://www.360docs.net/doc/079779307.html,GA in selecting parameters ofν-GSVR model

The procedure of the CCGA–ν-GSVR model is as follows:?rst step,Normalize the training data set and the value range of parameters;second step,use the evolution individuals generated by CCGA asν-GSVR parameters;third step,according to the normalized training data,conduct training to calculate the regres-sion values;forth step,determine whether the current parameter combinations meet the parameter optimization accuracy require-ments,if the requirement is met,stop the parameter optimization. The optimal parameter combination obtained will be used as the parameter ofν-GSVR for traf?c?ow prediction.Otherwise,repeat steps2–4until the accuracy of parameter optimization is met.The speci?c calculation process is shown in Fig.2.

To ensure the CCGA optimization ef?ciency,this paper uses the reciprocal of the root mean square error as?tness function,and then the?tness function is calculated as follows.

fitness?

?????????????

RMSE

p?1

??????????????????????????????????????????????????

e1=nT∑

t?1

eY netTàYetTT2

se15T

Where n is the number of input samples,Y n(t)is the regressed value for the sample data,Y(t)is the actual value for the sample data.

In view of the radial basis function's good ability to learn in the application process of SVR[11–14],this paper selects radial basis function as the kernel function ofν-GSVR model.The radial basis function is expressed as the following equation.

Kex i;x jT?expàjj x iàx j jj2

2δ

e16T

5.The numerical test

Urban traf?c?ow is characteristic of?uid,and the distribution in time is continuous,that is,the traf?c?ow at the next time of the road section is intrinsically linked with the traf?c?ow in the?rst few intervals of the road section.Meanwhile,the road section is a part of the larger road transport network,and the traf?c?ow of a road section will be in?uenced by the traf?c?ow in the upstream road sections.In addition,the weather condition affects the traf?c ?ow to a large extent.Therefore,we can select traf?c data for the ?rst few intervals of the section,the upstream traf?c data and weather conditions at the time to predict the traf?c?ow of the road section for the next time step.

Taking the data detected from intersection of Culture Road and Shi-Full Road in Banqiao for the numerical test.Assuming that t represents the current time,Y(tt1)represents the traf?c?ow for the next time step,while X1(t),X2(t)and X3(t)represent the traf?c ?ow for the three upstream sections of the road.The weather condition is set as the sixth in?uencing factor,in this case X4(t), which is quanti?ed as1for heavy snow or sleet,0.75for light snow or sleet,0.5for heavy rain,0.25for light rain,and0for sunny or cloudy conditions.The result of tentative calculation indicates that the forecasting performance is best,when the?rst two times intervals of the traf?c?ow are select as the input vector.At this point,we obtained the six in?uencing factors of the traf?c?ow Y(tt1),X?{Y(tà1),Y(t),X1(t),X2(t),X3(t),X4(t)}.

Traf?c?ow data was detected by a Speed Spy(SI3K-band) radar traf?c detector.The sample window of10min gave90sets of data for the?ve Friday evening peak hours from March7,2014to April4,2014(17:00–20:00).The?rst72data from the?rst four Friday nights were used as training samples for the model.The remaining18data from the?fth Friday night peak hour traf?c?ow were used to test the prediction accuracy of the model.

The proposed CCGA–ν-GSVR model has been implemented in Matlab7.1programming language.The experiments are made on a 1.81GHz Core(TM)2CPU personal computer with2.0GB memory under Microsoft Windows XP professional.Model initialization:

C value ranges[0.01,1000],νvalue ranges[0.01,1],δvalue ranges

[0.01,1],genetic population size popsize?60,maximum evolution generation G max?50,crossover probability P c?0.3,mutation prob-ability P m?0.8,relative error of adjacent-generation optimal individual?tness E?0.00001.The combination of optimal para-meters ofν-GSVR are obtained by the CCGA,C?584.5,ν?0.87 andδ?0.21.The developed model was used to forecast the traf?c ?ow.The chart for the comparison between actual traf?c?ow and model?tness value is described in Fig.3.The actual traf?c ?ow and model prediction results are shown in Table2.The results show that the?tness results are basically consistent with the actual traf?c?ow variation curve,where the root mean square error of regressed value is less than3,the root mean square error of prediction is less than13,and the prediction accuracy satis?es the actual application requirements.

To compare the parameter optimization ef?ciency of CCGA,this paper also used SGA to optimize the parameters ofν-GSVR model. Using the same computer,the same population size,crossover probability and mutation probability,the statistical results for the ?tness values and genetic algebra of the two algorithms are plotted against time in Fig.4.

The analyses as shown in Fig.4illustrate that,within the running time of2000s,the use of Cat map for the initialization of parent population and the introduction of cloud crossover and mutation operations,the running time of CCGA for each iteration is more time consuming than SGA.This extra computational time results in the CCGA solving fewer generations than the SGA model for a given period of time.However,based on the ergodic characteristics of Cat map,the maximum?tness value of the CCGA search for optimal solution is double that of the SGA algorithm. The introduction of cloud theory-based genetic manipulation reduced the range of maximum?tness value and minimum?tness value so that more individuals from CCGA search can be concen-trated in the range of the optimal solution.The overall ef?ciency to ?nd the optimal solution using CCGA is signi?cantly higher than that of SGA algorithm,indicating that CCGA is more suitable for the optimization ofν-GSVR model parameters.

