https://eprints.soton.ac.uk/65935/01/Forr_09.pdf

Recent advances in surrogate-based optimization

Computation-intensive design problems are becoming increasingly common in manufacturing industries. The computation burden is often caused by expensive analysis and simulation processes in order to reach a comparable level of accuracy as physical testing data. To address such a challenge, approximation or metamodeling techniques are often used. Metamodeling techniques have been developed from many different disciplines including statistics, mathematics, computer science, and various engineering disciplines. These metamodels are initially developed as “surrogates” of the expensive simulation process in order to improve the overall computation efficiency. They are then found to be a valuable tool to support a wide scope of activities in modern engineering design, especially design optimization. This work reviews the state-of-the-art metamodel-based techniques from a practitioner’s perspective according to the role of metamodeling in supporting design optimization, including model approximation, design space exploration, problem formulation, and solving various types of optimization problems. Challenges and future development of metamodeling in support of engineering design is also analyzed and discussed.Copyright © 2006 by ASME

https://www.sfu.ca/~gwa5/index_files/Microsoft%20Word%20-%20ASME-Metamodeling-6-12-06.pdf

Review of Metamodeling Techniques in Support of Engineering Design Optimization

AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation

This paper addresses the solution of bound-constrained optimization problems using algorithms that require only the availability of objective function values but no derivative information. We refer to these algorithms as derivative-free algorithms. Fueled by a growing number of applications in science and engineering, the development of derivative-free optimization algorithms has long been studied, and it has found renewed interest in recent time. Along with many derivative-free algorithms, many software implementations have also appeared. The paper presents a review of derivative-free algorithms, followed by a systematic comparison of 22 related implementations using a test set of 502 problems. The test bed includes convex and nonconvex problems, smooth as well as nonsmooth problems. The algorithms were tested under the same conditions and ranked under several criteria, including their ability to find near-global solutions for nonconvex problems, improve a given starting point, and refine a near-optimal solution. A total of 112,448 problem instances were solved. We find that the ability of all these solvers to obtain good solutions diminishes with increasing problem size. For the problems used in this study, TOMLAB/MULTIMIN, TOMLAB/GLCCLUSTER, MCS and TOMLAB/LGO are better, on average, than other derivative-free solvers in terms of solution quality within 2,500 function evaluations. These global solvers outperform local solvers even for convex problems. Finally, TOMLAB/OQNLP, NEWUOA, and TOMLAB/MULTIMIN show superior performance in terms of refining a near-optimal solution.

/pdf/derivative-free-optimization-a-review-of-algorithms-and-2qmveq3j89.pdf

Derivative-free optimization: a review of algorithms and comparison of software implementations

We review the space-mapping (SM) technique and the SM-based surrogate (modeling) concept and their applications in engineering design optimization. For the first time, we present a mathematical motivation and place SM into the context of classical optimization. The aim of SM is to achieve a satisfactory solution with a minimal number of computationally expensive "fine" model evaluations. SM procedures iteratively update and optimize surrogates based on a fast physically based "coarse" model. Proposed approaches to SM-based optimization include the original algorithm, the Broyden-based aggressive SM algorithm, various trust-region approaches, neural SM, and implicit SM. Parameter extraction is an essential SM subproblem. It is used to align the surrogate (enhanced coarse model) with the fine model. Different approaches to enhance uniqueness are suggested, including the recent gradient parameter-extraction approach. Novel physical illustrations are presented, including the cheese-cutting and wedge-cutting problems. Significant practical applications are reviewed.

https://desi.iteso.mx/erayas/documents/CirOpt_course/Lectures/Space_Mapping/Bandler_04Jan_SM_State_of_the_Art.pdf

Space mapping: the state of the art

DACE - A Matlab Kriging Toolbox

DACE - A Matlab Kriging Toolbox, Version 2.0

Aspects of the Matlab toolbox DACE

We present a significant improvement to the novel implicit space mapping (ISM) concept for EM-based microwave modeling and design. ISM calibrates a suitable coarse (surrogate) model against a fine model (full-wave EM simulation) by relaxing certain coarse model preassigned parameters. Based on an explanation of residual response misalignment, our new approach further fine-tunes the surrogate by exploiting an "output space" mapping (OSM). An accurate design of an HTS filter, easily implemented in Agilent ADS, emerges after only four EM simulations using ISM and OSM with sparse frequency sweeps. For the first time also, frequency space mapping is implemented in an ISM framework.

Jacob Søndergaard

Papers

Space mapping: the state of the art

DACE - A Matlab Kriging Toolbox

DACE - A Matlab Kriging Toolbox, Version 2.0

Aspects of the Matlab toolbox DACE

EM-based surrogate modeling and design exploiting implicit, frequency and output space mappings