A multivariate normal boundary intersection PCA-based approach to reduce dimensionality in optimization problems for LBM process

Laser beam machining (LBM) is a promising manufacturing process that exhibits several desirable quality characteristics. Given a large number of objective functions, the level of complexity increases in an optimization problem. Therefore, this study presents a multivariate application of the normal boundary intersection (NBI) method to reduce dimensionality in optimization problems of the LBM process. Such an approach is capable of exploring the entire solution space with only a small number of Pareto points, and generating equispaced frontiers based on the objective functions written in terms of principal component scores. Hence, a design of experiment with three input parameters and six quality characteristics was undertaken to appropriately model the process requirements applied to AISI 314S steel. The results indicate that the proposed methodology is capable of achieving optimal values for interest characteristics. In addition, this approach shows a reduction in computational effort of approximately 91.89% (from 259 to 21 subproblems) in obtaining the best solution for rough operation.