Approximation concepts for optimum structural design — a review

Abstract

This paper reviews the basic approximation concepts used in structural optimization. It also discusses some of the most recent developments in that area since the introduction of approximation concepts in the nfid-seventies. The paper distinguishes between local, medium-range and global approximations; it covers function approximations and problem approximations. It shows that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements. The largest number of developments have been in the areas of local function approximations and use of intermediate variable and response quantities. It appears also that some new methodologies emerge which could greatly benefit from the introduction of new computer architectures.

Comparison-Based Optimizers Need Comparison-Based Surrogates

“…Such method, also known as "Response Surface Method", has been used for long in the Numerical Engineering community [2]. Because Evolutionary Algorithms (EAs) require a lot of fitness evaluations, much work has been devoted in the last decade to specifically tune meta-model assisted approaches to EAs (see e.g.…”

Weighted Gradient-Enhanced Kriging for High-Dimensional Surrogate Modeling and Design Optimization

“…= lift, drag, and pitching moment coefficients O VER the past two decades, surrogate-based modeling and optimization have played an increasingly important role in different areas of aerospace engineering [1][2][3][4][5][6][7][8], such as aerodynamic design optimization [9,10], structural optimization [11], and multidisciplinary design optimization of aircraft or spacecraft [12], where high-fidelity and expensive numerical simulations, such as computational fluid dynamics (CFD) or computational solid dynamics (CSD), are often employed. Surrogate model is also called "response surface model", "metamodel", "approximation model", or "emulator" by the literature in different research areas.…”

Improving Local Convergence in Particle Swarms by Fitness Approximation Using Regression

“…The most obvious feature of Fig. 11.14 is that outside the range α d ∈ [1,2] there is a large increase in offline error.…”

“…Unless otherwise stated, all Moving Peaks parameters are set as specified by scenario 2; please refer to Table 11.2 for details 1 .…”

“…For example, in aerodynamic structure optimization, since simulations for computational fluid dynamics are usually very expensive, approximate models were developed [1,16]. Fitness approximation was also used in conjunction with an evolutionary algorithm for protein structure prediction to cut down the computational cost [27].…”