The effective capacity of inter-urban motorway networks is an essential component of traffic control and information systems, particularly during periods of daily peak flow. However, slightly inaccurate capacity predictions can lead to congestion that has huge social costs in terms of travel time, fuel costs and environment pollution. Therefore, accurate forecasting of the traffic flow during peak periods could possibly avoid or at least reduce congestion. Additionally, accurate traffic forecasting can prevent the traffic congestion as well as reduce travel time, fuel costs and pollution. However, the information of inter-urban traffic presents a challenging situation; thus, the traffic flow forecasting involves a rather complex nonlinear data pattern and unforeseen physical factors associated with road traffic situations. Artificial neural networks (ANNs) are attracting attention to forecast traffic flow due to their general nonlinear mapping capabilities of forecasting. Unlike most conventional neural network models, which are based on the empirical risk minimization principle, support vector regression (SVR) applies the structural risk minimization principle to minimize an upper bound of the generalization error, rather than minimizing the training errors. SVR has been used to deal with nonlinear regression and time series problems. This investigation presents a short-term traffic forecasting model which combines SVR model with continuous ant colony optimization (SVRCACO), to forecast inter-urban traffic flow. A numerical example of traffic flow values from northern Taiwan is employed to elucidate the forecasting performance of the proposed model. The simulation results indicate that the proposed model yields more accurate forecasting results than the seasonal autoregressive integrated moving average (SARIMA) time-series model.
Traditionally, there has been a wide variety of forecasting approaches applied to forecast the traffic flow of inter-urban motorway networks. Those approaches could be classified according to the type of data, forecast horizon, and potential end-use (Dougherty, 1996); including historical profiling (Okutani & Stephanedes, 1984), state space models (Stathopoulos & Karlafits, 2003), Kalman filters (Whittaker, Garside & Lindveld, 1994), and system identification models (Vythoulkas, 1993). However, traffic flow data are in the form of spatial time series and are collected at specific locations at constant intervals of time. The above-mentioned studies and their empirical results have indicated that the problem of forecasting inter-urban motorway traffic flow is multi-dimensional, including relationships among measurements made at different times and geographical sites. In addition, these methods have difficultly coping with observation noise and missing values while modeling. Therefore, Danech-Pajouh and Aron (1991) employed a layered statistical approach with a mathematical clustering technique to group the traffic flow data and a separately tuned linear regression model for each cluster. Based on the multi-dimensional pattern recognition requests, such as intervals of time and geographical sites, non-parametric regression models (Smith, Williams & Oswald, 2002) have also successfully been employed to forecast motorway traffic flow. The ARIMA model and extended models are the most popular approaches in traffic flow forecasting (Kamarianakis & Prastacos, 2005) (Smith et al., 2002). Due to the stochastic nature and the strongly nonlinear characteristics of inter-urban traffic flow data, the artificial neural networks (ANNs) models have received much attention and been considered as alternatives for traffic flow forecasting models (Ledoux, 1997) (Yin, Wong, Xu & Wong, 2002). However, the training procedure of ANNs models is not only time consuming but also possible to get trapped in local minima and subjectively in selecting the model architecture.
Key Terms in this Chapter
Evolutionary Algorithm (EA): is a generic population-based meta-heuristic optimization algorithm. An EA uses some mechanisms inspired by biological evolution: reproduction, mutation, recombination, natural selection and survival of the fittest. Evolutionary algorithms consistently perform well approximating solutions to all types of problems because they do not make any assumption about the underlying fitness landscape.
Ant Colony Optimization Algorithm (ACO): inspired by the behavior of ants in finding paths from the colony to food, is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs. A short path gets marched over faster, and thus the pheromone density remains high as it is laid on the path as fast as it can evaporate.
Pheromone: A pheromone is a chemical that triggers an innate behavioral response in another member of the same species. There are alarm pheromones, food trail pheromones, sex pheromones, and many others that affect behavior or physiology. In this article, food trail pheromones are employed, which are common in social insects.
Support Vector Machines (SVMs): Support vector machines (SVMs) were originally developed to solve pattern recognition and classification problems. With the introduction of Vapnik’s e-insensitive loss function, SVMs have been extended to solve nonlinear regression estimation problems which are so-called support vector regression (SVR). SVR applies the structural risk minimization principle to minimize an upper bound of the generalization error. SVR has been used to deal with nonlinear regression and time series problems.
Artificial Neural Networks (ANNs): A network of many simple processors (“units” or “neurons”) that imitates a biological neural network. The units are connected by unidirectional communication channels, which carry numeric data.
Autoregressive Integrated Moving Average (ARIMA): A generalization of an autoregressive moving average (ARMA) model. These models are fitted to time series data either to better understand the data or to predict future points in the series. The model is generally referred to as an ARIMA(p,d,q) model where p, d, and q are integers greater than or equal to zero and refer to the order of the autoregressive, integrated, and moving average parts of the model respectively.
Seasonal Autoregressive Integrated Moving Average (SARIMA): A kind of ARIMA model to conduct forecasting problem while seasonal effect is suspected. For example, consider a model of daily road traffic volumes. Weekends clearly exhibit different behavior from weekdays. In this case it is often considered better to use a SARIMA (seasonal ARIMA) model than to increase the order of the AR or MA parts of the model.