由於台灣屬於海島型態，自然資源有限，但也造就台灣依賴進出口的特性，進出口貿易成了不可或缺的商業行為。因此，隨著台灣經濟的發展，進出口貿易越加頻繁。因此，本研究對於出口貿易值提出了一個三階段預測模型，其主要是以萬用演算法為基礎之支援向量回歸預測模型結合小波轉換及萬用演算法為基礎之K-means分群演算法。本研究所使用的萬用演算法分別為基因演算法、粒子群演算法、螢火蟲演算法以及差分進化演算法，藉由這些萬用演算法來尋找支援向量回歸的最佳參數。首先利用小波轉換進行資料前處理，將資料去除雜訊，接著再使用萬用演算法為基礎之K-means分群演算法進行分群處理，減少資料差異性太大或離群值的影響，提高預測的準確度，最後再將各群資料個別放入所建立的萬用演算法為基礎之支援向量回歸模型進行預測。
為了驗證本研究所提出之整合預測模型是否可有效增加預測的準確性，本研究將比較使用小波轉換或不使用小波轉換的差異性，亦探討分群和不分群狀況下的分群準確性。實驗結果證明，同時結合小波轉換及分群分析為基礎的支援向量回歸可得到較好的預測結果，藉此提升了預測的準確度。

Since Taiwan is lack of natural resources, exports play an important role in the economy development in Taiwan. Exports have critical influence on the level of economic growth, internal trade, economic stability, employment and the balance of payments.
In order to develop a predicting system for export trade value, this study proposes a three-stage forecasting model which integrates wavelet transform, metaheuristics based K-means algorithms and metaheuristics based support vector regression (SVR). For metaheuristics algorithms, this study applies genetic algorithm, particle swarm optimization algorithm, firefly algorithm and differential evolution algorithm to optimize the parameters for K-means algorithm and support vector regression. Firstly, the wavelet transform is utilized to reduce the noises for data preprocessing. Then, this study employs metaheuristics based K-means algorithms for clustering analysis. Finally, a forecasting model is built for each cluster individually.
For evaluation, this study compares methods with and without clustering. In addition, both non-wavelet transform and wavelet transform for data preprocessing are investigated. The experimental results indicate that the forecasting algorithm with both wavelet transform and clustering has better performance. Therefore, this can enhance the forecasting ability.

Acar, Y. & Gardner Jr, E. S., "Forecasting method selection in a global supply chain," International Journal of Forecasting, vol. 28, no. 4, pp. 842-848, 2012.
Ahmadyfard, A. & Modares, H., "Combining PSO and k-means to enhance data clustering," in Telecommunications, 2008. IST 2008. International Symposium on, 2008, pp. 688-691.
Babu, G. P. & Murty, M. N., "A near-optimal initial seed value selection in k-means means algorithm using a genetic algorithm," Pattern Recognition Letters, vol. 14, no. 10, pp. 763-769, 1993.
Cai, L., Qu, S., & Li, X., "Self-adapt evolution SVR in a traffic flow forecasting," in Signal Processing, Communication and Computing (ICSPCC), 2013 IEEE International Conference on, 2013, pp. 1-5.
Cai, Z.-J., Sheng, L., & Xiao-bin, Z., "Tourism demand forecasting by support vector regression and genetic algorithm," in Computer Science and Information Technology, 2009. ICCSIT 2009. 2nd IEEE International Conference on, 2009, pp. 144-146.
Castro-Neto, M., Jeong, Y.-S., Jeong, M.-K., & Han, L. D., "Online-SVR for short-term traffic flow prediction under typical and atypical traffic conditions," Expert Systems with Applications, vol. 36, no. 3, Part 2, pp. 6164-6173, 2009.
Chang, P.-C., Liu, C.-H., & Fan, C.-Y., "Data clustering and fuzzy neural network for sales forecasting: A case study in printed circuit board industry," Knowledge-Based Systems, vol. 22, no. 5, pp. 344-355, 2009.
