TY - JOUR

T1 - Asymptotic Bayesian Optimization

T2 - A Markov sampling-based framework for design optimization

AU - Jerez, D. J.

AU - Jensen, H. A.

AU - Beer, M.

AU - Chen, J.

N1 - Funding Information: The research reported here was supported in part by ANID (National Agency for Research and Development, Chile) under grant number 1200087 . Also, this research has been supported by ANID, Chile and DAAD (German Academic Exchange Service) under CONICYT-PFCHA/ Doctorado Acuerdo Bilateral DAAD Becas Chile/2018-62180007. These supports are gratefully acknowledged by the authors.

PY - 2022/1

Y1 - 2022/1

N2 - This paper presents a Markov sampling-based framework, called Asymptotic Bayesian Optimization, for solving a class of constrained design optimization problems. The optimization problem is converted into a unified two-phase sample generation problem which is solved by an effective Markov chain Monte Carlo simulation scheme. First, an exploration phase generates designs distributed over the feasible design space. Based on this information, an exploitation phase obtains a set of designs lying in the vicinity of the optimal solution set. The proposed formulation can handle continuous, discrete, or mixed discrete-continuous design variables. Appropriate adaptive proposal distributions for the continuous and discrete design variables are suggested. The set of optimal solutions provides valuable sensitivity information of the different quantities involved in the problem with respect to the design variables. Representative examples including an analytical problem involving nonlinear benchmark functions, a classical engineering design problem, and a performance-based design optimization problem of a structural system under stochastic excitation are presented to show the effectiveness and potentiality of the proposed optimization scheme. Validation calculations show that the scheme is a flexible, efficient and competitive choice for solving a wide range of classical and complex engineering design problems.

AB - This paper presents a Markov sampling-based framework, called Asymptotic Bayesian Optimization, for solving a class of constrained design optimization problems. The optimization problem is converted into a unified two-phase sample generation problem which is solved by an effective Markov chain Monte Carlo simulation scheme. First, an exploration phase generates designs distributed over the feasible design space. Based on this information, an exploitation phase obtains a set of designs lying in the vicinity of the optimal solution set. The proposed formulation can handle continuous, discrete, or mixed discrete-continuous design variables. Appropriate adaptive proposal distributions for the continuous and discrete design variables are suggested. The set of optimal solutions provides valuable sensitivity information of the different quantities involved in the problem with respect to the design variables. Representative examples including an analytical problem involving nonlinear benchmark functions, a classical engineering design problem, and a performance-based design optimization problem of a structural system under stochastic excitation are presented to show the effectiveness and potentiality of the proposed optimization scheme. Validation calculations show that the scheme is a flexible, efficient and competitive choice for solving a wide range of classical and complex engineering design problems.

KW - Discrete-continuous optimization

KW - Dynamic systems

KW - Markov sampling method

KW - Metropolis–Hastings algorithm

KW - Performance-based design

KW - Proposal distributions

KW - Stochastic optimization

UR - http://www.scopus.com/inward/record.url?scp=85119177180&partnerID=8YFLogxK

U2 - 10.1016/j.probengmech.2021.103178

DO - 10.1016/j.probengmech.2021.103178

M3 - Article

AN - SCOPUS:85119177180

VL - 67

JO - Probabilistic Engineering Mechanics

JF - Probabilistic Engineering Mechanics

SN - 0266-8920

M1 - 103178

ER -