Abstract
Methods based on Gaussian stochastic process (GSP) models and expected improvement (EI) functions have been promising for box-constrained expensive optimization problems. These include robust design problems with environmental variables having set-type constraints. However, the methods that combine GSP and EI sub-optimizations suffer from the following problem, which limits their computational performance. Efficient global optimization (EGO) methods often repeat the same or nearly the same experimental points. We present a novel EGO-type constraint-handling method that maintains a so-called tabu list to avoid past points. Our method includes two types of penalties for the key “infill” optimization, which selects the next test runs. We benchmark our tabu EGO algorithm with five alternative approaches, including DIRECT methods using nine test problems and two engineering examples. The engineering examples are based on additive manufacturing process parameter optimization informed using point-based thermal simulations and robust-type quality constraints. Our test problems span unconstrained, simply constrained, and robust constrained problems. The comparative results imply that tabu EGO offers very promising computational performance for all types of black-box optimization in terms of convergence speed and the quality of the final solution.
Highlights
Engineering design optimization problems often involve expensive black-box functions such as finite element methods (FEM), computational fluid dynamics (CFD), or thermal simulations based on Green’s functions
In the same direction as the results presented by Viana et al (2013), we found that by using tabu efficient global optimization (EGO) with a penalty added in expected improvement function, a reduction in the dispersion of the results can be achieved as long as the optimization cycles evolve
We propose the incorporation of tabu list penalties in infill optimization to improve the computational performance of EGO methods for a variety of black-box optimization problems
Summary
Engineering design optimization problems often involve expensive black-box functions such as finite element methods (FEM), computational fluid dynamics (CFD), or thermal simulations based on Green’s functions. The method for performing infill optimizations using the inexpensive GSP meta-models is generally not a major concern in the context of the EGO method because the computational overhead often has less importance than the costs of the expensive black-box runs. Many types of non-linear programming approaches can be applied, including DIRECT methods (Jones 2009a; Liu et al 2017), constraint importance mode-pursuing sampling for continuous global optimization (CIMPS, Kazemi et al 2010), and constrained local metric stochastic radial-based function (ConstrLMSRBF, Regis 2011) methods. The motivating application for this work is the optimal design of additive manufacturing process parameters informed by point-based thermal simulations (Frazier 2014; Schwalbach et al 2019) These thermal simulation outputs derive from a sum over Green’s function evaluations evaluated at discrete points in a physical twodimensional layer (Schwalbach et al 2019).
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