Chang, P.-C., Wang, Y.-W., & Liu, C.-H., "Combining SOM and GA-CBR for Flow Time Prediction in Semiconductor Manufacturing Factory," in Rough Sets and Current Trends in Computing. vol. 4259, S. Greco, Y. Hata, S. Hirano, M. Inuiguchi, S. Miyamoto, H. Nguyen, et al., Eds., ed: Springer Berlin Heidelberg, 2006, pp. 767-775.
Che, J. & Wang, J., "Short-term electricity prices forecasting based on support vector regression and Auto-regressive integrated moving average modeling," Energy Conversion and Management, vol. 51, no. 10, pp. 1911-1917, 2010.
Chen, C.-Y. & Fun, Y., "Particle swarm optimization algorithm and its application to clustering analysis," in Networking, Sensing and Control, 2004 IEEE International Conference on, 2004, pp. 789-794 Vol.2.
Chen, K.-Y., "Forecasting systems reliability based on support vector regression with genetic algorithms," Reliability Engineering & System Safety, vol. 92, no. 4, pp. 423-432, 2007.
Chen, K.-Y., "Combining linear and nonlinear model in forecasting tourism demand," Expert Systems with Applications, vol. 38, no. 8, pp. 10368-10376, 2011.
Chen, K.-Y. & Wang, C.-H., "Support vector regression with genetic algorithms in forecasting tourism demand," Tourism Management, vol. 28, no. 1, pp. 215-226, 2007.
Chen, P.-y. & Liu, L., "Study on coal logistics demand forecast based on PSO-SVR," in Service Systems and Service Management (ICSSSM), 2013 10th International Conference on, 2013, pp. 130-133.
Cherkassky, V. & Ma, Y., "Practical selection of SVM parameters and noise estimation for SVM regression," Neural Networks, vol. 17, no. 1, pp. 113-126, 2004.
Ding, Y., Song, X., & Zen, Y., "Forecasting financial condition of Chinese listed companies based on support vector machine," Expert Systems with Applications, vol. 34, no. 4, pp. 3081-3089, 2008.
Du, K. L., "Clustering: A neural network approach," Neural Networks, vol. 23, no. 1, pp. 89-107, 2010.
du Preez, J. & Witt, S. F., "Univariate versus multivariate time series forecasting: an application to international tourism demand," International Journal of Forecasting, vol. 19, no. 3, pp. 435-451, 2003.
Duan, K., Keerthi, S. S., & Poo, A. N., "Evaluation of simple performance measures for tuning SVM hyperparameters," Neurocomputing, vol. 51, pp. 41-59, 2003.
Duan, Q., Liao, T. W., & Yi, H. Z., "A comparative study of different local search application strategies in hybrid metaheuristics," Applied Soft Computing, vol. 13, no. 3, pp. 1464-1477, 2013.
Fang, S. F., Wang, M. P., Qi, W. H., & Zheng, F., "Hybrid genetic algorithms and support vector regression in forecasting atmospheric corrosion of metallic materials," Computational Materials Science, vol. 44, no. 2, pp. 647-655, 2008.
Gandomi, A. H., Yang, X.-S., & Alavi, A. H., "Mixed variable structural optimization using Firefly Algorithm," Computers & Structures, vol. 89, no. 23–24, pp. 2325-2336, 2011.
Gao, Y., "Forecasting of freight volume based on support vector regression optimized by genetic algorithm," in Computer Science and Information Technology, 2009. ICCSIT 2009. 2nd IEEE International Conference on, 2009, pp. 550-553.
Guanghui, W., "Demand Forecasting of Supply Chain Based on Support Vector Regression Method," Procedia Engineering, vol. 29, no. 0, pp. 280-284, 2012.
Guo, X., Sun, L., Li, G., & Wang, S., "A hybrid wavelet analysis and support vector machines in forecasting development of manufacturing," Expert Systems with Applications, vol. 35, no. 1–2, pp. 415-422, 2008.
