Intersection traffic flow forecasting based on ν-GSVR witha new hybrid evolutionary algorithm

Min-Liang HuangDepartment of Industrial Management, Oriental Institute of Technology, 58, Section 2, Sichuan Road, Panchiao, 220 Taipei, Taiwan

a r t i c l e i n f o

Article history:Received 7 May 2014Received in revised form19 June 2014Accepted 20 June 2014Communicated by: Wei Chiang HongAvailable online 4 July 2014

Keywords:Short-term traffic flow forecastingSupport vector machineGaussian loss functionGenetic algorithmChaos mapCloud model

a b s t r a c t

To deal well with the normally distributed random error existed in the traffic flow series, this paperintroduces the ν-Support Vector Regression (ν-GSVR) model with the Gaussian loss function to theprediction field of short-term traffic flow. A new hybrid evolutionary algorithm (namely CCGA) isestablished to search the appropriate parameters of the ν-GSVR, coupling the Chaos map, Cloud modeland genetic algorithm. Consequently, a new forecasting approach for short-term traffic flow, combiningν-GSVR model and CCGA algorithm, is proposed. The forecasting process considers the traffic flow for theroad during the first few time intervals, the traffic flow for the upstream road section and weatherconditions. A numerical example from the intersection between Culture Road and Shi-Full Road inBanqiao is used to verify the forecasting performance of the proposed model. The experiment indicatesthat the model yield more accurate results than the compared models in forecasting the short-termtraffic flow at the intersection.

& 2014 Elsevier B.V. All rights reserved.

1. Introduction

Intersection is a bottleneck in urban road traffic network andits passage capacity directly determines the network capacity [1].The congestion at the intersections wastes time, increases fuelconsumption and environmental pollution. Real-time traffic flowprediction can effectively save travel time, reduce environmentalpollution and save energy, when implemented in real time trafficcontrol and guidance. Short-term traffic flow prediction is also thekey technology for intelligent transportation systems; thereforethe short-term traffic flow prediction at intersections has a greatpractical significance. According to different principles, the currentshort-term traffic flow prediction methods can be classified intotwo types. The first type is the prediction method based on thedetermination of mathematical models, including the early com-mon autoregressive moving average model (ARMA) [2], the latermore complex ARIMA model [3] with higher accuracy and theKalman filter model [4]. The second type is the knowledge-basedintelligent 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 notreflect the uncertainty and nonlinearity of the process of trafficflow. Therefore it is ineffective in handling complex traffic flowprediction problems. The neural network algorithm is a typicalrepresentation of the second type method, because the neuralnetwork algorithm cannot overcome deficiencies in empirical

risk minimization. That is to say, when the sample size of studyis limited, the accuracy is difficult to guarantee; but when thesample size of study is large, it is easy to fall into the trap of over-fitting, 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 simplestructure, strong small sample promotion ability and it is based onstructural risk minimization criterion. Therefore, it can solve theproblems such as small sample, nonlinearity, high dimension, localminimum, and has been successfully applied to short-term trafficflow prediction [11–14]. But the standard SVR model cannoteffectively deal with the noise arising from the flow sequencedue to random factors. Zhu et al. [15] presented the short-termtraffic flow prediction model based on wavelet analysis and SVR,which had better prediction capabilities. Wavelet analysis has anunparalleled advantage in the handling of noise, but it is complexprocess and very time-consuming. Different from other predic-tions, short-term traffic prediction is done online in real time, andhas high real-time prediction requirements. That is to say thecomputational time is more “expensive” within the accuracy levelrequired of traffic flow prediction. Based on the Gaussian functionwhich can effectively handle normally distributed random errors,Wu [16] proposed a Gaussian loss function based ν-support vectorregression (ν-GSVR), which achieved good filtering results in theapplication of predicting product sales. This paper applies theν-GSVR model to forecast short-term traffic flow at intersections.