To compare the performance of the CCGA–ν-GSVR model in traf?c forecasting,this paper selects the ARIMA model,the PSO-BP neural network model proposed by Ye[9],the WD-SVM

prediction Fig.2.The process of CCGA–ν-GSVR.

M.-L.Huang/Neurocomputing147(2015)343–349347

model proposed by Zhu [15],and the improved CCGA –ν-SVR prediction model based on the GSVMR model proposed by Ren [12]as comparison models.The four models were calculated in the same computer using Matlab 7.1.Taking into account the fact that the increase in optimization time improves the optimization effect,the model parameters should be selected for each model to ensure the same maximum optimization time is achieved.In order to ensure the selection accuracy of SVR parameters the root mean square error was used to compare the performance of each method.

The comparison of the real traf ?c ?ow data and the forecasted results of the various modeling methods are given in Table 3.

It can be seen from Table 3that the SVR model is superior to ARIMA and PSO-BP in the capacity of the traf ?c ?ow forecasting.In terms of noise handling during in the prediction process the WA-SVM model ?rstly carried out noise reduction on the traf ?c ?ow sequence through wavelet analysis;eliminating the effects of random errors in the sequence of traf ?c ?ow in the SVM model.This has proven bene ?cial as the prediction accuracy was sig-ni ?cantly superior to that of un ?ltered CCGA –ν-SVR model.From the comparison of prediction results between CCGA –ν-SVR model and CCGA –ν-GSVR model,it can be seen that the proposed CCGA –ν-GSVR model also played a role in weakening these random errors,and the prediction accuracy showed a better correlation with the measured results than that of the CCGA –ν-SVR model.Although the noise reduction effect is inferior to wavelet analysis,the computational complexity of wavelet analysis is not conducive to the actual operation.For real-time traf ?c prediction,the real-time performance of algorithms is the determining factor for a given accuracy condition.In this sense,the proposed CCGA –ν-GSVR model is more suitable for the short-term traf ?c prediction at intersections.

6.Conclusions

Intersections are the bottleneck in urban road traf ?c network,and its passage capacity determines the network capacity.The real-time accurate prediction for the traf ?c ?ow at an intersection can effectively save travel time,ease road congestion,reduce environmental pollution and conserve energy.In this paper,a new approach for predicting short-term traf ?c ?ow based on the

Table 2

Forecasting result of CCGA –ν-GSVR model a .

Peak period X 1(t )X 2(t )X 3(t )X 4(t )Y(t à1)Y (t )Y (t t1)

Actual Forecasting Error

17:301112281240176182195202717:401072381190.25182195259250à917:501352511190195259188196818:001262411480259188233219à1418:101282461480.25188233221213à818:201482641380.5233221267258à918:301522631620.5221267291284à718:401462941420267291310297à1318:501392631610.25291310295286à919:001412701450.25310295228220à819:101472671320295228266254à1219:201232461420228266282271à1119:301162551230266282233240719401302381370282233237231à619:501012331320233237235221à1420:00

102231980.2523723518019616

“17:30”denotes the 17:30on 4April 2014,and so

on.

https://www.360docs.net/doc/079779307.html,parison of training.

Table 3

Comparison between four different models.

Peak period Actual CCGA –ν-GSVR CCGA –ν-SVR WA-SVR PSO-BP ARIMA 17:3019520220418922121617:4025925024626623723617:5018819617619516120818:0023321925122020124918:1022121321121519324518:2026725827927429624318:3029128427628526432218:4031029732130034533218:5029528631230126632819:0022822021023525820819:1026625427925529829419:2028227129929024930219:30233240224239258256194023723122524820920319:5023522121822226726120:00180

196189168226194RMSE

10.31

17.39

8.89

30.51

37.04

Fig.3.Fitting chart of CCGA –ν-GSVR.

M.-L.Huang /Neurocomputing 147(2015)343–349

348

CCGA–ν-GSVR method is proposed.The numerical test based on detected data is used for elucidating the forecasting accuracy of the proposed method.The prediction results of the proposed CCGA–ν-GSVR forecasting scheme are compared to those of the CCGA–ν-GSVR,CCGA–ν-SVR,WA-SVR,PSO-BP and ARIMA.The numerical test indicates that the proposed scheme obtain better prediction result and outperforms the?ve competing models.In short,the proposed forecasting scheme is a valid approach for short-term traf?c?ow predication.

In future researches,more in?uence factors should be consid-ered and other hybrid optimization methods should studied for more appropriate parameters ofν-GSVR model,for improving the performance of short-term traf?c?ow forecasting.

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Min-Liang Huang was born in1955.He received his

master of Industrial Education from National Taiwan

Normal University in1982.He is currently a senior

lecturer in the Department of Industrial Management

of Oriental Institute of Technology.His research inter-

ests are hybrid evolutionary algorithm,grey theory,and

computational intelligence.

M.-L.Huang/Neurocomputing147(2015)343–349349