Hassanzadeh, T. & Meybodi, M. R., "A new hybrid approach for data clustering using firefly algorithm and K-means," in Artificial Intelligence and Signal Processing (AISP), 2012 16th CSI International Symposium on, 2012, pp. 007-011.
Hong, W.-C., "Chaotic particle swarm optimization algorithm in a support vector regression electric load forecasting model," Energy Conversion and Management, vol. 50, no. 1, pp. 105-117, 2009.
Hong, W.-C., Dong, Y., Chen, L.-Y., & Wei, S.-Y., "SVR with hybrid chaotic genetic algorithms for tourism demand forecasting," Applied Soft Computing, vol. 11, no. 2, pp. 1881-1890, 2011.
Hong, W.-C., Dong, Y., Zheng, F., & Lai, C.-Y., "Forecasting urban traffic flow by SVR with continuous ACO," Applied Mathematical Modelling, vol. 35, no. 3, pp. 1282-1291, 2011.
Huang, J., Bo, Y., & Wang, H., "Electromechanical equipment state forecasting based on genetic algorithm – support vector regression," Expert Systems with Applications, vol. 38, no. 7, pp. 8399-8402, 2011.
Huang, W., Nakamori, Y., & Wang, S.-Y., "Forecasting stock market movement direction with support vector machine," Computers & Operations Research, vol. 32, no. 10, pp. 2513-2522, 2005.
Jain, A. K., Murty, M. N., & Flynn, P. J., "Data clustering: a review," ACM Comput. Surv., vol. 31, no. 3, pp. 264-323, 1999.
Jiansheng, W. & Enhong, C., "A Novel Hybrid Particle Swarm Optimization for Feature Selection and Kernel Optimization in Support Vector Regression," in Computational Intelligence and Security (CIS), 2010 International Conference on, 2010, pp. 189-194.
Ju, Y.-f. & Wu, S.-w., "Village electrical load prediction by genetic algorithm and SVR," in Computer Science and Information Technology (ICCSIT), 2010 3rd IEEE International Conference on, 2010, pp. 278-281.
Kao, L.-J., Chiu, C.-C., Lu, C.-J., & Chang, C.-H., "A hybrid approach by integrating wavelet-based feature extraction with MARS and SVR for stock index forecasting," Decision Support Systems, vol. 54, no. 3, pp. 1228-1244, 2013.
Kavousi-Fard, A., Samet, H., & Marzbani, F., "A new hybrid Modified Firefly Algorithm and Support Vector Regression model for accurate Short Term Load Forecasting," Expert Systems with Applications, vol. 41, no. 13, pp. 6047-6056, 2014.
Kazem, A., Sharifi, E., Hussain, F. K., Saberi, M., & Hussain, O. K., "Support vector regression with chaos-based firefly algorithm for stock market price forecasting," Applied Soft Computing, vol. 13, no. 2, pp. 947-958, 2013.
Kedia, V., Thummala, V., & Karlapalem, K., "Time Series Forecasting through Clustering-A Case Study," in COMAD, 2005, pp. 183-191.
Kennedy, J. & Eberhart, R., "Particle swarm optimization," in Neural Networks, 1995. Proceedings., IEEE International Conference on, 1995, pp. 1942-1948 vol.4.
Kim, K.-j., "Financial time series forecasting using support vector machines," Neurocomputing, vol. 55, no. 1–2, pp. 307-319, 2003.
Kuo, R. J., Zulvia, F. E., & Suryadi, K., "Hybrid particle swarm optimization with genetic algorithm for solving capacitated vehicle routing problem with fuzzy demand – A case study on garbage collection system," Applied Mathematics and Computation, vol. 219, no. 5, pp. 2574-2588, 2012.
Kwedlo, W., "A clustering method combining differential evolution with the K-means algorithm," Pattern Recognition Letters, vol. 32, no. 12, pp. 1613-1621, 2011.
Levis, A. A. & Papageorgiou, L. G., "Customer Demand Forecasting via Support Vector Regression Analysis," Chemical Engineering Research and Design, vol. 83, no. 8, pp. 1009-1018, 2005.