However, the SVR model does not give a method for optimizingthe combination of model parameters, and there is certaincross-error [17] in the commonly used cross validation. GA [18]

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Neurocomputing

http://dx.doi.org/10.1016/j.neucom.2014.06.0540925-2312/& 2014 Elsevier B.V. All rights reserved.

E-mail address: fg002@mail.oit.edu.tw

Neurocomputing 147 (2015) 343–349

in the optimization of model parameters has global optimization,robustness and self-adaptability [19,20]. But standard GA has somedeficiencies. While providing an evolution opportunity for theindividuals in the population, the random operation inevitablycauses degradation in the group, leading to some dependence onthe algorithm and the initial population and is prone to “pre-cocious” or local convergence. The direction of genetic evolution israndom and uncontrollable leading to slow searches for theoptimal solution or a satisfactory solution. To quickly and accu-rately search for the optimal parameter combinations of ν-GSVRmodel, the standard GA has been improved through the imple-mentation of Cat map and Cloud models. This paper proposesChaos Cloud genetic algorithm (CCGA), to optimize the parametercombinations of ν-GSVR model. Finally a new approach for fore-casting short-term traffic flows at an intersection is established,combining ν-GSVR with CCGA (CCGA–ν-GSVR). The proposedmodel considers the relationship between the short-term trafficflow and the real traffic flow during the first few time intervals,the traffic flow for the upstream road section and the weatherconditions.

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

2. ν-support vector regression model with Gaussian lossfunction

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

Suppose training set T¼{(x1,y1),…,(xl,yl)}, where xi is a d-dimen-sional input variable, and yi is the corresponding output value.Through a nonlinear mapping function Ф(x)¼{Ф(x1), Ф(x2)…Ф (xl)},SVR model maps the sample into a high dimensional feature spaceRdf, inwhich the optimal decision function is constructed as follows:

f ðxÞ ¼wTϕðxÞþb; wARdf ; bAR ð1Þ

Where, w is weight vector, b is bias value, and fitting function f(x) minimizes the following objective function (structural risk):

min12‖ω‖2þCRemp

� �ð2Þ

where ð1=2Þjjωjj2 is the expression for the complexity of thedecision function; the second item, empirical risk Remp, is for thetraining errors; C is a regulatory factor used to adjust the ratiobetween the model complexity and the training error Remp. Thetraining error Remp ¼ ð1=lÞ∑l

i ¼ 1jyi� f ðxiÞj can be measured with ε,the insensitive loss function defined by cðxi; yi; f ðxiÞÞ ¼ maxf0; yi� f ðxiÞ�� ���εg.In the standard support vector regression (ε-SVR) model, ε

insensitive factor controls the sparsity of the solutions and thegeneralization of models. However it is very difficult to reasonablydetermine the value of ε in advance. Therefore Scholkopf et al. [21]presented ν-SVR by introducing a parameter ν into the ε-SVRmodel. At this point, the ν-SVR model with the ε-insensitive lossfunction is shown as follows:

minw;b;ε;ζðnÞ

τðw; ε; ζðnÞÞ ¼ 12jjwjj2þCðνεþ1

l∑l

i ¼ 1ðζiþζni ÞÞ ð3Þ

s:t:

ðwxiþbÞ�yirεþζiyi�ðwxiþbÞrεþζniζðnÞZ0; εZ0

8><>: ð4Þ

Where: ζ(n)¼(ζ1,ζn1,…,ζl,ζnl ) is a slack variable, w is the d-dimen-sional row vector, C (CZ0) is a penalty coefficient, deciding thebalance between confidence risk and experience risk; νA[0,1] isthe upper bound of the proportion of error samples in the totalnumber of training samples and the lower bound of the proportionof support vectors in the total number of training samples; unlikestandard SVR, ε is 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 cannotdeal with the random error (white noise) in normal distributedprediction sequences; so the standard SVR theoretically does notguarantee the accuracy of time series prediction problems contain-ing white noise. The Gaussian function is in accord with thecharacteristics of normally distributed noise, thus it can minimizethe effects of normally distributed noise as the loss function of SVRto a certain extent.

