Route Choice Modelling Using Fuzzy logic and Adaptive Neuro-fuzzy

Modern Traffic and Transportation Engineering Research (MTTER)

MTTER Volume 2, Issue 4 Oct. 2013 PP. 11-19 www.mtter.org ○C American V-King Scientific Publishing11

Route Choice ModellingUsing Fuzzy logic and Adaptive Neuro-fuzzy

Subodh Kant Dubey *1, Deval Mishra 2, Shriniwas S Arkatkar 3, Ajit Pratap Singh 4, Ashoke Kumar Sarkar 5

Civil Engineering Department, Birla Institute of Technology & Science Pilani 333031, Rajasthan, India*1 [email protected]; 2 [email protected]; 3 [email protected]; 4 [email protected];

5 [email protected]

Abstract- The route choice phenomenon is a critical step intransportation planning process. It depends upon many factorssuch as travel time, distance, pavement condition etc. Routechoice preferences have been mainly modelled using randomutility models (RUM). These models are based on the conceptof maximized utility. They assume that decision makers makedecisions that maximize their utility. The problem with thesemodels is that they may not explain total utility (observed plusunobserved). Alternative formulations have been proposed toovercome this problem in the literature. These approachesmodel the decision maker’s perceptions using fuzzy sets andlinguistic variables through concepts from approximatereasoning and fuzzy control. Another approach is to modeldecision makers perception using artificial neural network(ANN) and combination of RUM plus fuzzy or ANN plus fuzzyknown as neuro-fuzzy. The main idea behind the application ofthese soft computing techniques is that, they are capable ofaccounting vagueness. The claim that soft computingtechniques provide better result than RUM is analysed in thispaper using revealed preference (RP) survey. The route choicepreference is dealt in this paper using nine route attributes(Distance, Time, Speed, Delay, Pavement condition, Parkedvehicle on side of road, Aesthetic, Comfort and familiarity ofroute). The modelling is done using three techniques, namelymultinomial logit model, fuzzy rule based inference system(FIS) and adaptive neuro-fuzzy inference system (ANFIS). Ithas been found that all three models have almost 100%prediction accuracy at aggregate level. At individual level FIShas better prediction accuracy than multinomial logit model.Neuro-fuzzy model is able to provide good results with lessnumber of attributes (five attributes only). Travel time,pavement condition, road side parking condition and aestheticswere found to be highly significant parameters. The resultsobtained through neuro-fuzzy model has low predictionaccuracy than FIS model due to the fact that as data size andnumber of attributes increases, computational time andmemory to run more number of iterations increases drastically,which require higher level computational facility. It was foundthat fuzzy and ANN based models are better from behavioralpoint of view than RUM, but if there is an interest only aboutend result (aggregate route-wise probability), any model can beutilized.

Keywords- Route Choice; Fuzzy and Neuro-Fuzzy Modelling

I. INTRODUCTION

The route choice problem is one of the critical steps infour step planning process. It is used to determine thedriver’s preference, given the set of different routes withcorresponding attributes (travel time, distance, etc). It plays amajor role in many traffic related problems such ascongestion, safety, etc. A better understanding of routechoice phenomenon will help alleviating these problems.From beginning, route choice modelling has been done

mostly using random utility models such as Logit and Probit.The problem that many researchers colligate with thesemodels is that they do not fully explain the utility associatedwith each choice. That means, these models explain theobserved utility value and add an error term for unobservedutility value. Another shortcoming which researchersassociate with these models is that they cannot explainvagueness (Attributes which can be explained betterlinguistically rather than numerically such as aesthetics,comfort, etc). To overcome this problem, researchers startedlooking for alternative modelling techniques, which canmodel vagueness and account/explain the unobserved utilityin a better way. Fuzzy logic is a tool, which can perfectlymodel vagueness. The basic advantage with fuzzy logic isthat it allows researchers to divide a big region into numberof small region with proper smooth transition andoverlapping. This basic advantage makes it possible to modelvague parameters such as aesthetic and comfort by dividingthem into small region as bad, good, very good etc. So withthe advent of fuzzy logic in transportation engineering,researchers started modelling route choice problem withfuzzy logic and found that it works well as compare totraditional random utility model. These two type of choicemodels namely probability based (Random utility models)and possibility based (Fuzzy theory) have been usedextensively for the purpose of modelling.

Many authors have employed random utility models toanalyse the effect of familiarity of route, variable massagesign (VMS) and radio information on travelers route choicepreference. Emmerink et al. [6] analysed the effect of VMSand radio traffic information on traveller’s route choicepreference. They used ordered probit, multiple logit andbivariate ordered probit concepts to model the responses andfound that both sources of information have similar effect.They also concluded that there is a positive correlationbetween the use of radio traffic information and variablemessage sign information. Abdel-Aty et al. [1] used binarylogit model to study the effect of advance traffic informationon route choice of drivers using stated preference (SP)survey. Jou et al. [11] examined the route choice preference offreeway travelers using ordered probit model. He found thattravelers either choose best or habitual route oncegeneralized cost saving exceeds the threshold value.