Li, J. & Cai, Z., "A Novel Automatic Parameters Optimization Approach Based on Differential Evolution for Support Vector Regression," in Advances in Computation and Intelligence. vol. 5370, L. Kang, Z. Cai, X. Yan, and Y. Liu, Eds., ed: Springer Berlin Heidelberg, 2008, pp. 510-519.
Li, M.-W., Hong, W.-C., & Kang, H.-G., "Urban traffic flow forecasting using Gauss–SVR with cat mapping, cloud model and PSO hybrid algorithm," Neurocomputing, vol. 99, no. 0, pp. 230-240, 2013.
Lin, Wan-Hsien, "An Integration Of Differential Evolution K-Means Algorithm and Support Vector Regression With Differential Evolution Algorithm For Forecasting Medical Cost Of Patients with Acute Hepatitis", 2014.
Lu, C.-J., "Sales forecasting of computer products based on variable selection scheme and support vector regression," Neurocomputing, vol. 128, no. 0, pp. 491-499, 2014.
Lu, C.-J., Lee, T.-S., & Lian, C.-M., "Sales forecasting for computer wholesalers: A comparison of multivariate adaptive regression splines and artificial neural networks," Decision Support Systems, vol. 54, no. 1, pp. 584-596, 2012.
Lu, C.-J. & Wang, Y.-W., "Combining independent component analysis and growing hierarchical self-organizing maps with support vector regression in product demand forecasting," International Journal of Production Economics, vol. 128, no. 2, pp. 603-613, 2010.
Łukasik, S. & Żak, S., "Firefly Algorithm for Continuous Constrained Optimization Tasks," in Computational Collective Intelligence. Semantic Web, Social Networks and Multiagent Systems. vol. 5796, N. Nguyen, R. Kowalczyk, and S.-M. Chen, Eds., ed: Springer Berlin Heidelberg, 2009, pp. 97-106.
Łukasik, S. & Żak, S., "Firefly algorithm for continuous constrained optimization tasks," in Computational Collective Intelligence. Semantic Web, Social Networks and Multiagent Systems, ed: Springer, 2009, pp. 97-106.
Mahmoud, E., Motwani, J., & Rice, G., "Forecasting US exports: An illustration using time series and econometric models," Omega, vol. 18, no. 4, pp. 375-382, 1990.
Maulik, U. & Bandyopadhyay, S., "Genetic algorithm-based clustering technique," Pattern Recognition, vol. 33, no. 9, pp. 1455-1465, 2000.
Michielssen, E., Ranjithan, S., & Mittra, R., "Optimal multilayer filter design using real coded genetic algorithms," IEE Proceedings J (Optoelectronics), vol. 139, no. 6, pp. 413-420, 1992.
Mullen, K., Ardia, D., Gil, D. L., Windover, D., & Cline, J., "DEoptim: An R package for global optimization by differential evolution," Journal of Statistical Software, vol. 40, no. 6, pp. 1-26, 2011.
Murthy, C. A. & Chowdhury, N., "In search of optimal clusters using genetic algorithms," Pattern Recognition Letters, vol. 17, no. 8, pp. 825-832, 1996.
Nalley, D., Adamowski, J., & Khalil, B., "Using discrete wavelet transforms to analyze trends in streamflow and precipitation in Quebec and Ontario (1954–2008)," Journal of Hydrology, vol. 475, no. 0, pp. 204-228, 2012.
Pai, P.-F. & Hong, W.-C., "Forecasting regional electricity load based on recurrent support vector machines with genetic algorithms," Electric Power Systems Research, vol. 74, no. 3, pp. 417-425, 2005.
Pai, P.-F., Hung, K.-C., & Lin, K.-P., "Tourism demand forecasting using novel hybrid system," Expert Systems with Applications, vol. 41, no. 8, pp. 3691-3702, 2014.
