A Fuzzy Neural Approach to Modelling Behavioural Rules in Agent-Based Route Choice Models
Rule 2: If driver is low-income, then the compliance is low
Both rules are generated fuzzy sets: B*1 and B*2. Defuzzification is the mechanism to transform these fuzzified outputs to a crisp value. This is implemented by using a defuzzification method to process the aggregated output B*. The centre of sums (COS) method is used to defuzzify the fuzzified output B*. This can be expressed as in Equation (3) below:
∫∑
∫ ∑
=
= =
Y n
i Bi Y
n
i Bi
dy y
dy y y y
1
* 1
) (
) ( μ
μ (3)
where Y is the rang of compliance level (1-4), n is the number of rules in the category, μBi(y) is the possibility value of y in fuzzy set Bi, and y* is the crisp value from defuzzification.
Rule 1: If driver is high-income, then the compliance is high.
Rule 2: If driver is low-income, then the compliance is low.
Input: Some Income Level
Defuzzification
Figure 5. Defuzzification Method of crisp input using if-then rules
4.3 Selection of ANN Architectures
Agent-based fuzzy-neural route choice models can be considered as a classification problem. Some of ANN architectures typically used for classification problems include [27]:
Back-Propagation: this is a general-purpose network paradigm.
Back-prop calculates an error between desired and actual output and propagates the error back to each node in the network. The back-propagated error drives the learning at each node.
Fuzzy ARTMAP: this is a general purpose classification network, and is a system of layers which are connected by a subsystem called a “match tracking system.” The version used in this study consisted of a single Fuzzy network and a mapping layer which controls the match tracking. If an incorrect association is made during learning, the match tracking system increases vigilance in the layers until a correct match is made. If necessary, a new category is established to accommodate a correct match.
Radial Basis Function Networks: these are networks which make use of radially symmetric and radially bounded transfer functions in their hidden (“pattern”) layer. These are general-purpose networks which can be used for a variety of problems including system modelling, prediction, classification.
Learning Vector Quantization (LVQ): this architecture is a classification network, originally suggested by [28], which assigns vectors to one of several classes. An LVQ network contains a Kohonen layer (known as hidden layer) which learns and performs the classification. LVQ provides equal numbers of PEs for each class in the Kohonen.
The development of a neural network model also involves the selection of a suitable objective function and modification of learning rules and transfer functions. Classification rate was selected as the objective function. It represents the percentage of correctly classified observations. A large number of learning rules and transfer functions were also explored. During training and testing phases, it was found that LVQ provided the best CR performance over the other architectures. The CR was favourable around 71-78 per cent as shown in Table 7.
Table 7. LVQ Best Model Performance before Calibrating Membership Function
AITS Scenarios % Classification
Rate Qualitative Delay Information 77.97 Quantitative Real-time Delay Information 75.79 Quantitative Real-time Delay on Best
Alternative Route
77.36 Predictive Delay Information 71.09 Prescriptive Best Alternative Route 74.09
4.4 Calibration of Membership Function
Figures 6(a) to 6(l) present the initial membership functions compared with the calibrated membership function. Initially, the functions have huge degree of overlapping. For example, Figures 6(a) and 6(b) depict membership function of driver’s age. The membership function for drivers under 18 years old is defined as
“Driver is young” with possibility 1 and for drivers’ age 64 years old is defined as “Driver is young” with possibility 0. On the other hand, the membership function for drivers’ age 18 years is defined as “Driver is old” with possibility 0 and drivers’ age over 65 years is defined as “Driver is old” with possibility 1.
After calibration, by reducing the degree of overlapping, the new membership functions for driver’s age can be obtained as shown in Figures 6(a) and 6(b). The drivers’ age of under 18 years old is defined as “Driver is young” with possibility 1 and for over 49 years old is defined as “Driver is young” with possibility 0. The membership function for drivers’ age of 30 years old is defined as
“Driver is old” with possibility 0 whereas drivers’ age of over 65 years is defined as “Driver is old” with possibility 1. The other membership functions were also modified in the same technique.
Their results are presented in Figures 6(c)-6(l). Having these functions, all fuzzified inputs and outputs can then be trained and tested. The huge improvements have been found for all models as presented in Table 8 below.
6(a). Driver is old 7(b) Driver is young
6(c). Driver’s income is high 6(d). Driver’s income is low
6(e). Driver is well-educated 6(f). Driver is less-educated
6(g). Flexibility of working time is high
6(h). Flexibility of working time is high
6(i). Familiarity is high 6(j). Familiarity is low
6(k). Compliance is high 6(l). Compliance is low
Figure 6. Modified membership function for which if-then rules (neural-based training) are constructed
Table 8. LVQ Best Model Performance after Calibrating Membership Function
AITS Scenarios % Classification
Rate Qualitative Delay Information 96.36 Quantitative Real-time Delay Information 90.79 Quantitative Real-time Delay on Best
Alternative Route
95.45 Predictive Delay Information 94.43 Prescriptive Best Alternative Route 92.44
4.5 Comparative Evaluation of Fuzzy-Neural Approach, Probit, Logit, and ANN Models
The study also compared the fuzzy-neural models to the binary probit, logit and ANN models using the same data set. The findings showed that binary probit and logit models provided a prediction accuracy of about 61 per cent. The ANN models gave a better degree of accuracy (about 96 per cent) while the developed fuzzy-neural models had an accuracy of 90– 96 per cent. A more detailed description of capabilities for all modelling approaches investigated can be found in [24]. It should be mentioned that while the ANN models may have been more accurate than the binary models, their disadvantage is that the rules are not easily interpreted. In this study, fuzzy sets were used to address this limitation by incorporating them into the representation of ANNs.
The model results from this approach can then be interpreted in terms of if-then rules.
5. SUMMARY AND FUTURE RESEARCH DIRECTIONS
The work reported in this study is part of an ongoing research topic thesis which aims to model driver behaviour using cognitive agents. The behavioural surveys which provide a useful insight into commuters’ needs and preferences for traffic information in the Brisbane metropolitan area have been utilised for model development. A comparative evaluation between fuzzy-neural approach, binary logit, probit and ANN models was also reported in this paper. The fuzzy-neural method was shown to be a suitable approach to modelling route choice behaviour and deriving the rules for implementing agent-based driver behaviour models. The development of the agent-based route choice models will help improve the reliability and credibility of simulation models and their use under ATIS environment. However, there is a need to have extended data collection for further development, calibration, and validation.
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