The second type of modeling is based on concept fromfuzzy theory and approximate reasoning. Lotan andKoutsopoulcs [14] presented a modeling framework for routechoice under the presence of information, based on fuzzylogic and approximate reasoning. Teodorovića et al. [23]

http://www.ijcet.org/



presented a fuzzy rule based inference system to modeldriver’s route choice behavior in presence of ATIS. Theygenerated the real and ATIS predicated travel time usingnormal distribution and measured the behavior of 30 driversfor a month to establish a relation between route choicepreference and pre trip information effect. Later again, Lotan[15] improved his framework with two stages: the first onepresents the information integration and second one presentsthe decision process. Kikuchi [12] presented a method todefuzzify the fuzzy number with its application intransportation related problems. Arslan and Khisty [2]

developed a hybrid model using concept from fuzzy logictheory and analytical hierarchy process (AHP) to explaindriver’s route choice preference from behavioral point ofview. The fuzzy “if-then” rule was used to capture essentialpreferences, pair wise, among alternatives that a driver mayconsider. AHP was employed to measure imaginarypsychological process. Bovy and Fiorenzo-Catalano [3]

propose to utilize a trip utility function as the basis for adoubly stochastic generation function. Relevant routes arecreated through optimal path search in the given network bystochastically varying network attributes and attributepreferences. Variation in link impedances reflects differencesamong travelers in the perception of link attributes andnetwork knowledge. Variation in the parameter valuesreflects differences among travelers in the preferences forthese attributes. As state-of-the-art literature review by Prato[20] envisaged future research directions towards theimprovement in amount and quality of collected data, theconsideration of the latent nature of the set of alternatives,the definition of route relevance and choice set efficiencymeasures, the specification of models able to contextuallyaccount for taste heterogeneity and substitution patterns, andthe adoption of random constraint approaches to representjointly choice set formation and choice process.

In contrast to above mentioned approaches, some authorshave argued that both approaches are complementary to eachother rather than competitive. Dubois and Prade [5] haveargued that both probability based models (Random utilitymodels) and possibility based models (Fuzzy logic) shouldgo side by side. These two models are not conflicting to eachother, rather complementary to each other. They presentedsome misunderstanding and gaps of the relationship betweenprobability theory and fuzzy theory and also pointed out thebridges. Teodorovid and Kikuchi [22] presented the use offuzzy-set theory as applied to the motorist's choice of a route,in which the attributes of alternatives are weightedsubjectively and the utilities of individual attributes werealso measured subjectively. Among the attributes, travel timeof each alternative route was considered as the mostimportant criterion. Despite the fact that travel time is ameasurable parameter, a driver's notion of travel time, whenhe makes the route choice is often fuzzy. The perceivedtravel time is neither a deterministic nor a probabilisticvariable. It is a fuzzy notion depending upon his level ofurgency, personality and many other qualitative factors. Hisdecision is based on the comparison of travel times onalternative routes rather than the absolute travel time. Thus,his preference for a route is based on comparison of fuzzynumbers. As a result, his certainty of choosing a route is alsonot crisp. Teodorović [24] insisted that probability and fuzzy

theories should exist side by side, that it is possible tocombine them, and that both have a very important role inexplaining complex transportation processes. A morepractical approach proposed by Mizutani and Akiyama [18] ishybrid model based on random utility models and softcomputing techniques, called fuzzy logit model, in order todescribe various aspects of travel behavior effectively.

Some authors have also applied artificial neural network(ANN) to model choice related problem. Hensher and Ton [8]

examined ANN (actually a multilayer feed forward network)models to simulate single-user choice in an urban context.These models are specified and calibrated on disaggregatestated preferences (SP) data and compared with nested logitmodels. Edara [7] used ANN to develop mode choice modeland compared the results with multinomial logit and linearregression model. The author compared the results of threemodels based on mean square error, average relativevariance, and residuals Estimates and concluded that theneural networks approach gives better results than logit andregression models. Cantarella and de Luca [4] used Multi-layer feed forward neural network (MLFNN) for choicemodeling to support travel demand analysis with betterresults as compare to Random utility models (RUM). Kim etal. [13] used artificial neural network for modeling the driver’sroute choice preference to analyze the variation of drivers'preference as function of their social-economiccharacteristics. They found that artificial neural networkgives better results as compare to its corresponding fuzzyinference and multinomial logit model. Lee et al. [17] usedbinary logistic regression, artificial neural network andhybrid tree to model driver’s compliance. They found thatprediction accuracy of 62.2% for binary logistic regression,73% prediction rate for ANN with three variables, mainlyknowledge about alternative route, anticipated travel timesaving and level of confidence in an alternate route andfinally mixed performance for hybrid tree with predictionrate varying from 86% to 48% based on knowledge ofalternate route and anticipated travel time saving.

