A New Hybrid Method for Parameter Optimization of SVR
Jiang Xie*, Taifeng Sun*, Jieyu Zhang**, and Wu Zhang*
*School of Computer Engineering and Science, Shanghai University
No.99, Shangda Road, Shanghai 200444, China
**School of Material Science and Engineering, Shanghai University
No.99, Shangda Road, Shanghai 200444, China
The performance of Support Vector Regression (SVR) depends heavily on its parameters, but some optimization methods based on Grid Search (GS) or evolutionary algorithms still have several issues that must be addressed. This paper proposes a new hybrid method (PSO-SS) that combines Particle Swarm Optimization (PSO) and Scatter Search (SS) to optimize the parameters of the SVR. In PSO-SS, to improve the search capability of PSO and reduce the likelihood of the PSO becoming trapped in the local optimum, the initial PSO population is generated by the diversification generation method and the improvement method of SS, and the velocity updating formula of PSO is improved by adding diversity information. On the StatLib and UCI datasets, our experiments show that the PSO-SS method is an effective parameter optimization method compared with other methods. In addition, an SVR model with its parameters optimized by PSO-SS (PSO-SS-SVR) is used to predict the grain size of aluminum alloys. The experimental results show that the PSO-SS-SVR method outperforms Back Propagation Neural Network (BPNN), PSO-SVR and the empirical model.
-  M. A. Easton, M. Qian, A. Prasad, and D. H. StJohn, “Recent Advances in Grain Refinement of Light Metals and Alloys,” Current Opinion in Solid State & Materials Science, Vol.20, No.1, pp. 13-24, 2016.
-  S. Lin, C. Aliravci, and M. O. Pekguleryuz, “Hot-Tear Susceptibility of Aluminum Wrought Alloys and the Effect of Grain Refining,” Metall. Mater. Trans. A, Vol.38, No.5, pp. 1056-1068, 2007.
-  M. A. Easton and D. H. StJohn, “The Effect of Grain Refinement on the Formation of Casting Defects in Alloy 356 Castings,” lnt. J. Cast Metals Res., Vol.12, No.6, pp. 393-408, 2000.
-  Z. Fan, Y. Wang, Y. Zhang, T. Qin, X. R. Zhou, G. E. Thompson, T. Pennycook, and T. Hashimoto, “Grain Refining Mechanism in the Al/Al–Ti–B System,” Acta Mater., Vol.84, pp. 292-304, 2015.
-  M. Easton and D. StJohn, “An Analysis of the Relationship Between Grain Size, Solute Content, and the Potency and Number Density of Nucleant Particles,” Metall. Mater. Trans. A, Vol.36, No.7, pp. 1911-1920, 2005.
-  M. Easton and D. StJohn, “Improved Prediction of the Grain Size of Aluminum Alloys that Includes the Effect of Cooling Rate,” Mater. Sci. Eng. A, Vol.486, No.1, pp. 8-13, 2008.
-  M. Qian, P. Cao, M. A. Easton, S. D. McDonald, and D. H. StJohn, “An Analytical Model for Constitutional Supercooling-Driven Grain Formation and Grain Size Prediction,” Acta Mater., Vol.58, No.9, pp. 3262-3270, 2010.
-  D. H. StJohn, M. Qian, M. Easton, and P. Cao, “The Interdependence Theory: The Relationship Between Grain Formation and Nucleant Selection,” Acta Mater., Vol.59, No.12, pp. 4907-4921, 2011.
-  M. Haghdadi, A. Zarei-Hanzaki, A. R. Khalesian, and H. R. Abedi, “Artificial Neural Network Modeling to Predict the Hot Deformation Behavior of an A356 Aluminum Alloy,” Materials & Design, Vol.49, pp. 386-391, 2013.
-  H. G. Ramos, T. Rocha, J. Král, D. Pasadas, and A. L. Ribeiro, “An SVM Approach with Electromagnetic Methods to Assess Metal Plate Thickness,” Measurement, Vol.54, No.8, pp. 201-206, 2014.
-  I. Ghosh, S. K. Das, and N. Chakraborty, “An Artificial Neural Network Model to Characterize Porosity Defects During Solidification of A356 Aluminum Alloy,” Neural Computing & Applications, Vol.25, No.3, pp. 653-662, 2014.
-  N. S. Reddy, A. K. P. Rao, M. Chakraborty, and B. S. Murty, “Prediction of Grain Size of Al–7Si Alloy by Neural Network,” Mater. Sci. Eng. A, Vol.391, pp. 131-140, 2005.
-  H. Pouraliakbar, S. Firooz, M. R. Jandaghi, G. Khalaj, and A. Nazari, “Predicting the Ultimate Grain Size of Aluminum Sheets Undergone Constrained Groove Pressing,” Int. J. Adv. Manuf. Technol., Vol.86, pp. 1639-1658, 2016.
-  M. Buscema, “Back Propagation Neural Networks,” Substance Use & Misuse, Vol.33, No.2, pp. 233-270, 1998.
