Robust parameter optimization based on multivariate normal boundary intersection

• A Multiobjective Robust Parameter Design (MRPD) problem is considered.
• Several methods from the literature are researched to solve the MRPD problem.
• A new multivariate Normal Boundary Intersection (NBI) method is proposed.
• Comparative studies indicate the relevance of the new method.
• A case study on end milling process with combined arrays illustrates the method.

Normal Boundary Intersection (NBI) is traditionally used to generate equally spaced and uniformly spread Pareto Frontiers for multi-objective optimization programming (MOP). This method tends to fail, however, when correlated objective functions must be optimized using Robust Parameter Designs (RPD). In such multi-objective optimization programming, there can be reached impractical optima and non-convex frontiers. To reverse this shortcoming, it is common to apply Principal Component Analysis (PCA), which provides uncorrelated objective functions. The aim of this paper is to combine the Robust Parameter Designs, Principal Component Analysis, and Normal Boundary Intersection approaches into a novel method called RPD-MNBI. This approach finds equally spaced Pareto optimal frontiers that are capable of minimizing noise variables’ effects. To validate this proposal, this study investigates an end milling process. The most important empirical finding is that the original correlation structure is preserved. On the other hand, the Weighted Sums and Normal Boundary Intersection-Mean Square Error methods, modify the process behavior, resulting in unreal optima. Finally, confirmation runs using an L9 Taguchi design were performed for 10%, 50%, and 90% weights. The proposed method provides process robustness according to confidence intervals for both mean and standard deviation.