An Adaptive Aggregation-Based Approach for Expensively Constrained Black-Box Optimization Problems

Abstract

Expensive constraints are commonly seen in real-world engineering design. However, metamodel based design optimization (MBDO) approaches often assume inexpensive constraints. In this work, the situational adaptive Kreisselmeier and Steinhauser (SAKS) method was employed in the development of a hybrid adaptive aggregation-based constraint handling strategy for expensive black-box constraint functions. The SAKS method is a novel approach that hybridizes the modeling and aggregation of expensive constraints and adds an adaptive strategy to control the level of hybridization. The SAKS strategy was integrated with a modified trust region-based mode pursuing sampling (TRMPS) algorithm to form the SAKS-trust region optimizer (SAKS-TRO) for single-objective design optimization problems with expensive black-box objective and constraint functions. SAKS-TRO was benchmarked against five popular constrained optimizers and demonstrated superior performance on average. SAKS-TRO was also applied to optimize the design of an industrial recessed impeller.

Metamodel-based multidisciplinary design optimization methods for aerospace system

“…Shan and Wang proposed a Pareto set pursing method for multi-objective optimization problems by aggregating multiple objectives into a single fitness function that reflects the dominance of sample points [84]. Other variants have also been developed for high-dimensional expensive black-box optimization problems [81,85] or high-dimensional expensive constrained black-box optimization problems [86].…”

“…To further solve problems with numerous constraints, the constraint aggregation method, which lumps numerous constraints into one or a few constraints to significantly reduce the computational cost, has drawn considerable interest in recent years. The Kreisselmeier-Steinhauser function [173] is a well-known constraint aggregation method that has been used in various applications [86,174,175]. Moreover, based on Refs.…”

Constrained optimization in simulation: efficient global optimization and Karush-Kuhn-Tucker conditions

“…Bagheri et al (2017a) investigates aerodynamic shape design, focusing on subsonic airfoil section design. Cheng et al (2018) mentions that engineering often uses deterministic simulations such as FEA and computational ‡uid dynamics (CFD) for product and process design, and details the design of an industrial recessed impeller for use in slurry pumping applications. Durantin et al (2016) discusses a rocket motor design.…”

An effective parameter optimization with radiation balance constraint in CAM5 (version 5.3)

“…The observations of LWCF and SWCF are from CERES-EBAF (Clouds and the Earth's Radiant Energy System-Energy Balanced and Filled; Loeb et al, 2014). PRECT is from GPCP (Global Precipitation Climatology Project; Adler et al, 2003), and Q850 and T850 are from ERA-Interim, which was produced by the ECMWF (Dee et al, 2011).…”

“…However, the constrained optimization methods used to calibrate parameters with physical constraints in climate models remain to be further studied. Cheng et al (2018) showed that penalty functions and the separation of objective and constraint methods are popular for solving constrained problems. Penalty methods encourage the search toward feasible regions by increasing the objective function value with a penalty value for the points that violate the constraints.…”