Pan, H., Cheng, G., & Ding, J., "Drilling Cost Prediction Based on Self-adaptive Differential Evolution and Support Vector Regression," in Intelligent Data Engineering and Automated Learning – IDEAL 2013. vol. 8206, H. Yin, K. Tang, Y. Gao, F. Klawonn, M. Lee, T. Weise, et al., Eds., ed: Springer Berlin Heidelberg, 2013, pp. 67-75.
Partal, T. & Küçük, M., "Long-term trend analysis using discrete wavelet components of annual precipitations measurements in Marmara region (Turkey)," Physics and Chemistry of the Earth, Parts A/B/C, vol. 31, no. 18, pp. 1189-1200, 2006.
Paterlini, S. & Krink, T., "High performance clustering with differential evolution," in Evolutionary Computation, 2004. CEC2004. Congress on, 2004.
Price, K., Storn, R. M., & Lampinen, J. A., Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series): Springer-Verlag New York, Inc., 2005.
Qi, X. & Yan, X., "Forecast of the Total Volume of Import-export Trade Based on Grey Modelling Optimized by Genetic Algorithm," in Intelligent Information Technology Application, 2009. IITA 2009. Third International Symposium on, 2009, pp. 545-547.
Qin, C. & Jinping, M., "Optimizing the Ant Clustering Model Based on K-Means Algorithm," in Computer Science and Information Engineering, 2009 WRI World Congress on, 2009, pp. 699-702.
Samadzadegan, F. & Saeedi, S., "Clustering of lidar data using particle swarm optimization algorithm in urban area," Laserscanning09, vol. 38, pp. 334-339, 2009.
Senthilnath, J., Omkar, S. N., & Mani, V., "Clustering using firefly algorithm: Performance study," Swarm and Evolutionary Computation, vol. 1, no. 3, pp. 164-171, 2011.
Shahrabi, J., Hadavandi, E., & Asadi, S., "Developing a hybrid intelligent model for forecasting problems: Case study of tourism demand time series," Knowledge-Based Systems, vol. 43, no. 0, pp. 112-122, 2013.
Shi, N., Liu, X., & Guan, Y., "Research on k-means Clustering Algorithm: An Improved k-means Clustering Algorithm," in Intelligent Information Technology and Security Informatics (IITSI), 2010 Third International Symposium on, 2010, pp. 63-67.
Siamak, S. G., Bahrami Jovein, H., & Ramezanianpour, A. A., "Hybrid support vector regression – Particle swarm optimization for prediction of compressive strength and RCPT of concretes containing metakaolin," Construction and Building Materials, vol. 34, no. 0, pp. 321-329, 2012.
Taguchi, G., Introduction to quality engineering: designing quality into products and processes, 1986.
Tan, C. & Pedersen, C. N. S., "Financial time series forecasting using improved wavelet neural network," Aarhus Universitet, Datalogisk Institut, 2009.
Tay, F. E. H. & Cao, L., "Application of support vector machines in financial time series forecasting," Omega, vol. 29, no. 4, pp. 309-317, 2001.
Tay, F. E. H. & Cao, L. J., "Modified support vector machines in financial time series forecasting," Neurocomputing, vol. 48, no. 1–4, pp. 847-861, 2002.
Thissen, U., van Brakel, R., de Weijer, A. P., Melssen, W. J., & Buydens, L. M. C., "Using support vector machines for time series prediction," Chemometrics and Intelligent Laboratory Systems, vol. 69, no. 1–2, pp. 35-49, 2003.
Tiwari, M. K. & Chatterjee, C., "Development of an accurate and reliable hourly flood forecasting model using wavelet–bootstrap–ANN (WBANN) hybrid approach," Journal of Hydrology, vol. 394, no. 3–4, pp. 458-470, 2010.
Tu, Yi-Hsien, Hsien-Lun, W., & Chi-Chen, W., "An Evaluation of Comparison between Multivariate Fuzzy Time Series with Traditional Time Series Model for Forecasting Taiwan Export," in Computer Science and Information Engineering, 2009 WRI World Congress on, 2009, pp. 462-467.

