Application of Artiﬁcial Intelligence Approach for Optimizing

Management of Road Trafﬁc

Charlène Béatrice Bridge-Nduwimana

, Abdessamad Malaoui

and Jilali Antari

Polydisciplinary Faculty of Beni Mellal, Sultan Moulay Slimane University, Morocco

Polydisciplinary Faculty of Taroudant, Ibn Zohr University, Morocco

Keywords:

Road trafﬁc. Fuzzy system. Artiﬁcial intelligence. Combination

Abstract:

An approach based on the artiﬁcial intelligence is proposed for the management of road trafﬁc. By a fuzzy

system, we are looking for purely numerical parametric characteristics and those that inﬂuence its structure. In

fact, we use input and output data from a portion of the road trafﬁc to identify a fuzzy model which makes pos-

sible the evaluation of the results of the estimated parameters obtained. This has been achievable through the

combination of parametric and structural adjustment algorithms with the backpropagation algorithm. Conse-

quently, the obtained results show that adaptive models are successfully used in the analysis and the manage-

ment of road trafﬁc through the efﬁciency of this combination.

1 INTRODUCTION

Overall, we will deal with the problem of identifying

fuzzy models from input-output data. Sometimes we

need to have the parameters of a system without kno-

wing all the members. Through an example we de-

monstrate this fuzzy identiﬁcation (RASTEGAR and

al., 2011). With the fuzzy modeling formalism of sys-

tems focusing particularly on the Takagi-Sugeno mo-

del (CHEN and XIAO, 1999) , we represent the non-

linear behavior of a system by a composition of "If

. . . Then" rules, concatenating a set of sub-models lo-

cally linear. In what follows, the fuzzy model has been

identiﬁed for a signal based on data in autoregressive

way. This method is simple and allowed us to generate

data without other variables in addition. The model is

capable to predict other data on the process being stu-

died once the optimization phase is over.

To build such models, we approach the applica-

tion of a competitive agglomeration method : the al-

gorithm of Gustafson and Kessel (PALACIO, 2007),

(WU and al., 2018), which belongs to fuzzy cluste-

ring methods based on the minimization of an objec-

tive function. Finally, after having considered the ge-

neral methodology for the construction of the Takagi-

Sugeno fuzzy model from data, we will comment on

what we will obtain as results.

This paper is organised as follows. Section 2 de-

velops Takagi-Sugeno’s fuzy model and discusses the

types of adjustments made to fuzzy systems. Section

3 concisely discusses about achievements in scientiﬁc

research related to the subject. And Sect. 4 explains

the approaches adopted and the results of the simula-

tions are established in Sect. 5. Finally, we conclude

this paper in Sect. 6.

For all our simulations, we carried out fuzzy clus-

tering simulations for the structural adjustment, pa-

rametric adjustment simulations with the GLS and

WLS algorithms (OLSSON and al., 2000) combined

with the backpropagation (ELMZABI, 2005) algo-

rithm simultaneously. They give Root Mean Square

Error (RMSE) on the validation set between the pre-

dicted values and measured data.

2 TAKAGI-SUGENO’S (TS)

FUZZY MODELS

Developing an artiﬁcial intelligence to process a large

amount of data is therefore an excellent idea. Today,

the practical advantages of artiﬁcial intelligence are in

fairly pragmatic operations. A fuzzy system is a sys-

tem that integrates human expertise and aims to emu-

late the reasoning of human experts in complex sys-

tems. It is an important part of artiﬁcial intelligence.

In fuzzy systems, the basic idea is to model pro-

cesses as would the human being (BOUZID and

S.BENMERIEM, 2013). The relationships between

input and output variables are explicitly represen-

Bridge-Nduwimana, C., Malaoui, A. and Antari, J.

Application of Artiﬁcial Intelligence Approach for Optimizing Management of Road Trafﬁc.

DOI: 10.5220/0009771200050010

In Proceedings of the 1st International Conference of Computer Science and Renewable Energies (ICCSRE 2018), pages 5-10

ISBN: 978-989-758-431-2

ted in the form of "If . . . Then . . . " rules, ie : If

HYPOTHESIS (antecedent part) Then CONCLUSION

(consequent part) (ISHIBUSHI and al., 1995). The

above form allows to interpret the results and to deter-

mine the action of each rule and express an inference

(MILAN and al., 2018) mechanism such that if a

fact (hypothesis) is known, then another fact (conclu-

sion) can be inferred. The Takagi-Sugeno fuzzy mo-

del (RASTEGAR and al., 2011) uses linear functions

in the consequent part : for i rule and j output, we

have : y

= f

(x).

