With the increasing adoption of complex simulations in engineering design involving finite element analysis (FEA) and computational fluid dynamics (CFD), design optimization problems are increasingly high-dimensional, computationally expensive, and black-box (HEB). In addition, computationally expensive constraints are commonly seen in realworld engineering optimization problems, which pose challenges for existing optimizers. Surrogates, or metamodels, are mathematical functions that are used to approximate computationally expensive models. Use of surrogates in metamodel-based design optimization (MBDO) methods has shown promise in the literature for optimization of expensive and black-box problems. However, current MBDO approaches are often not suitable for high-dimensional problems and often do not support expensive constraints. The goal of this work is to develop surrogate-based methods suitable for efficient single and multi-objective optimization of HEB problems with expensive inequality constraints.

This work integrated the concept of trust regions with the Mode Pursuing Sampling (MPS) MBDO method to create the Trust Region-based MPS (TRMPS) optimizer, which dramatically improved performance and efficiency for single-objective high-dimensional problems with inexpensive constraints. To address expensive constraints, an adaptive aggregation-based constraint handling strategy is proposed by hybridizing a function aggregation method with surrogate modeling. The strategy, called the Situational Adaptive Kreisselmeier and Steinhauser (SAKS) method, formed the basis for two new optimizers for solving single and multi-objective HEB problems with expensive constraints. The new methods, called SAKS-Trust Region Optimizer (SAKS-TRO) and SAKS-Multiobjective Trust Region Optimizer (SAKS-MTRO), demonstrated significant performance improvement when benchmarked against other optimizers. SAKS-TRO and SAKS-MTRO were successfully applied to two real engineering design applications:​ multi-objective optimization of a semiconductor substrate, and single and multi-objective optimization of a recessed impeller for slurry pumps.