LSSVR uses the ε-insensitive function as the loss function,uses the sum of the squares of the slack variables and changesthe inequality constraints into equality constraints, which aimsto simplify the solution of SVR. The ν-GSVR is the establishmentof the relationship between slack variables and the loss functionand normally distributed noise under the condition that theinequality constraints are not changed, and slack variable is alsosquared [22]. At this point, the ν-GSVR optimization problem isas follows:

minω;b;ε;ζðnÞ

τðw; ζðnÞ; εÞ ¼ 12jjwjj2þCðνεþ1

l∑l

i ¼ 1

12ðζ2i þζn2i ÞÞ ð5Þ

s:t:

ðwxiþbÞ�yirεþζiyi�ðwxiþbÞrεþζniζðnÞZ0; εZ0

8><>: ð6Þ

where: ζ(n)¼(ζ1,ζn1,…,ζl,ζnl ) is the slack variable; w is d-dimen-sional row vector; C (C40) is the penalty coefficient; ν valuerange is [0,1]; ε is the present as optimization variable; its valuewill be given as part of the solution. Literature [16] makes adetailed proof on the existence and uniqueness of ν-GSVR modelsolution.

The calculation steps for ν-GSVR model are as follows:Step 1: Suppose the known training set T¼{(x1,y1),…,(xi,yi),…,

(xl,yl)}, where xiARd, yiAR, i¼ 1;…; l; Step 2: Select the appro-priate positive ν and C, and the kernel function K (xi, yi); Step 3:Construct and solve the optimization problem, and the basic

Fig. 1. The architecture of ν-GSVR.

M.-L. Huang / Neurocomputing 147 (2015) 343–349344

structure is shown in Fig. 1

mina;an

wðα;αnÞ ¼ 12

∑l

i;j ¼ 1ðαn

i �αiÞðαn

j �αjÞKðxi; xjÞ� ∑l

i ¼ 1ðαn

i �αiÞyi

þ l2C

∑l

i ¼ 1ðαn2

i þα2i Þ ð7Þ

s:t:

∑l

i ¼ 1ðαn

i �αiÞ ¼ 0

∑l

i ¼ 1ðαn

i þαiÞrCυ

0rαi; αn

i rC=l; i¼ 1;…; l

8>>>>>>><>>>>>>>:

ð8Þ

Get the optimal solution α(n)¼(α1,αl, α1n,…,αln) Step 4: Constructdecision function

f ðxÞ ¼ ∑l

i ¼ 1ðαn

i �αiÞKðxi; xÞþb ð9Þ

where b is calculated as follows; select the two components aj orak in the open interval (0, C/l), then

b¼ 12

yjþyk�ð ∑l

i ¼ 1ðan

i �aiÞKðxixjÞþ ∑l

i ¼ 1ðan

i �aiÞKðxixkÞÞ" #

ð10Þ

Parameter ε can be calculated by the following two equations:

ε¼ ∑l

i ¼ 1ðan

i �aiÞKðxixjÞþb�yj or ε¼ yk� ∑l

i ¼ 1ðan

i �aiÞKðxixkÞ�b

ð11Þ

3. A new hybrid optimization algorithm

The parameter selection in SVR prediction model determines thegeneralization performance of the model, but there is no effectiveway to determine the optimal parameter combination, and there iscross error in traditional cross validation [23]. In view of this, throughthe improvement on the standard genetic algorithm (SGA) based onCat map and Cloud models, this paper presents CCGA to determinethe parameter combinations of ν-GSVR model.