-  T. Kurita, “Support Vector Machine and Generalization,” J. Adv. Comput. Intell. Intell. Inform., Vol.8, No.2, pp. 84-92, 2004.
-  X. Zhang, D. Qiu, and F. Chen, “Support Vector Machine with Parameter Optimization by a Novel Hybrid Method and its Application to Fault Diagnosis,” Neurocomputing, Vol.149, pp. 641-651, 2015.
-  F. Kang and J. Li, “Artificial Bee Colony Algorithm Optimized Support Vector Regression for System Reliability Analysis of Slopes,” J. Comput. Civ. Eng., Vol.30, No.3, p. 04015040, 2016.
-  Z. Zhu, J. Peng, Z. Zhou, X. Zhang, and Z. Huang, “PSO-SVR-Based Resource Demand Prediction in Cloud Computing,” J. Adv. Comput. Intell. Intell. Inform., Vol.20, No.2, pp. 324-331, 2016.
-  Y. Yu, Y. Li, and J. Li, “Forecasting Hysteresis Behaviours of Magnetorheological Elastomer Base Isolator Utilizing a Hybrid Model Based on Support Vector Regression and Improved Particle Swarm Optimization,” Smart Mater. Struct., Vol.24, No.3, p. 035025, 2015.
-  Y. Yu, Y. Li, J. Li, and X. Gu, “Self-Adaptive Step Fruit Fly Algorithm Optimized Support Vector Regression Model for Dynamic Response Prediction of Magnetorheological Elastomer Base Isolator,” Neurocomputing, Vol.211, pp. 41-52, 2016.
-  H. R. Ansari and A. Gholami, “An Improved Support Vector Regression Model for Estimation of Saturation Pressure of Crude Oils,” Fluid Phase Equilibria, Vol.402, No.3, pp. 124-132, 2015.
-  D. Novitasari, I. Cholissodin, and W. F. Mahmudy, “Hybridizing PSO with SA for Optimizing SVR Applied to Software Effort Estimation,” Telkomnika, Vol.14, No.1, pp. 245-253, 2016.
-  Y. Bao, Z. Hu, and T. Xiong, “A PSO and Pattern Search based Memetic Algorithm for SVMs Parameters Optimization,” Neurocomputing, Vol.117, No.14, pp. 98-106, 2013.
-  J. Zhang, W. Chen, P. Sun, X. Zhao, and Z. Ma, “Prediction of Protein Solvent Accessibility Using PSO-SVR with Multiple Sequence-Derived Features and Weighted Sliding Window Scheme,” BioData Mining, Vol.8, No.1, p. 3, 2015.
-  W. Hu, L. Yan, K. Liu, and H. Wang, “A Short-Term Traffic Flow Forecasting Method Based on the Hybrid PSO-SVR,” Neural Process Lett, Vol.43, No.1, pp. 155-172, 2016.
-  M. Hasanipanah, A. Shahnazar, H. B. Amnieh, and D. J. Armaghani, “Prediction of Air-Overpressure Caused by Mine Blasting Using a New Hybrid PSO–SVR Model,” Engineering with Computers, Vol.33, pp. 23-31, 2017.
-  M. Rafael, M. Lagunab, and F. Gloverb, “Principles of Scatter Search,” European J. of Operational Research, Vol.169, No.2, pp. 359-372, 2006.
-  L. Manuel and M. Rafael, “Scatter Search,” Search Methodologies, Springer US, pp. 119-141, 2014.
-  J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” IEEE Int. Conf. on Neural Networks, pp. 1942-1948, 2002.
-  J. C. Geng, Z. Cui, and X. S. Gu, “Scatter Search Based Particle Swarm Optimization Algorithm for Earliness/Tardiness Flowshop Scheduling with Uncertainty,” Int. J. of Automation and Computing, Vol.13, No.3, pp. 285-295, 2016.
-  M. A. González, C. R. Vela, and R. Varela, “Scatter Search with Path Relinking for the Flexible Job Shop Scheduling Poblem,” European J. of Operational Research, Vol.245, No.1, pp. 35-45, 2015.
-  M. Momma and K. P. Bennett, “A Pattern Search Method for Model Selection of Support Vector Regression,” Proc. of the 2002 SIAM Int. Conf. on Data Mining, pp. 261-274, 2002.
-  J. D. Rodriguez, A. Perez, and J. A. Lozano, “Sensitivity Analysis of k-Fold Cross Validation in Prediction Error Estimation,” IEEE Trans. on Pattern Analysis & Machine Intelligence, Vol.32, No.3, pp. 569-575, 2010.
-  E. G. Ortiz-García, S. Salcedo-Sanz, A. M. Pérez-Bellido, and J. A. Portilla-Figueras, “Improving the Training Time of Support Vector Regression Algorithms Through Novel Hyper-Parameters Search Space Reductions,” Neurocomputing, Vol.72, No.16, pp. 3683-3691, 2009.