رگرسیون بردار پشتیبانی با الگوریتم ژنتیک در پیش بینی تقاضای گردشگری

This study applies a novel neural network technique, support vector regression (SVR), to tourism demand forecasting. The aim of this study is to examine the feasibility of SVR in tourism demand forecasting by comparing it with back-propagation neural networks (BPNN) and the autoregressive integrated moving average (ARIMA) model. To build an effective SVR model, SVR's parameters must be set carefully. This study proposes a novel approach, known as genetic algorithm (GA)-SVR, which searches for SVR's optimal parameters using real value GAs, and then adopts the optimal parameters to construct the SVR models. The tourist arrivals to China during 1985–2001 were employed as the data set. The experimental results demonstrate that SVR outperforms the BPNN and ARIMA models based on the normalized mean square error (NMSE) and mean absolute percentage error (MAPE).

In the past few decades, the tourism industry has emerged as the fastest growing sector, and has spread widely around the world. Tourism expenditure has become an important source of economic activity, employment, tax revenue, income and foreign exchange. Therefore, every country needs to understand its international visitors and tourism receipts, to help formulate responsive policies on tourism quickly. Furthermore, the tourism industry is characterized by unstockpiled economics (such as empty hotel rooms and air flight seats), resulting in a requirement for accurate forecasts of tourism demand, in both the short and long term. In tourism demand forecasting, the relevant researche models firstly emphasize econometrics (Hiemstra & Wong, 2002; Smeral, Witt, & Witt, 1992; Song & Witt, 2000). These investigations concluded that econometric models can help the policymakers formulate appropriate economic strategies in order to influence tourism demand and generate accurate demand forecasts. However, such methods are time-consuming, costly and the influent factors are difficult to research. Although time series methods cannot fully explain the relations between variables, they require less empirical evidence than econometrics and, hence, are appropriate for tourism research issues. For instance, Lim and McAleer (2002) employed Box–Jenkins’ autoregressive integrated moving average (ARIMA) model to forecast tourist arrivals to Australia from Hong Kong, Malaysia and Singapore. Goh and Law (2002) applied the time series SARIMA and MARIMA with interventions in forecasting tourism demand using ten arrival series for Hong Kong. Recently, neural networks have been successfully employed for modelling time series. Unlike conventional statistical models, neural networks are data-driven, non-parametric, weak models which let “the data speak for themselves”. Law and Au (1999) first applied feed-forward neural networks to forecast Japanese demand for travel to Honk Kong. Law (2000) extended the applicability of neural networks in tourism demand forecasting by incorporating the back-propagation learning process into nonlinearly separable tourism demand data. Experimental results demonstrate that the neural networks model forecasts outperformed multiple regression, moving average and exponent smoothing. However, the neural networks suffer from several weaknesses, such as the need for a large number of controlling parameters, difficulty in obtaining a stable solution and the danger of over-fitting. In 1995, Vapnik developed a neural network algorithm called support vector machine (SVM), which is a novel learning machine based on statistical learning theory, and which adheres to the principle of structural risk minimization seeking to minimize an upper bound of the generalization error, rather than minimize the training error (the principle followed by neural networks). This induction principle is based on the bounding of the generalization error by the sum of the training error and a confidence interval term depending on the Vapnik–Chervonenkis (VC) dimension. Based on this principle, SVM achieves an optimum network structure by striking a right balance between the empirical error and the VC-confidence interval. This balance eventually leads to better generalization performance than other neural network models (Tay & Cao, 2001). Additionally, the SVM training process is equivalent to solving linearly constrained quadratic programming problems, and the SVM-embedded solution meaning is unique, optimal and unlikely to generate local minima. Originally, SVM has been developed to solve pattern recognition problems. However, with the introduction of Vapnik's ε-insensitive loss function, SVM has been extended to solve nonlinear regression estimation problems, such as new techniques known as support vector regression (SVR), which have been shown to exhibit excellent performance ( Vapnik, Golowich, & Smola, 1997). Recently, SVR has emerged as an alternative and powerful technique to solve the nonlinear regression problem. It has achieved great success in both academic and industrial platforms due to its many attractive features and promising generalization performance. Despite its superior features, SVR is limited in academic research and industrial applications because the user must define various parameters (so-called hyper-parameters) appropriately. To construct the SVR model efficiently, SVR's parameters must be set carefully (Duan, Keerthi, & Poo, 2001; Keerthi, 2002; Lin, 2001). Inappropriate parameters in SVR lead to over-fitting or under-fitting (Lin, 2001). Different parameter settings can cause significant differences in performance. Therefore, selecting optimal hyper-parameter is an important step in SVR design. However, no general guidelines are available to select these parameters (Cristianini & Shawe-Taylor, 2000; Gunn, 1997; Schölkopf & Smola, 2002; Vapnik (1995) and Vapnik (1998)). Therefore, in this study, we propose real-value genetic algorithms (RGA) to determine free parameters of SVR, known as GA-SVR, which optimizes all SVR's parameters simultaneously from the training data. Then, the tourism demand, as represented by the number of world-wide visitors to China, was predicted. The proposed approach was compared with the back-propagation neural networks (BPNN) and traditional time series models, such as ARIMA, so as to show that the SVR model is substantially featured with an excellent forecasting capacity. This study includes eight sections. Section 2 introduces theories related to SVR. Section 3 summarizes the existing practical approaches to the choice of hyper-parameters. Section 4 elaborates on the GA-SVR model proposed in this study. Section 5 describes the data source and experimental settings. Section 6 analyzes the results of RGA and optimizes SVR's parameters, and also explains the determining parameters process of the BPNN and ARIMA models. Section 7 discusses and analyzes the experimental results. Section 8 concludes the study and suggests directions for future investigations.

This study applied SVR to the forecasting fields of tourism demand time series. To build stable and reliable forecasting models, the parameters of SVR must be specified carefully. Since the five-fold cross validation training error can be applied to the forecasting error estimation, the RGA, integrated using five-fold cross validation, was first applied to the training sets to obtain the optimal parameters. Thereafter, these optimal parameters were employed to build the actual GA-SVR forecasting models. Generally, the experimental results show that the forecasting errors made by GA-SVR and BPNN model used only data-driven methods without model identity, and that any prior assumptions about the properties of the data would be much smaller than that of traditional ARIMA model. The experimental results also indicate that the superior application of artificial intelligence technique is perfectly applicable to the forecasting operation of a nonlinear time series. Moreover, the experimental results also suggest that within the forecasting fields of tourism demand, the GA-SVR is typically a reliable forecasting tool, with the forecasting capacity more precise than that of BPNN. The previous discussion indicates that the SVR exhibits excellent and reliable forecasting capacity. The said advantages of SVR are actually constructed by the below factors: (1) Unlike BPNN models, which implement the empirical risk minimization principle, SVR implements the structural risk minimization principle which attempts to minimize an upper bound of the generalization error rather than minimize the training error. This critical inherent feature of SVR leads to a better forecasting error than that of BPNN. (2) The BPNN probably cannot converge to global solutions. However, within the SVR, the process for training is equivalent to solving a linearly constrained quadratic programming, and the solution of SVR is unique, optimal and global. Compared with the BPNN, within the forecasting fields of time series, the SVR has an inherently excellent performance. However, the number of input nodes influences both the autoregressive structures of time series and the forecasting performance. Thus, to develop a technique available to determine the number of input nodes in SVR systemically and structurally will be an important direction for future development.