3.1. Standard genetic algorithm

By the joint action of reproduction, crossover, mutation andother genetic operators, GA makes the population continuouslyevolve and eventually arrive at the optimal solution. Due to theself-organization, self-adaptation, self-learning and essential par-allel characteristics of GA, it has been widely used in parameterestimation, pattern recognition, machine learning, neural net-works, industrial control and many other areas; however, theshortcomings of the GA including the slow search for optimalsolution 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 conductedin-depth studies on the encoding of GA, the determination ofcontrol parameters, the mechanism of action operators andhave presented numerous improved methods [24–26], but inthe 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 goodergodicity and uniformity, resistance to fall into small cycles andfixed points, as well as the characteristics of cloud droplets of theCloud models such as randomness and stable orientation, thispaper 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 valuesensitivity. The current existing chaos optimization approacheshave mostly used the logistic map as a chaotic sequence generator.The probability density of the chaotic sequence generated by thelogistic map obeys the Chebyshev distribution similar to the ‘bathtub’ curve, and such a distribution hinders the global search capa-bility and efficiency of the algorithm. To overcome the shortcomingsof the logistic map, the Cat map with the advantages of goodergodicity and uniformity, its resistance to fall into small cycles andfixed points, is used in the initialization of the parent population of GA.

3.2.1. Cat mapThe two-dimensional Cat map [31] equation is as follows:

xnþ1 ¼ ðxnþynÞmod 1ynþ1 ¼ ðxnþ2ynÞmod 1

(ð12Þ

Where: x mod 1¼x�[x]; now, the two Lyapunov indices of Catmap are L1 ¼ lnðð3þ

ffiffiffi5

pÞ=2Þ40 and L2 ¼ lnðð3�

ffiffiffi5

pÞ=2Þo0, indi-

cating that Cat map has chaotic characteristics.

3.2.2. Analysis of chaotic characteristics of Cat map and logistic mapLogistic map equation:

xnþ1 ¼ uxnð1�xnÞ ð13ÞWhere xn is the nth iteration value of variable x and u is a

control parameter. When u¼4, the system completely is in achaotic state [32,33]. Furthermore x0 can take any initial valuesexcept for 0.25, 0.5 and 0.75 within the interval of (0,1).

To analyze the chaotic characteristics of Cat map and logisticmap, suppose the initial values of logistic map are 0.2, 0.4, 0.6 and0.8 whilst the initial values of Cat map are 0, 0.2, 0.4, 0.6, 0.8 and 1.After 50,000 iterations the distribution graph for the two mapswithin the range of [0,1] was obtained. The statistics for the valueswith the maximum and minimum number of occurrences werecarried out and the results obtained are shown in Table 1.

The statistics in Table 1 show the maximum frequency of thelogistic map within (0;0.01) and (0.99;1) exceeds 3000 times,while the average value frequency within (0.01,0.99) interval isonly about 500 times. So, when the optimal solution is in themidrange, the application of the logistic map in the generation ofthe parent population makes it difficult to ensure an efficientsearch for the optimal solution. Meanwhile the maximum fre-quency of occurrence for the Cat map is E560 times and theminimum frequency is E440 times, this indicates that the Catmap is more evenly distributed. Secondly the initial values of Catmap can range between 0 and 1, which is not permissible for the

Table 1Comparison on chaotic distribution of logistic map and Cat map.

Logistic map Cat map

Initial value 0.2 0.4 0.6 0.8 0 0.2 0.4 0.6 0.8 1Max frequency 3222 3241 3239 3284 559 563 547 556 546 559Min frequency 283 290 289 291 450 440 452 437 458 450

M.-L. Huang / Neurocomputing 147 (2015) 343–349 345

logistic map. Therefore the Cat map has better chaotic distributioncharacteristics, and its application in the initialization of parentpopulation for GA is able to better able to maintain the populationdiversity for an ergodic search theoretically.