Some authors have gone one step ahead and combinedfuzzy and ANN to obtain even better results as compared toindividual model results. Vythoulkas and Koutsopoulos [25]

extended the basic fuzzy inference model by incorporatingvarying weights to each rule to show its importance indecision process. They also presented an ANN basedcalibration method to calculate the weights. Hawas [9]

adapted a fuzzy rule based inference system to model theroute choice behavior with seven attributes such as highwaytype, travel time, speed, pavement condition, etc. The authorlater automated the knowledge base with neuro-fuzzy to finetune the parameters and hence membership functions forbetter results. Lee [16] used a hybrid approach to model routechoice behavior considering randomness and vaguenessuncertainty. Firstly they developed a latent class multinomiallogit (LCML) model to consider the heterogeneity amongdrivers. The heterogeneity means driver perceptions maydiffer at the individual level of familiarity with roadnetworks. Secondly, a fuzzy based model was developed toconsider the vagueness of driver perceptions. The perceivedlevels of travel time of drivers and the linguistic informationsuch as light congestion and heavy congestion for roadnetworks were dealt in the fuzzy model. Finally, a combinedmodel was established based on the estimated results of theLCML and the fuzzy models.




In spite of numerous works, the claim that fuzzy andANN are better than RUM or vice-versa still persists basedon different authors work. Therefore, in this paper all threetypes of models namely RUM based mainly Multinomiallogit model (MNL), Fuzzy rule based inference system (FIS)and adaptive neuro-fuzzy inference system (ANFIS) aredeveloped to model route choice preference using revealedpreference (RP) survey method to evaluate the final routechoice probability and to compare the results using thesethree models.

II. DATA COLLECTION AND DESCRIPTION

Data was collected between origin named Connaughtplace and destination named India gate, Delhi (India) duringpeak hours for a period of one week in the month of March2011. There exist three routes between these two places asshown in Fig 1. Revealed preference survey was conductedfor the purpose of collecting data pertaining to route choicepreference of travelers. Mostly cars, bikes and auto travelerswere interviewed for their preferences based on nineattributes, namely Distance, Time, Speed, Delay, pavementcondition, Parked vehicle on side of road, Aesthetics,Comfort and familiarity of route. Each traveler was askedhis/her perceived values corresponding to above mentionedattributes for all three routes and a final value for each routeon a scale of 1-10 (route preference value). Linguisticvariables such as pavement condition, parked vehicle on sideof road, aesthetic, comfort and familiarity of route wereaccounted by linguistic terms (very bad, bad, fare, good andvery good). A total of 150 samples were collected. All threeroutes are described below as given in table 1. The distancewas calculated using Google Maps and travel time wasmeasured using three different motorized vehicles, namelycars, bikes and auto rickshaws during morning and eveningpeak hours. The average travel time, which was estimated foreach of the routes, was finally considered for the purpose ofdeciding travel time characteristics of different routesselected for the study.

Fig. 1 Three selected routes between Connaught place and India gate, Delhi

TABLE 1 CHARACTERISTICS OF THE ROUTES SELECTED FOR THE STUDY

Route Route name Type Distance(Km)

Averagetravel time

(Min.)

R1Janpath andIndia gate C-Hexagon

Arterialroad 4.0 15

R2 KasturbaGandhi marg

Arterialroad 3.4 18

R3 Barakhambaroad

Arterialroad 3.4 22

III. DATA MODELLING

For the purpose of modelling route choice preferences oftravellers, three types of models were developed, namelyfuzzy rule based inference system (FIS), adaptive neuro-fuzzy inference system (ANFIS) and multinomial logitmodel. The detail descriptions of all the three models aregiven below.

A. Fuzzy Based Modelling

In fuzzy based modelling rule based fuzzy is used. Therule based fuzzy is in the form of “if-then” relationship. Inthe route choice problem considered in this paper, rules arein the form of

If Travel time is t1 and distance is d1……… Then routepreference value is r1.

The fuzzy process comprises of three steps namelyfuzzification, inference and defuzzification. In thefuzzification process inputs are converted into fuzzy valueusing membership functions. In inference step rules areformed based on observed data and correspondingrelationship. In the final step all the interacted inputs shapeis defuzzified to get the output. A detail description of fuzzytheory can be found in Ross [21] and Murat and Uludag[19].The Input parameters, which were obtained fromsurvey study, were used in the first stage. The given valuesof these parameters were converted to fuzzy usingmembership functions in the second stage. The rules wereused for inference in the third stage. .Rules used in the fuzzylogic model, were formed after statistical analysis of theinput and output parameters. The model output was obtainedusing Mamdani inference mechanism. In order to evaluatethe performance of Fuzzy-based model, (agreement with theobserved data), fuzzy output was defuzzified using Centroidmethod. By defuzzification of output, values of each routefor each attendee were determined that helped to evaluatethe 4 routes globally for the whole survey. Using rules, afuzzy output that shows the utility of route was obtained andthe fuzzy output was converted to crisp numbers using adefuzzification method in the fourth stage. At the end, routeutility was obtained as a crisp number. After these processes,choice probabilities of routes were determined byMultinomial Logit Formula.

