Optimum selection of cutting conditions in high-speed and ultra-precision machining processes often poses a challenging task due to several reasons; such as the need for costly experimental setup and the limitation on the number of experiments that can be performed before tool degradation starts becoming a source of noise in the readings. Moreover, oftentimes there are several objectives to consider, some of which may be conflicting, while others may be somewhat correlated. Pareto-optimality analysis is needed for conflicting objectives; however the existence of several objectives (high-dimension Pareto space) makes the generation and interpretation of Pareto solutions difficult. The approach adopted in this paper is a modified multi-objective efficient global optimization (m-EGO). In m-EGO, sample data points from experiments are used to construct Kriging meta-models, which act as predictors for the performance objectives. Evolutionary multi-objective optimization is then conducted to spread a population of new candidate experiments towards the zones of search space that are predicted by the Kriging models to have favorable performance, as well as zones that are under-explored. New experiments are then used to update the Kriging models, and the process is repeated until termination criteria are met. Handling a large number of objectives is improved via a special selection operator based on principle component analysis (PCA) within the evolutionary optimization. PCA is used to automatically detect correlations among objectives and perform the selection within a reduced space in order to achieve a better distribution of experimental sample points on the Pareto frontier. Case studies show favorable results in ultra-precision diamond turning of Aluminum alloy as well as high-speed drilling of woven composites.
Multi-Fidelity Multi-Objective Efficient Global Optimization Applied to Airfoil Design Problems