3.3. Crossover and mutation based on Cloud model

Cloud models have the characteristics of random and biasstability [34]. The random property avoids a local minimumsolution, and the bias stability aids the positioning of the globaloptimum. Thus, introduction of Cloud models into the GA canreduce optimization time-consuming and improve the ability toavoid falling into local minimums when used with both the basiccloud generated algorithm and the Y-condition cloud generatedalgorithm which perform the mutation operation and the cross-over operation respectively.

Suppose T is the language value in the domain u, map CT(x):u-[0,1], 8 xA u, x-CT(x), then the distribution of CT(x) on u is calledthe membership cloud under T. In the case of obeying the normaldistribution, CT(x) is known as the normal Cloud models [35]. Theoverall characteristics of the Cloud models can be represented bythe three digital features including desired E, entropy S andhyperentropy H.

E is the expectation of spatial distribution of cloud droplet in thedomain as well as the point that is the most able to representthe qualitative concept. S represents the measurable granularity ofthe qualitative concept, and the greater the entropy S the larger theconcept. H is the uncertain measurement of entropy and is jointlydetermined by the randomness and fuzziness of the entropy.

The Cloud models have the characteristics of the uncertaintywith certainty and stability with change, and thus reflect the basicprinciple of the evolution of a species in nature. The Cloud modelsparameter E represents the parent's good individual geneticcharacteristics and the offspring's inheritance from the parent.The entropy S and hyper-entropy H indicate the uncertainty andfuzziness 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 dropletsis called the cloud generator [35]. The basic cloud generator andY-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; outputthe quantitative values of n cloud droplets and the certainty of therepresentative concept.

1. To generate S1, a normal random number with the expectationsof S and the standard deviation of H.

2. To generate xi, the normal random number with the expecta-tions of E and the standard deviation of S1.

3. Suppose xi should be a specific quantitative value of qualitativeconcept, called cloud droplets, the calculation mi ¼ e�ðxi �EÞ=2nðS1Þ2

is conducted.4. Suppose mi should be the certainty for the qualitative concept

of xi.5. {xi,mi} completely reflect the conversion process from qualita-

tive to quantitative.6. Repeat steps 1–5, till the n cloud droplets (xi,mi) are all

generated.

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

1. To generate Sn, a normal random number with the expectationsof S and the standard deviation of H.

2. Calculate cloud droplet xi, xi ¼ E7Sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�2 lnðμ0Þ

p.

3. Repeat steps 1–2, till the n cloud droplets (xi,m0) are allgenerated.

3.4. CCGA

The shortcomings of standard GA are overcome by adoptingreal-coding, using Cat map for the generation of initial population,using the Y-condition cloud of normal Cloud models to achievecrossover operation and using the basic cloud to achieve mutationoperation. The computing process of CCGA is as follows:

Step 1: Generation of initial population by Cat map: use Eq. (12)to produce the initial population, in order to make it be asuniformly distributed as possible in the solution space, over-come the heterogeneity of the initial population generated byrandom sequence and improve the diversity of the population.Step 2: Select each individual genes as the ν-GSVR modelparameters to calculate the individual fitness.Step 3: Selection, copying and migration.

① Copy the best individual to the next generation.② Select an elite population, and copy it.③ Replace the worst individual by a randomly generatedindividual.

Step 4: Y-condition cloud crossover.① Randomly generate membership m0 according to theuniform distribution.② If μ0 is less than crossover probability pc, E is be calculatedby:

E¼ fitnessðiÞfitnessðiÞþ fitnessðjÞxiþ

fitnessðjÞfitnessðiÞþ fitnessðjÞxj ð14Þ

Where: xi and xj respectively are the parent individuals ofthe crossover operation; fitness (i) and fitness (j) are thefitnesses of the two parent individuals;

③ S¼variable search range/c1.④ H¼S/c2.⑤ Use the Y-condition cloud generator to produce two off-spring individuals.Step 5: Mutation of normal cloud.

① Take the original individual as E.② S¼variable search range/c3.③ H¼S/c4.④ Activate normal cloud generator to produce clouddroplets (xi,mi).⑤ If mi is less than the mutation probability pm, xi will beregarded as the post-mutation individual.