For modelling purpose, all nine attributes were used. Thetriangular membership function was used to fuzzify inputsand the centroid method was used for defuzzification. Ingeneral, the triangular membership function can be specifiedfrom the formula below:




Where, L and R are the left and right bounds and C is thecenter of the symmetric triangle.

The membership functions of few attributes such as time,distance, delay are given below in figure 2, as examples. Thenumber and the range of the classes of triangular functionsfor variables such as, travel time, distance and delay werefixed based on the perceived values of various respondentsconsidered for this study. Although, the range of thevariables mentioned above, is higher than the actual values,it may be noted that the range of actual values is well definedwithin the perceived range.

A total of 112 rules were derived based on observed data.Route preferences score as given by travelers were used asoutput and compared against the predicted preference value.The observed and predicted values are plotted is shownbelow in the figure 3.

From the figure 3, it can be seen that model predictedvalue are very close to the observed value, except the factthat model predicted value never touches the scale value of10. It is due to the fact that in case when travelers assignroute preference value to a particular route irrespective ofother attribute value for the particular route. However, fuzzypredicts the value based on final shape, obtained byintersection of all input membership functions.

B. Model Evaluation

For evaluating the performance of FIS model, root meansquare error (RMSE), and Theil’s error values werecalculated. RMSE provides information regardingperformance of training process. However, Theil’s errormeasure provides additional insights on the nature of sourceof error in the models. Theil’s error value ranges between 0and 1. A value of 0 indicates perfect fit. A detaileddescription of Theil test can be found in Theil [26]. TheRMSE and Theil’s error value for FIS model was found to be0.0306 and 0.062805, respectively. Therefore, it can beinferred that FIS model performs better at individual level.The final route-wise observed and predicted probabilities aregiven below in Table 2.

TABLE 2 ROUTE WISE OBSERVED VS PREDICTEDPROBABILITIES USING FIS

Route Observed probability Estimated probabilityR1 42.11 46.2R2 31.58 31R3 26.32 23

C. Neuro-Fuzzy Based Modelling

The neuro-adaptive learning method works similarly tothat of neural networks. Neuro-adaptive learning techniquesprovide a method for the fuzzy modeling procedure to learninformation about a data set. A network-type structure,similar to that of a neural network, maps inputs through inputmembership functions and associated parameters. Then,through output membership functions and associatedparameters to outputs, can be used to interpret theinput/output map.

The parameters associated with the membershipfunctions change through the learning process. Thecomputation of these parameters (or their adjustment) isfacilitated by a gradient vector. This gradient vectorprovides a measure of how well the fuzzy inference systemis modeling the input/output data for a given set ofparameters. When the gradient vector is obtained, any ofseveral optimization routines can be applied in order toadjust the parameters to reduce some error measure. Thiserror measure is usually defined by the sum of the squareddifference between actual and desired outputs. It uses eitherback propagation or a combination of least squaresestimation and back-propagation for membership functionparameter estimation. The modeling approach used byANFIS is similar to many system identification techniques.First, one may hypothesize a parameterized model structure(relating inputs to membership functions to rules to outputsto membership functions, and so on). Next, one can collectinput/output data in the form that will be used by ANFIS fortraining. Then, ANFIS can be used to train the FIS model toemulate the training data presented to it by modifying themembership function parameters according to a chosen errorcriterion. In general, this type of modeling works well, if thetraining data presented to ANFIS for training (estimating)membership function parameters is fully representative ofthe features of the data that the trained FIS is intended tomodel. In some cases however, data is collected using noisymeasurements, and the training data cannot berepresentative of all the features of the data that will bepresented to the model. In such situations, model validationis helpful.

(a) Time (b) Distance




(c) Delay (d) Route preference score

Fig. 2 Membership function of few inputs for FIS

Fig. 3 Observed Vs predicted route preference score using FIS.

Model validation is the process by which the inputvectors from input/output data sets on which the FIS was nottrained, are presented to the trained FIS model, to see howwell the FIS model predicts the corresponding data set outputvalues. One problem with model validation for modelsconstructed using adaptive techniques is selecting a data setthat is both representative of the data, the trained model isintended to emulate, yet sufficiently distinct from thetraining data set so as not to render the validation processtrivial. If the collected data is of large size, hopefully thisdata contains all the necessary representative features, so theprocess of selecting a data set for checking or testingpurposes is made easier. However, if we expect to bepresenting noisy measurements to the model, it is possiblethat the training data set does not include all of therepresentative features one wants to model. The testing dataset allows checking the generalization capability of theresulting fuzzy inference system. The idea behind using acheck data set for model validation is that after a certainpoint in the training, the model begins over-fitting thetraining data set. In principle, the model error for thechecking data set tends to decrease as the training takes placeup to the point that over-fitting begins, and then the modelerror for the checking data suddenly increases. Over-fitting isaccounted for by testing the FIS trained on the training dataagainst the checking data, and choosing the membershipfunction parameters to be those associated with the minimumchecking error, if these errors indicate model over-fitting. Adetailed description of ANFIS can be found in Jang [10].