So, it can be seen as a combination (TOMAR and

al., 2018) of the linguistic model and the mathemati-

cal regression (TOMAR and al., 2018) model in the

sense that the antecedents describe fuzzy regions in

the input space in which the consequent functions are

valid. Basically, this model can encode the expertise,

either directly from the prior knowledge of the pro-

blem, or indirectly from a set of learning data. It is

very easy to identify because the conclusion of each

rule is linear and its parameters can be estimated from

the numerical data using optimization (MILAN and

al., 2018) methods such as least squares algorithms.

We will use more particularly these models be-

cause they allow to approach non-linear systems by a

combination (TOMAR and al., 2018) of several linear

and simple local models. They are written as follows

(IQDOUR, 2006) :

: I f x

is A

T hen

t,i

= β

+ x

(1)

(i = 1, 2, ..., c) indicates the i

fuzzy rule, x

(t =

1, 2, ..., N) is the input variable (x

∈ R

t,i

is the

output of the i

rule relative to the input x

, A

a fuzzy

set (YANG and HU, 2018) and β

= (β

, β

, ..., β

)

2.1 Structural Adjustment

Structural adjustement is about determining the cor-

rect number of rules to use in a fuzzy system (DASS

and SRIVASTAVA, 2018), (KASHANI and MOHAY-

MANY, 2011). The structure to be searched for will

have to be rich enough to allow for optimal learning,

but not too much to avoid noise modeling in the data.

2.2 Parametric Adjustment

Once the number of rules determined, it is necessary

to estimate the parameters (β

) for each conclusion of

the rules. If we have :







0 · · · 0

0 µ

· · · 0

0 0 · · · µ







(2)

X =













, y =













(3)

And if we have :

= [1 X],

X =



. . . W



2.2.1 Weighted Least Square (WLS)

The localized linearization method causes the resolu-

tion of c independent optimization problems. Linear

parameters obtained do not depend on how the rules

are aggregated. The criterion to be minimized is :

J =

∑

i=1

∑

t=1



ˆy

− x



(4)

The determination of the linear parameters β

passes by the minimization of the criteria of each local

model. This amounts to solving c independent weigh-

ted least squares problems whose solution is :





−1

y (5)

2.2.2 Global Least Square (GLS)

The global system resulting from this method (IQ-

DOUR, 2006), approximates the database with more

perfection. But nothing tells us that the linear models

thus obtained are optimal in their areas of expertise.

Linear parameters are obtained by solving the equa-

tion :

Xβ = y or





β =

y (6)

The criterion to be minimized for GLS is :

J =

∑

t=1



ˆy

− y



(7)

3 A STATE OF THE ART

Accurate data from accident and road databases

can be essential for modeling, mapping, identifying

hazardous road segments and other studies to make

decisions in a road network. Researches relating to

the problems that are in the databases of road trafﬁc

and which propose solutions exist and bring a plus.

Among them, we have :

C. Yixin and X. Deyun (CHEN and XIAO, 1999)

represent an extension of the Takagi-Sugeno-Kang

model (ETSK). Its analytic expression has been de-

livered and an algorithm to identify such a mo-

del has been proposed. TSK with variable weight

ICCSRE 2018 - International Conference of Computer Science and Renewable Energies

(VWTSK) was made to present the fuzzy control-

ler algorithm of the ETSK model even deﬁnition of

fuzzy rules since they are roughly equivalent. The si-

mulation of this algorithmshows that the ETSK mo-

del can give more precision on the long-term pre-

dictions and the control algorithmcan reach a better

controlmore efﬁcient that Proportional-Integral- Deri-

vative fuzzy regulation (PID). Furthermore, an adap-

tive control identiﬁcation or method for a system ba-

sed on FCM-KNN (Fast Fuzzy C-Means—K-Nearest

Neighbors) and PSO (Particle Swarm Optimization)

has been proposed by Rastegar et al. (RASTEGAR

and al., 2011). The model identify the structure and

parameters of the nonlinear model : the fuzzy set and

the number of rules, and the location of the member-

ship functions are automatically pulled from the sys-

tem data. In comparison with other identiﬁcation me-

thods, larger values corresponding to a lower num-

ber of fuzzy rules have been achieved. Thus, their

results showed that the proposed control model can

control the process just by using a database of the

TS Adaptive Fuzzy Model initialization process. On

the other hand, C. N. Babu and B. E. Reddy (BABU

and REDDY, 2015), for the prediction of time-based

internet trafﬁc that is very volatile in nature, have ex-

plored the applicability of various forecasting models.

