The least square support vector regression coupled with parallel sampling scheme metamodeling technique and application in sheet forming optimization

The least square support vector regression (LS-SVR) metamodel technique is proposed for sheet metal forming optimization. The major advantage of proposed approach is to build metamodel by consideration of empirical risk minimization (ERM) and structure risk minimization (SRM). In order to construct robust and accurate metamodel based LS-SVR, suitable quantity and intervals of samples are recommended. Thus, a parallel intelligent sampling scheme based on a boundary and best neighbor searching method (BBNS) is proposed to improve the efficiency and accuracy of metamodel. The BBNS was suggested and corresponding practical engineer problems were successfully solved by Hu and Li [Hu W, Li GY, Zhong ZH. Optimization of sheet metal forming processes by adaptive response surface based on intelligent sampling method. J Mater Process Technol 2008;197(1–3):77–88; Hu Wang, Li GY, Li Enying, Zhong ZH. Development of metamodeling based optimization system for high nonlinear engineering problems. Adv Eng Software 2008;39(8)629–45]. To increase the efficiency of metamodel based optimization method, the parallel architecture is implemented for BBNS due to its drawbacks. For validation of developed method, both of serial and parallel BBNS scheme are applied for the nonlinear function. The parallel BBNS is also verified to be an accuracy and efficiency scheme. Finally, the practical nonlinear engineering problems are optimized by suggested methodology and satisfied results are also obtained.