Hybrid kernel principal component regression and penalty strategy of multiple adaptive genetic algorithms for estimating optimum parameters in abrasive waterjet machining

Abstract

The quality of machined surface can be improved by choosing the right values of the associated parameters through an optimization process. Recently, researchers have used nonlinear programming models, soft-computing approaches, and hybrid of them to estimate the surface roughness of abrasive waterjet (AWJ) machining. Some researchers have performed a second order polynomial regression (SOPR) as a basis in developing a nonlinear programming in AWJ machining. Nevertheless, the SOPR was developed without considering the existence of multicollinearity which can lead to inappropriate prediction. Besides, it also needs a specific nonlinear regression model in advance. It will be difficult to specify an appropriate nonlinear model of SOPR since it does not usually involve all combination variables in its model. Instead, kernel principal component regression (KPCR) will be employed to overcome the weaknesses of the SOPR. After development and model selection in the KPCR models, the best KPCR is used as an objective function in a nonlinear programming model of AWJ with a certain set of constraints. Single genetic algorithm (GA) and its variants can be conducted to solve the nonlinear programming problem. However, they can yield different decision values due to randomness of their initial population which implies that the best decision values may not converge in a certain optimum solution. Under this circumstance, multiple adaptive probabilities genetic algorithm (MAPGA) combined with a penalty method to solve the optimization problem is proposed. Hybrid of KPCR and MAPGA gives more stable solution compared to hybrid of KPCR with single genetic algorithm and original adaptive probabilities genetic algorithm. Our proposed technique also provides an optimum solution in reasonable time.