They considered during their study ARIMA (AutoRe-

gressive Integrated Moving Average), ANN (Artiﬁ-

cial Neural Network), Zhang’s ARIMA-ANN hybrid

model, Khashei and Bijari’s ARIMA-ANN hybrid

model, the ARIMA-ANN multiplicative model, MA

(Moving Average Filter) ﬁlter based on the ARIMA-

ANN hybrid model. One-step and/or multi-step pre-

dictions have been made. The measures of the er-

ror performance, MAE (Mean Absolute Error) and

RMSE (RootMean Squared Error) are used to eva-

luate accuracy (BOVEIRI and ELHOSENY, 2018),

(HAIDI and al., 2018), (CHEN and al., 2018). The

results of the forecast in both cases showed that the

MA ﬁlter based on the ARIMA-ANN hybrid model

outperformed all the others models, both in terms of

MAE and RMSE and is therefore suitable for more

accurate prediction of internet trafﬁc data.

4 APPROACHES

At ﬁrst, we generate (ISHIBUSHI and al., 1997)

fuzzy rules of the TS model. We use classiﬁcation

(KASHANI and MOHAYMANY, 2011), (MURU-

GAN and al., 2019), (SHANKAR and al., 2018) ,

(MUHAMMAD and al., 2019) , (HURRAH and al.,

2019) algorithm (Gustafson Kessel : GK (BABUSKA

and al., 2002) to estimate the number and initial po-

sitions of cluster centers where each one allows us

to determine a fuzzy relationship between inputs and

outputs by checking their similarity. Then we adopt

fuzzy generation algorithms to predict fuzzy output.

Even though there is no indication of this kind of pro-

blem, the GK algorithm (WU and al., 2018) makes it

possible by giving the state or the quality of the road

trafﬁc taken as example from the output of the fuzzy

model.

Secondly, we generate fuzzy rules from a base of

examples where we want to classify the outputs into

a set of predeﬁned fuzzy classes. Then we use the

ﬁrst approach for fuzzy rule generation, we apply a

weighted or generalized least squares ﬁt to compare

the fuzzy and predeﬁned outputs of our model (Fig.

1).

Figure 1: Approaches.

5 RESULTS

5.1 First Simulation

In Figs. 2 and 3, we represent the results after a si-

mulation realized on matlab R2017a. There are the

membership functions, the linear β

and nonlinear pa-

rameters that are estimated with the WLS or GLS al-

gorithms.

And in the following tables, Tables 1 and 2, we

present the results on different values of the set of in-

put in order to capture the sensitivity and the effects

of these two methods on our example.

5.2 Second Simulation

In order to estimate road trafﬁc (IHUEZE and ON-

WURAH, 2018) parameters, we use a database

consisting of daily measured values for January 2012.

These values were taken in the Gironde region, a

french department located in the south-west of the

Application of Artiﬁcial Intelligence Approach for Optimizing Management of Road Trafﬁc

Figure 2: For 31 values with WLS algorithm.

Figure 3: For 31 values with GLS algorithm.

Table 1: Results obtained with WLS algorithm.

Values Clusters RMSE Errors

11 4 0.0076 6.3315 × 10

−4

21 4 0.0217 0.0099

31 4 0.0467 0.0676

51 4 0.0580 0.1717

71 6 0.0498 0.1763

151 8 0.0494 0.3678

501 26 0.0226 0.2554

Table 2: Results obtained with GLS algorithm.

Values Clusters RMSE Errors

11 4 0.0074 6.0077 × 10

−4

21 4 0.0213 0.0095

31 4 0.0460 0.0655

51 4 0.0582 0.1730

71 6 0.0498 0.1758

151 8 0.0446 0.2997

501 28 0.0185 0.1709

country in the New Aquitaine region. You should

know that a very simple autonomous car is only a ca-

tegorization in real time to identify all objects on the

road and deﬁne the behavior to adopt.

The performance criterion chosen remains the root

mean squared error. We chose to sort three complete

classes of the database that normally contains several

classes (see Tables 3 and 4). We want to estimate the

ratio between the length and speed provided. This is

indeed an important data that characterizes the portion

of the road taken into consideration.