van der Merwe, D. W. & Engelbrecht, A. P., "Data clustering using particle swarm optimization," in Evolutionary Computation, 2003. CEC '03. The 2003 Congress on, 2003, pp. 215-220 Vol.1.
Wang, C.-C., "A comparison study between fuzzy time series model and ARIMA model for forecasting Taiwan export," Expert Systems with Applications, vol. 38, no. 8, pp. 9296-9304, 2011.
Wang, J., Li, L., Niu, D., & Tan, Z., "An annual load forecasting model based on support vector regression with differential evolution algorithm," Applied Energy, vol. 94, no. 0, pp. 65-70, 2012.
Wang, Y.-W., Liu, C.-H., & Fan, C.-Y., "The Hybrid Model Development of Clustering and Back Propagation Network in Printed Circuit Board Sales Forecasting," in Opportunities and Challenges for Next-Generation Applied Intelligence. vol. 214, B.-C. Chien and T.-P. Hong, Eds., ed: Springer Berlin Heidelberg, 2009, pp. 213-218.
Wong, H.-L., Tu, Y.-H., & Wang, C.-C., "Application of fuzzy time series models for forecasting the amount of Taiwan export," Expert Systems with Applications, vol. 37, no. 2, pp. 1465-1470, 2010.
Wu, Q., "The forecasting model based on wavelet ν-support vector machine," Expert Systems with Applications, vol. 36, no. 4, pp. 7604-7610, 2009.
Wu, Q., "Product demand forecasts using wavelet kernel support vector machine and particle swarm optimization in manufacture system," Journal of Computational and Applied Mathematics, vol. 233, no. 10, pp. 2481-2491, 2010.
Xiong, T., Bao, Y., & Hu, Z., "Multiple-output support vector regression with a firefly algorithm for interval-valued stock price index forecasting," Knowledge-Based Systems, vol. 55, no. 0, pp. 87-100, 2014.
Yan, X. & Chowdhury, N. A., "Mid-term electricity market clearing price forecasting utilizing hybrid support vector machine and auto-regressive moving average with external input," International Journal of Electrical Power & Energy Systems, vol. 63, no. 0, pp. 64-70, 2014.
Yang, X.-S., "Firefly Algorithms for Multimodal Optimization," in Stochastic Algorithms: Foundations and Applications. vol. 5792, O. Watanabe and T. Zeugmann, Eds., ed: Springer Berlin Heidelberg, 2009, pp. 169-178.
Yang, X.-S. & He, X., "Firefly algorithm: recent advances and applications," International Journal of Swarm Intelligence, vol. 1, no. 1, pp. 36-50, 2013.
Yeh, C.-Y., Huang, C.-W., & Lee, S.-J., "A multiple-kernel support vector regression approach for stock market price forecasting," Expert Systems with Applications, vol. 38, no. 3, pp. 2177-2186, 2011.
Yi, H., Duan, Q., & Liao, T. W., "Three improved hybrid metaheuristic algorithms for engineering design optimization," Applied Soft Computing, vol. 13, no. 5, pp. 2433-2444, 2013.
Zhang, D., Zhu, H., & Zhang, J., "Forecasting of Customs Export Based on Gray Theory," in Business Intelligence and Financial Engineering, 2009. BIFE '09. International Conference on, 2009, pp. 630-633.
Zhao, M., Tang, H., Guo, J., & Sun, Y., "Data Clustering Using Particle Swarm Optimization," in Future Information Technology, ed: Springer, 2014, pp. 607-612.
Zheng, L., Zhang, Y., Yu, S., Yu, M., & Chen, J., "Use of differential evolution in low NOx combustion optimization of a coal-fired boiler," 2010.
Zou, H. F., Xia, G. P., Yang, F. T., & Wang, H. Y., "An investigation and comparison of artificial neural network and time series models for Chinese food grain price forecasting," Neurocomputing, vol. 70, no. 16–18, pp. 2913-2923, 2007.