For the purpose of tuning membership function of inputparameters, all the observed data is fed to ANFIS in requiredformat. The type of membership function can be chosen overa range starting from triangular to Gaussian. In this study,triangular form of membership function was chosen afterexamination of statistical dispersion of the survey resultswhich proved it to be the most convenient. Few of selectedinput parameters tuned membership function in shown belowin fig 4.

A total of 107 rules were derived based on observed data.Route preferences score as given by travelers were used asoutput and compared against the predicated preference valuefor each of the traveler. The observed and predicted valuesare shown below in the figure 5.

From the figure 5, it can be noted that ANFIS predictedvalue are very close to the observed value. The root meansquare error (RMSE) and Theil’s error value was found to be0.0393 and 0.048754, respectively. Therefore, ANFIS alsoperforms better at individual level. The final route-wiseobserved and predicted probabilities are given below inTable 3.

TABLE 3 ROUTE-WISE OBSERVED VS PREDICTEDPROBABILITIES USING ANFIS

Route Observed probability Estimated probability

R1 42.11 47.6

R2 31.58 28.2

R3 26.32 24.1




(a) Distance (b) Time

(c) Speed (d) Route preference score

Fig. 4 Membership function of input parameters for ANFIS

Fig. 5 Observed Vs predicted route preference score using ANFIS.

D. Multinomial Logit Model

One of the best known stochastic choice models is thelogit model. Logit Model was first introduced in the case ofbinary choice. The Multinomial Logit represents thegeneralization of the original model to more than twoalternatives. The logit model is based on the assumption thatrandom variables representing random terms are independentand distributed using Gumbel’s probability density function.It may be denoted by f (e), the probability density function ofrandom variable that is Gumbel distributed. The f(e) can beexpressed as shown in the equation (1):

]eexp[μe(e) f η)μ(εη)μ(ε (1)Where:

η = location parameterµ = scale parameter

Using assumption about Gumbel’s distribution, it can beshown, that the probability that a given passenger q choosesalternative Ai within the choice set Cq as equation (2):

k

i

v

v

eep(i)

(2)

Where Vi = Deterministic part of ith routes’ utility.

To check the applicability of multinomial logit (MNL)model for the modeling of route choice preference usingcollected data, it is necessary to test the assumptionindependence of irrelevant alternatives (IIA). If IIAassumption holds valid, data can be modeled using MNL,




otherwise other models such as ordered logit and probitshould be used. To test the assumption, Hausman test wasconducted. The chi-square value obtained through Hausmantest was 6.3425. Therefore, it can be concluded that IIAassumption hold valid and MNL can be applied to model thepresent data. The MNL model developed is shown below intable 4. For modeling utility following approach is used:

From the responses the fuzzy weight of each of theattributes such as distance, time, etc. are calculated using thefollowing equation

Where, Wjk = fuzzy values of an attribute perceived by a user,

k= number of users

j = 1,2,3 represent the lower, middle and upper value of afuzzy set.

After, calculating the fuzzy weights, the utility for eachroute can be formed from the weighted sum of the attributesof choice. Hence, for example, the utility for route “r” couldbe given by the following equation:

U(r)= b1*V1(r)+b2*V2(r)+b3*V3(r)+b4*V4(r)+….

Where:

U(r)= the utility of travel for the given route r,

b1, b2, b3, b4 …..= calculated weight of each attribute

V1, V2, V3, V4…… = score of choice parameters given by user.

The attribute named familiarity of route was droppedfrom the analysis due to the fact that all the travelers weremostly familiar with all three routes.

The t-statistics are 1.00, 1.28, 1.65, and 1.96 atconfidence level of 68%, 85%, 90% and 95% respectively.In this study, a variable having t-statistics below 1.28 isconsidered as insignificant. Therefore, it can be inferred thatthe variables, namely, travel time, pavement condition, sideparking condition and aesthetic are found to be significant.Though other variables, such as distance, speed and delay donot have significant t-value, but are still in the modelformation because of strong theoretical base. This findingmay be applicable only for the present study, as number ofsamples was 150. For the present study, while conducting aquestionnaire survey, it was found that a variable, namelytravel time was better perceived by the respondents ascompared to the variables distance, speed and delay. Hence,the reason for getting travel time significant which reflectsindirectly variables such as distance, speed and delay, maybe related to the better perception of the respondents for thethree routes considered in the study. The route-wiseprobabilities obtained from estimated model along with theobserved probabilities are given below in Table 5.