Step 6: Go to Step 2, till it meets the optimal stoppingconditions, where c1–c4 is the control parameter.

3.5. Analysis of effects of control parameter value

According to “3δ” rule [36], S value determines the horizontalwidth of cloud cover, that is, it determines the search range ofindividual during crossover and mutation operation. The values ofc1 and c3 generally are recommended to be within the interval[6,6P] where P is size of the population. To a certain extent toogreat a value for H may lead to the loss of “bias stability” in theCloud models. However too small a value for Hmay lead to the lossof “randomness”. Therefore the values of c2 and c4 are recom-mended to be within [1,10]. Although S and H are the importantparameters for the Cloud models, after several generations, therandomness of E and μ conceals the difference in the evolutionresult due to the difference between the values. That is the

M.-L. Huang / Neurocomputing 147 (2015) 343–349346

difference in value among the control parameters c1–c4 within acertain range do not have a major effect on the final evolutionperformance. Comprehensively considering the optimization,speed and accuracy of an algorithm, this experiment takes c1¼c3¼3P, c1¼c4¼6. Of course, in the process of practical applicationthe values of parameters c1–c4 can be properly determinedaccording to a variable search range, population size and searchaccuracy.

4. CCGA in selecting parameters of ν-GSVR model

The procedure of the CCGA–ν-GSVR model is as follows: firststep, Normalize the training data set and the value range ofparameters; second step, use the evolution individuals generatedby CCGA as ν-GSVR parameters; third step, according to thenormalized training data, conduct training to calculate the regres-sion values; forth step, determine whether the current parametercombinations 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 theparameter of ν-GSVR for traffic flow prediction. Otherwise, repeatsteps 2–4 until the accuracy of parameter optimization is met. Thespecific calculation process is shown in Fig. 2.

To ensure the CCGA optimization efficiency, this paper uses thereciprocal of the root mean square error as fitness function, andthen the fitness function is calculated as follows.

fitness¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiRMSE

p ¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið1=nÞ ∑

n

t ¼ 1ðYnðtÞ�YðtÞÞ2

s ð15Þ

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

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

Kðxi; xjÞ ¼ exp �jjxi�xjjj22δ2

!ð16Þ

5. The numerical test

Urban traffic flow is characteristic of fluid, and the distributionin time is continuous, that is, the traffic flow at the next time of theroad section is intrinsically linked with the traffic flow in the firstfew intervals of the road section. Meanwhile, the road section is apart of the larger road transport network, and the traffic flow of aroad section will be influenced by the traffic flow in the upstreamroad sections. In addition, the weather condition affects the trafficflow to a large extent. Therefore, we can select traffic data for thefirst few intervals of the section, the upstream traffic data and

weather conditions at the time to predict the traffic flow of theroad section for the next time step.

Taking the data detected from intersection of Culture Road andShi-Full Road in Banqiao for the numerical test. Assuming that trepresents the current time, Y(tþ1) represents the traffic flow forthe next time step, while X1(t), X2(t) and X3(t) represent the trafficflow for the three upstream sections of the road. The weathercondition is set as the sixth influencing factor, in this case X4(t),which is quantified as 1 for heavy snow or sleet, 0.75 for lightsnow or sleet, 0.5 for heavy rain, 0.25 for light rain, and 0 for sunnyor cloudy conditions. The result of tentative calculation indicatesthat the forecasting performance is best, when the first two timesintervals of the traffic flow are select as the input vector. At thispoint, we obtained the six influencing factors of the traffic flowY (tþ1), X¼{Y(t�1),Y(t),X1(t),X2(t),X3(t),X4(t)}.

