Support vector machines (SVMs) have been successfully applied to a number of applications such as including handwriting recognition, particle identification (e.g., muons), digital images identification (e.g., face identification), text categorization, bioinformatics (e.g., gene expression), function approximation and regression, and database marketing, and so on. Although SVMs have become more widely employed to forecast time-series data (Tay and Cao, 2001, Cao, 2003 and Kim, 2003) and to reconstruct dynamically chaotic systems (Müller et al., 1997, Mukherjee et al., 1997, Mattera and Haykin, 1999 and Kulkarni et al., 2003), a highly effective model can only be built after the parameters of SVMs are carefully determined (Duan, Keerthi, & Poo, 2003).
Min and Lee (2005) stated that the optimal parameter search on SVM plays a crucial role in building a prediction model with high prediction accuracy and stability. The kernel-parameters are the few tunable parameters in SVMs controlling the complexity of the resulting hypothesis (Cristianini, Campell, & Taylor, 1999). Shawkat and Kate (2007) pointed out that selecting the optimal degree of a polynomial kernel is critical to ensure good generalization of the resulting support vector machine model. They proposed an automatic selection for determining the optimal degree of polynomial kernel in SVM by Bayesian and Laplace approximation method estimation and a rule based meta-learning approach. In addition, to construct an efficient SVM model with RBF kernel, two extra parameters: (a) sigma squared and (b) gamma, have to be carefully predetermined. However, few studies have been devoted to optimizing the parameter values of SVMs. Evolutionary algorithms often have to solve optimization problems in the presence of a wide range of problems (Dastidar et al., 2005, Shin et al., 2005, Yaochu and Branke, 2005 and Zhang et al., 2005). In these algorithms, genetic algorithms (GAs) have been widely and successfully applied to various types of optimization problems in recent years (Goldberg, 1989, Fogel, 1994, Cao, 2003, Alba and Dorronsoro, 2005 and Alba and Dorronsoro, 2005; Aurnhammer and Tonnies, 2005, Venkatraman and Yen, 2005, Hokey et al., 2006, Cao and Wu, 1999 and McCall, 2005). Therefore, this paper proposes a hybrid genetic-based SVR model, HGA-SVR, which can automatically optimize the SVR parameters integrating the real-valued genetic algorithm (RGA) and integer genetic algorithm, for increasing the predictive accuracy and capability of generalization compared with traditional machine learning models.
In addition, a wide range of approaches including time-varying splines (Harvey & Koopman, 1993), multiple regression models (Ramanathan, Engle, Granger, Vahid-Araghi, & Brace, 1997), judgmental forecasts, artificial neural networks (Hippert & Pedreira, 2001) and SVMs (Chen et al., 2004 and Tian and Noore, 2004) have been employed to forecast electricity load. One of the most crucial demands for the operation activities of power systems is short-term hourly load forecasting and the extension to several days in the future. Improving the accuracy of short-term load forecasting (STLF) is becoming even more significant than before due to the changing structure of the power utility industry (Tian & Noore, 2004). SVMs have been applied to STLF and performed well. Unfortunately, there is still no consensus as to the perfect approach to electricity demand forecasting (Taylor & Buizza, 2003).
Several studies have proposed optimization methods which used a genetic algorithm for optimizing the SVR parameter values. To overcome the problem of SVR parameters, a GA-SVR has been proposed in a earlier paper (Hsu, Wu, Chen, & Peng, 2006) to take advantage of the GAs optimization technique. However, few studies have focused on concurrently optimizing the type of SVR kernel function and the parameters of SVR kernel function. The present study proposed a novel and specialized hybrid genetic algorithm for optimizing all the SVR parameters simultaneously. Our proposed method was applied to predicting maximum electrical daily load and its performance was analyzed. An actual case of forecasting maximum electrical daily load is illustrated to show the improvement in predictive accuracy and capability of generalization achieved by our proposed HGA-SVR model.
The remainder of this paper is organized as follows. The research gap for obtaining optimal parameters in SVR is reviewed and discussed in Section 2. Section 3 details the proposed HGA-SVR, ideas and procedures. In Section 4 an experimental example for predicting the electricity load is described to demonstrate the proposed method. Discussions are presented in Section 5 and conclusions are drawn in the final Section.
