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 real-world 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.
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Thesis advisor: Wang, Gary
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