Traffic flow data was detected by a Speed Spy (SI3 K-band)radar traffic detector. The sample window of 10 min gave 90 sets ofdata for the five Friday evening peak hours from March 7, 2014 toApril 4, 2014 (17:00–20: 00). The first 72 data from the first fourFriday nights were used as training samples for the model. Theremaining 18 data from the fifth Friday night peak hour traffic flowwere used to test the prediction accuracy of the model.

The proposed CCGA–ν-GSVR model has been implemented inMatlab 7.1 programming language. The experiments are made on a1.81 GHz Core(TM) 2 CPU personal computer with 2.0 GB memoryunder Microsoft Windows XP professional. Model initialization:C value ranges [0.01, 1000], ν value ranges [0.01,1], δ value ranges[0.01,1], genetic population size popsize¼60, maximum evolutiongeneration Gmax¼50, crossover probability Pc¼0.3, mutation prob-ability Pm¼0.8, relative error of adjacent-generation optimalindividual fitness E¼0.00001. The combination of optimal para-meters of ν-GSVR are obtained by the CCGA, C¼584.5, ν¼0.87and δ¼0.21. The developed model was used to forecast the trafficflow. The chart for the comparison between actual traffic flowand model fitness value is described in Fig. 3. The actual trafficflow and model prediction results are shown in Table 2. The resultsshow that the fitness results are basically consistent with theactual traffic flow variation curve, where the root mean squareerror of regressed value is less than 3, the root mean square errorof prediction is less than 13, and the prediction accuracy satisfiesthe actual application requirements.

To compare the parameter optimization efficiency of CCGA, thispaper also used SGA to optimize the parameters of ν-GSVR model.Using the same computer, the same population size, crossoverprobability and mutation probability, the statistical results for thefitness values and genetic algebra of the two algorithms areplotted against time in Fig. 4.

The analyses as shown in Fig. 4 illustrate that, within therunning time of 2000 s, the use of Cat map for the initialization ofparent population and the introduction of cloud crossover andmutation operations, the running time of CCGA for each iterationis more time consuming than SGA. This extra computational timeresults in the CCGA solving fewer generations than the SGA modelfor a given period of time. However, based on the ergodiccharacteristics of Cat map, the maximum fitness value of the CCGAsearch for optimal solution is double that of the SGA algorithm.The introduction of cloud theory-based genetic manipulationreduced the range of maximum fitness value and minimum fitnessvalue so that more individuals from CCGA search can be concen-trated in the range of the optimal solution. The overall efficiency tofind the optimal solution using CCGA is significantly higher thanthat of SGA algorithm, indicating that CCGA is more suitable forthe optimization of ν-GSVR model parameters.

To compare the performance of the CCGA–ν-GSVR model intraffic forecasting, this paper selects the ARIMA model, the PSO-BPneural network model proposed by Ye [9], the WD-SVM predictionFig. 2. The process of CCGA–ν-GSVR.

M.-L. Huang / Neurocomputing 147 (2015) 343–349 347

model proposed by Zhu [15], and the improved CCGA–ν-SVRprediction model based on the GSVMR model proposed by Ren[12] as comparison models. The four models were calculated in thesame computer using Matlab 7.1. Taking into account the fact thatthe increase in optimization time improves the optimizationeffect, the model parameters should be selected for each modelto ensure the same maximum optimization time is achieved. Inorder to ensure the selection accuracy of SVR parameters the rootmean square error was used to compare the performance of eachmethod.

The comparison of the real traffic flow data and the forecastedresults of the various modeling methods are given in Table 3.

It can be seen from Table 3 that the SVR model is superior toARIMA and PSO-BP in the capacity of the traffic flow forecasting. Interms of noise handling during in the prediction process the WA-SVM model firstly carried out noise reduction on the traffic flowsequence through wavelet analysis; eliminating the effects ofrandom errors in the sequence of traffic flow in the SVM model.This has proven beneficial as the prediction accuracy was sig-nificantly superior to that of unfiltered CCGA–ν-SVR model. Fromthe comparison of prediction results between CCGA–ν-SVR modeland CCGA–ν-GSVR model, it can be seen that the proposed CCGA–ν-GSVR model also played a role in weakening these randomerrors, and the prediction accuracy showed a better correlationwith 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 conduciveto the actual operation. For real-time traffic prediction, the real-time performance of algorithms is the determining factor for agiven accuracy condition. In this sense, the proposed CCGA–ν-GSVR model is more suitable for the short-term traffic predictionat intersections.