TABLE 4 MNL MODEL DESCRIPTION

Variable Coefficient Standarderror t-test

Distance -0.62883189 0.5633016 -1.116

Travel time 0.17336053 0.10259275 1.690

Speed 0.07368519 0.10612618 0.694

Delay 0.06026305 0.12207270 0.494

Pavement condition 2.14580072 0.80322959 2.671

Side parkingcondition 1.10618762 0.89522178 1.312

Aesthetic 0.75455924 0.48341134 1.561

Comfort 0.30447467 0.40561074 0.751

TABLE 5 OBSERVED VS ESTIMATED PROBABILITIES USING MNL

Route Observed probability Estimated probability

R1 42.11 41.0

R2 31.58 33.0

R3 26.32 26.0

It can be noted from Table 5, that MNL predictions arevery close to the observed values. The root mean squareerror (RMSE) is 0.0106.

IV. CONCLUSIONS

The following are the important findings which could bemade from this study:

1. The fuzzy rule based inference model (FIS) has betterprediction rate at individual level as compared to ataggregate level. The RMSE and Theil’s error values forthe model are 0.0306 and 0.062805, respectively.

2. The adaptive neuro-fuzzy model (ANFIS) is very muchsimilar to the FIS model at individual rate. The extraadvantage with ANFIS is that it gives approximatelysimilar results with almost half of number ofmembership functions, for a particular variable. It alsorequires less number of rules as compared to FIS, whichcould be very beneficial for large size of database. TheRMSE and Theil’s error values for the model are 0.0393and 0.048754, respectively. The reason behind higherRMSE of the model is due to high computational efforts,but in spite of that it can be noted that it performs betterat individual level as compared to FIS model, asindicated through lesser Theil’s error value.

3. The multinomial logit model gives better results ascompared to both FIS and ANFIS model at aggregatelevel. The RMSE for the model is 0.0106.

4. The variables namely travel time, pavement condition,side parking condition and aesthetic parameters arefound to be highly significant in this study as comparedto the parameters such as distance, speed and delay.Therefore, on the basis of above four findings, it can beconcluded that all three models FIS, ANFIS and MNLhave similar performance at aggregate level. From thelbehavioural point of view, FIS and ANFIS are better ascompared to the MNL model.

V. LIMITATIONS AND FUTURE SCOPE OF THE STUDY

The present study considered only 150 samples for anidentified network, for the purpose of model developmentusing three approaches, namely, Fuzzy rule based InferenceSystem (FIS), Adaptive Neuro-Fuzzy Inference System(ANFIS) and Multinomial Logit Model (MNL). Thefindings based on this study are applicable only for this




study. The authors would like to collect more samples andcheck the consistency of the findings given in the presentstudy. Also, a new fuzzy based model combining route andmode choice may be developed. In future, relatively largernetwork, comprising of more than three routes, havingdifferent as well as mixed land-uses may be considered.Membership functions with different shapes such astrapezoidal shape may be deployed in order to get betterresults. The models developed for route choice along withmode choice considering public transportation network, canbe used for transportation planning and traffic managementespecially. Furthermore, route choice probability determinedwith this model can be used for developing trafficassignment models. With a combined model of Fuzzy Logicand traffic assignment, some transportation planning relatedpolicies can be investigated.

REFERENCES

[1] Abdel-Aty, M. A., Kitamura, R., and Jovanis, Using statedpreference data for studying the effect of advanced trafficinformation, Transportation Research Part C, Vol. 5, pp. 39-50, 1997.

[2] Arslan, T., and Khisty, C. J., A rational approach to handlingfuzzy perceptions in route choice, European Journal ofOperational Research, Vol. 168, pp. 571–583, 2006.

[3] Bovy, P.H.L., Fiorenzo-Catalano, S., Stochastic route choiceset generation: behavioral and probabilistic foundations.Transportmetrica, Vol. 3, No. 3, 173-189, 2007.

[4] Cantarella, G. E., and Luca, S. D., Multilayer feed forwardnetworks for transportation mode choice analysis: An analysisand a comparison with random utility models, TransportationResearch Part C, Vol. 13, pp. 121-155, 2005.

[5] Dubois, D. and Prade, H., Fuzzy sets and probability:misunderstandings, bridges and gaps, Proceedings of thesecond IEEE conference on fuzzy systems, San -Francisco, pp.1059-1068, 1993.

[6] Emmerink, R. H. M., Nijkamp, P., Rietveld, P., and VanOmmeren, J. N., Variable message signs and radio trafficinformation: An integrated empirical analysis of drivers’ routechoice behavior, Transportation Research Part A, Vol. 30,pp.135-153, 1996.