Table 3: Results for WLS algorithm.

Class Clusters RMSE Errors

CL1 : 4 0.0324 0.0326

CL2 : 4 1.3714×10

−

4 5.8305×10

−

CL3 : 4 5.3609×10

−

4 8.9092×10

−

Table 4: Results for GLS algorithm.

Class Clusters RMSE Errors

CL1 : 4 0.0313 0.0304

CL2 : 4 1.3724×10

−

4 5.8389×10

−

CL3 : 4 5.3909×10

−

4 9.0088×10

−

A better approximation is an added value for predic-

tion which is very useful in applications because it al-

lows to generate trafﬁc data for localities where mea-

surements are not available. When the linear function

is bounded and the activation function is derivable,

it is possible to use powerful learning algorithms ba-

sed on the search for a minimum of the error func-

tion, in particular the backpropagation (WANG and

MENDEL, 1992) of the gradient which includes hid-

den layers. So, to update the connection weight within

a network so that it succeeds in the task that is asked

of it, and thus apply our example to artiﬁcial intelli-

gence (JOHNSON and al., 2018), we used the method

of backpropagation (HASSABIS and al., 2017).

Table 5: Results for WLS & Backpropagation algo-

rithm.

Class Clusters RMSE Errors

CL1 : 4 0.0311 0.0299

CL2 : 4 1.3712×10

−

4 5.8284×10

−

CL3 : 4 5.3922×10

−

4 9.0137×10

−

Table 6: Results for GLS & Backpropagation algo-

rithm.

Class Clusters RMSE Errors

CL1 : 4 0.0298 0.0276

CL2 : 4 1.3723×10

−

4 5.8380×10

−

CL3 : 4 5.3864×10

−

4 8.9941×10

−

5.3 Comments

The results obtained in Figs. (2) and (3) show that

whatever the WLS or GLS algorithm we can have a

ICCSRE 2018 - International Conference of Computer Science and Renewable Energies

good estimate justiﬁed by the mean squared error not

by the graph. We can note that the choice of the num-

ber of clusters in the algorithm depends on how much

data appears to us. It is important to ﬁnd a number of

clusters that best estimate the input. In statistics, ge-

neralized least squares are techniques for estimating

parameters unknows in a linear regression model. In-

deed, GLS is used to perform a linear regression when

there is some degree of correlation between values

in a model. In this case, the classical weighted least

square method can be statistically ineffective or even

give misleading inferences.

In accordance with previous results (in Tables 5

and 5), the results show that backpropagation asso-

ciated with GLS, under conditions of poor speciﬁca-

tion, provides realistic indices of model implementa-

tion and less biased parameter values for paths that

overlap with the real model. However, despite the re-

commendations of the literature that WLS should be

used when data is not distributed normally, we ﬁnd

that under no circumstances is the WLS method better

than the other two methods of estimating parameters

in terms of bias and implementation. In fact, only for

large sample and for implementation indices close to

those obtained for backpropagation and the GLS me-

thod. In addition for wrongly speciﬁed models, WLS

gives low estimates reliable and overly optimistic va-

lues of ﬁt.

With simulations performed with WLS / GLS

methods associated with backpropagation simulta-

neously, if we increase the number of iterations there

is noise added because it takes more time during the

simulation. It will be the same if we increase the num-

ber of hidden layers where a certain amount of in-

formation will be lost. It is advisable to consider few

layers hidden to avoid noise and a number of reaso-

nable iterations that best justiﬁes the convergence of

the error towards zero. Then the class CL1 is the best

estimated by the GLS associated with backpropaga-

tion method which is more conﬁdent and is likely to

help us make a decision.

6 CONCLUSION

In this work the fuzzy model TS has been identi-

ﬁed for our example and for a signal of the road trafﬁc

studied based on data in an autoregressive way. This

method is simple and allowed us to generate data wi-

thout the need to use other variables in addition. Mo-

reover, once the optimization phase is over, the model

is capable to predict other data on the process being

studied. We used design methods based on a learning

that allows to iteratively deﬁne the best set of parame-

ters : the optimization of fuzzy rules (WLS, GLS) and

the optimization of membership functions. We also

have proposed one of the WLS or GLS optimization

models with backpropagation to test the convergence

of the error. The results obtained show that even with

a non linear we can hope to obtain quite satisfactory

performance.

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