6. Conclusions

Intersections are the bottleneck in urban road traffic network,and its passage capacity determines the network capacity. Thereal-time accurate prediction for the traffic flow at an intersectioncan effectively save travel time, ease road congestion, reduceenvironmental pollution and conserve energy. In this paper, anew approach for predicting short-term traffic flow based on the

Table 2Forecasting result of CCGA–ν-GSVR modela.

Peak period X1(t) X2(t) X3(t) X4(t) Y(t�1) Y(t) Y(tþ1)

Actual Forecasting Error

17:30 111 228 124 0 176 182 195 202 717:40 107 238 119 0.25 182 195 259 250 �917:50 135 251 119 0 195 259 188 196 818:00 126 241 148 0 259 188 233 219 �1418:10 128 246 148 0.25 188 233 221 213 �818:20 148 264 138 0.5 233 221 267 258 �918:30 152 263 162 0.5 221 267 291 284 �718:40 146 294 142 0 267 291 310 297 �1318:50 139 263 161 0.25 291 310 295 286 �919:00 141 270 145 0.25 310 295 228 220 �819:10 147 267 132 0 295 228 266 254 �1219:20 123 246 142 0 228 266 282 271 �1119:30 116 255 123 0 266 282 233 240 71940 130 238 137 0 282 233 237 231 �619:50 101 233 132 0 233 237 235 221 �1420:00 102 231 98 0.25 237 235 180 196 16

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

Fig. 4. Comparison of training.

Table 3Comparison between four different models.

Peak period Actual CCGA–ν-GSVR CCGA–ν-SVR WA-SVR PSO-BP ARIMA

17:30 195 202 204 189 221 21617:40 259 250 246 266 237 23617:50 188 196 176 195 161 20818:00 233 219 251 220 201 24918:10 221 213 211 215 193 24518:20 267 258 279 274 296 24318:30 291 284 276 285 264 32218:40 310 297 321 300 345 33218:50 295 286 312 301 266 32819:00 228 220 210 235 258 20819:10 266 254 279 255 298 29419:20 282 271 299 290 249 30219:30 233 240 224 239 258 2561940 237 231 225 248 209 20319:50 235 221 218 222 267 26120:00 180 196 189 168 226 194

RMSE 10.31 17.39 8.89 30.51 37.04

Fig. 3. Fitting chart of CCGA–ν-GSVR.

M.-L. Huang / Neurocomputing 147 (2015) 343–349348

CCGA–ν-GSVR method is proposed. The numerical test based ondetected data is used for elucidating the forecasting accuracyof the proposed method. The prediction results of the proposedCCGA–ν-GSVR forecasting scheme are compared to those of theCCGA–ν-GSVR, CCGA–ν-SVR, WA-SVR, PSO-BP and ARIMA. Thenumerical test indicates that the proposed scheme obtain betterprediction result and outperforms the five competing models. Inshort, the proposed forecasting scheme is a valid approach forshort-term traffic flow predication.

In future researches, more influence factors should be consid-ered and other hybrid optimization methods should studied formore appropriate parameters of ν-GSVR model, for improving theperformance of short-term traffic flow forecasting.

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Min-Liang Huang was born in 1955. He received hismaster of Industrial Education from National TaiwanNormal University in 1982. He is currently a seniorlecturer in the Department of Industrial Managementof Oriental Institute of Technology. His research inter-ests are hybrid evolutionary algorithm, grey theory, andcomputational intelligence.

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