[7] Edara, P. K., Mode Choice Modeling Using Artificial NeuralNetworks, Masters' thesis, Department of Civil Engineering,Virginia, 2003.

[8] Hensher, D. A., and Ton, T. T., A comparison of thepredictive potential of artificial neural networks and nestedlogit models for commuter mode choice, TransportationResearch Part E, Vol. 36, pp. 155-172, 2000.

[9] Hawas, Y. E., Development and Calibration of Route ChoiceUtility Models:Neuro-Fuzzy Approach, Journal of TransportationEngineering, Vol. 130, pp. 171-182, 2004.

[10] Jang, J. S. R., ANFIS : Adaptive-Network-Based FuzzyInference System, IEEE Transactions on Systems, Man, andCybernetics, vol. 23, pp. 665-685, 1993.

[11] Jou, R. C., Hensher, D. A., and Chen, K. H., Route ChoiceBehaviour of Freeway Travelers Under Real-time TrafficInformation Provision - Application of the Best Route andthe Habitual Route Choice Mechanisms, TransportationPlanning and Technology, Vol. 30, pp. 545-570, 2007.

[12] Kikuchi, S., A method to defuzzify the fuzzy number:transportation problem application, Fuzzy Sets and Systems,Vol. 116, pp. 3-9, 2000.

[13] Kim, J., Sung, S., Namgung, M., and Jang, Y., Developmentof dynamic route choice behavioral applied intelligent systemtheory, Proceedings of the Eastern Asia Society forTransportation Studies, Vol. 5, Japan, pp. 1615 – 1630, 2005.

[14] Lotan, T., and Koutsopoulos, H., Approximate reasoningmodels for route choice behavior in the presence ofinformation, Transportation and Traffic Theory, Vol. , , pp.71-88, 1993.

[15] Lotan, T., Modeling discrete choice behavior based onexplicit information, IEEE Transactions on Systems, Man,and Cybernetics, Vol. 28, pp. 100-114, 1998.

[16] Lee, B., Fujiwara, A., Sugie, Y., and Namgung, M., Routechoice behavior model considering randomness andvagueness uncertainty, Proceeding of 13th Mini-EUROconference, Italy, No. 12, pp. 1-7, 2008.

[17] Lee, C., Ran, B., Yang, F., and Loh, W. Y., A hybrid treeapproach to modelling alternate route choice behavior withonline information, Journal of Intelligent TransportationSystems, Vol. 14, pp. 209-219, 2010.

[18] Mizutani, K., and Akiyama, T., An approach of hybrid modelsbased on fuzzy reasoning and logit models,Infrastructure planning review, Vol.18, pp. 509-516, 2001.

[19] Murat Y. Z. and N. Uludag. Route choice modelling in urbantransportation networks using fuzzy logic and logisticregression methods”, Journal of Scientific & IndustrialResearch, Vol. 67, pp. 19-27, 2008.

[20] Prato C.G. Route choice modeling: past, present and futureresearch directions, Journal of Choice Modeling, Vol. 2, No.1, pp. 65-100, 2009.

[21] Ross, T. J., Fuzzy logic with engineering application, JohnWiley & Sons, West Sussex, 2004.

[22] Teodorovic, D. and M. Kikuchi, Transportation route choicemodel using fuzzy inference technique, in: B.M. Ayyub(Ed.),Proceedings ISUMA'90, The 1st InternationalSymposium on Uncertainty Modeling and Analysis, IEEEComputer Press, College Park, 1990.

[23] Teodorovic, D., Vukanovic, S., and Obradovic, K., Modelingroute choice with advance traveler information by fuzzy logic,Transportation Planning and Technology, Vol. 22, pp. 1-25,1998.

[24] Teodorović, D., Fuzzy logic systems for transportationengineering: the state of the art, Transportation Research PartA, Vol. 33, pp. 337-364, 1999.

[25] Vythoulkas, P. C., and Koutsopoulos, H. N., Modelingdiscrete choice behavior using concepts from fuzzy set theory,approximate reasoning and neural networks, TransportationResearch Part C, Vol. 11, pp. 51-73, 2003.

[26] Theil, H., Economic Forecasts and Policy, Amsterdam: NorthHolland, 1958.

Mr. Subodh Kant Dubey (Date of Birth5-01-1988) is currently pursuing hisdoctorate from University of Texas,Austin. Before joining for his doctoeralstudy he worked as a project officer in thetransportation division at IIT Madras,India. As a student, he is a high-endperformer, and obtained hisundergraduate degree in the area of Civil

Engineering in the year 2009 from Jayam college of Engineering &Tech affiliated to Anna University, Chennai, India and postgraduate degree in the area of Transportation Engineering in theyear 2011, from Birla Institute of Tech & Science (BITS-Pilani),India. He has presented and published five research papers in




national and international conference proceedings. Discrete ChoiceModelling is his area of research interest.

