Multi-Objective Optimization for High-Dimensional Expensively Constrained Black-Box Problems

Multi-objective optimization (MOO) problems with computationally expensive constraints are commonly seen in real-world engineering design. However, metamodel-based design optimization (MBDO) approaches for MOO are often not suitable for high-dimensional problems and often do not support expensive constraints. In this work, the situational adaptive Kreisselmeier and Steinhauser (SAKS) method was combined with a new multi-objective trust region optimizer (MTRO) strategy to form the SAKS-MTRO method for MOO problems with expensive black-box constraint functions. The SAKS method is an approach that hybridizes the modeling and aggregation of expensive constraints and adds an adaptive strategy to control the level of hybridization. The MTRO strategy uses a combination of objective decomposition and K-means clustering to handle MOO problems. SAKS-MTRO was benchmarked against four popular multi-objective optimizers and demonstrated superior performance on average. SAKS-MTRO was also applied to optimize the design of a semiconductor substrate and the design of an industrial recessed impeller.