Mr. Dewal Mishra (Date of Birth 07-12-1989) post graduate degree in the area ofTransportation Engineering in the year 2013,from Birla Institute of Tech & Science(BITS-Pilani), India. He obtained hisundergraduate degree in the area of CivilEngineering in the year 2011 from IPSAcademy, Indore, India. Publictransportation planning, design, operation

and management is his area of research interest.

Dr. Shriniwas S. Arkatkar (Date ofBirth 15-11-1977) is currently working asan Assistant Professor in the Departmentof Civil Engineering at BITS, Pilani. He ishaving more than 10 years of experienceof teaching, research and consultancy inthe field of transportation engineering.Before joining BITS, he pursued his Ph.D.research in the Transportation EngineeringDivision, Department of Civil

Engineering, IIT Madras. His doctoral research work is in the areaof ‘Study of Heterogeneous Traffic Flow Characteristics at MicroLevel’. He obtained his undergraduate degree in the area of CivilEngineering in the year 1999 and post graduate degree in the areaof Urban Planning in the year 2001, from Visvesvaraya NationalInstitute of Technology (VNIT), Nagpur, India. Traffic flowmodeling, Transportation Systems Design Planning andManagement and Traffic Safety are his areas of research interest.He has published sixty research papers in the International andNational journals and conference proceedings. He has alsopublished one research monograph in Germany. Two of his papershave received an award for excellence in research in the area of‘Traffic Engineering’. He is currently a member of Indian RoadsCongress (IRC) and Transportation Research Group of India(TRG). He is also a member of ‘Principal Technical Agency’,which is responsible for overall development of PMGSY roads inRajasthan under NRRDA, Ministry of Rural Roads. Currently, heis working on the following reaserch projects: (i) DeterminingComposite Index to Measure the Perceived Inadequacy of PublicTransportation in Jaipur, (ii) Impact of PMGSY Roads onAccessibility in Rural Areas, (iii)Study of traffic flow onExpressways, and (iv) Road Safety Audit for NH-11.

Prof. A. P. Singh (Date of Birth 30-06-1973) is the Dean (Instruction Division)and currently working as a Professor in theDepartment of Civil Engineering of BITS,Pilani. He has professional experience ofabout 18 years in teaching research andconsultancy in the area of overall CivilEngineering. Prof. A. P. Singh has a vastexposure in the area of Civil Engineering.He has guided many bachelor and

master’s degree students and has published more than thirtyresearch papers in international and national journals andconference proceedings. He has been involved in the overalldevelopment of Transportation Engineering Division of CivilEngineering Department of BITS Pilani. He has taught significantnumber of courses in transportation engineering for master’s andbachelor’s degree programs as (i) Transportation Engineering (3Times), (ii) Pavement Analysis and Design (2 times), (iii)Environmental Impact Assessment (1 time). He is working as aconvener of the ‘Project Parivartan’ Team, which is worth Rs 400crores for renovation of BITS Pilani Campus at Pilani. In this

project, he is also looking after overall safety aspects (i) trafficmanagement plan, (ii) construction planning and management, (iii)safety aspects at site, etc. He is also a member of ‘PrincipalTechnical Agency’ which is responsible for overall development ofPMGSY roads in Rajasthan under NRRDA, Ministry of RuralRoads. He has been also actively involved in the Evaluation ofDetailed Project Reports (DPRs) of Rural Roads to be constructedby PWD Rajasthan under PMGSY Programme funded by theNational Rural Roads Development Agency (NRRDA), Ministryof Rural Development, Government of India. Currently, he isworking on the following research projects: (i) Impact of PMGSYRoads on Accessibility in Rural Areas, and (ii) Road Safety Auditfor NH-11.

Prof. A. K. Sarkar (Date of Birth 1-10-1952) is currently working as aProfessor in the Department of CivilEngineering of BITS, Pilani. He hasprofessional experience of about 20years in teaching research andconsultancy in the area ofTransportation Engineering andplanning, rural accessibility and traffic

safety. He has guided doctoral and master s degree students andhas published more than eighty research papers in international andnational journals and conference proceedings. Prof. Sarkar hassuccessfully completed several sponsored research projects both atnational and international levels. The projects are: (i) AccidentStudies on some stretches of National Highways in Eastern India,(ii) Enhancement of Transportation Engineering Education andTraining in University of Durban Westville, (iii) RuralAccessibility Planning, (iv) Integrated Approaches to Ruralaccessibility and Associated Economic Development, (v) RuralRoad Performance Prediction: NRRDA sponsored project onPerformance Evaluation and Development of PerformancePrediction Model for Rural Roads, etc. Prof. Sarkar is member ofseveral professional bodies and technical committees of differentgovernment departments. Currently, he is working on thefollowing research projects: (i) Impact of PMGSY Roads onAccessibility in Rural Areas, and (ii) Road Safety Audit for NH-11.


Route Choice Modelling Using Fuzzy logic and Adaptive Neuro-fuzzy

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