Modification of DIRECT for high-dimensional design problems

Engineering Optimization

Wang

et al. 2014

This article presents a global optimization algorithm via the extension of the DIviding RECTangles (DIRECT) scheme to handle problems with computationally expensive simulations efficiently. The new optimization strategy improves the regular partition scheme of DIRECT to a flexible irregular partition scheme in order to utilize information from irregular points. The metamodelling technique is introduced to work with the flexible partition scheme to speed up the convergence, which is meaningful for simulation-based problems. Comparative results on eight representative benchmark problems and an engineering application with some existing global optimization algorithms indicate that the proposed global optimization strategy is promising for simulation-based problems in terms of efficiency and accuracy.

Section: Introductionmentioning

confidence: 99%

A global optimization algorithm for simulation-based problems via the extended DIRECT scheme

Engineering Optimization

Wang

et al. 2014

“…In our further work, we will improve the optimization framework by using some new techniques (Shan and Wang 2010a;Tavassoli et al 2014) to enhance the performance of eDIRECT-C in high dimensions.…”

Section: Discussionmentioning

confidence: 99%

“…To handle high-dimensional cases, which will be our future work, both the optimization framework and metamodeling techniques should be improved, like (Shan and Wang 2010a;Tavassoli et al 2014;Cheng et al 2015). For efficiently handling constrained problems, the proposed eDIRECT-C algorithm has two main parts, i.e., the DIRECTtype constraint-handling technique and the adaptive metamodeling strategy.…”

Section: Group 3: High-dimensional Constrained Casesmentioning

confidence: 99%

Constrained global optimization via a DIRECT-type constraint-handling technique and an adaptive metamodeling strategy

Chen

et al. 2016

Struct Multidisc Optim

Recent metamodel-based global optimization algorithms are very promising for box-constrained expensive optimization problems. However, few of them can tackle constrained optimization problems. This article presents an improved constrained optimization algorithm, called eDIRECT-C, for expensive constrained optimization problems. In the eDIRECT-C algorithm, we present a novel DIRECT-type constraint-handling technique that separately handles feasible and infeasible cells. This technique has no user-defined parameter and is beneficial for exploring the undetected feasible regions and boundary of feasible regions. We also employ an adaptive metamodeling strategy to build appropriate metamodel types for objective and constraints respectively. This strategy yields more accurate predictions and therefore significantly speeds up the convergence. To assess the performance of eDIRECT-C, we compare it with some state-of-the-art metamodel-based constrained optimization algorithms and the original DIRECT algorithm on 13 benchmark problems and 4 engineering examples. The comparative results imply that the proposed algorithm is very promising for constrained problems in terms of the convergence speed, quality of final solutions and success rate.

“…The parameter θ largely affects the accuracy of a Kriging model . It can be determined with maximum likelihood estimation that is performed by solving the following optimization problem:

{bold-italicθ}^{*} = \arg \min_{bold-italicθ} ((), {(||, bold-italicR ((), bold-italicθ))}^{\frac{1}{m}} σ^{2}) .

In this paper, Equation is solved by a global optimization strategy, and the modified DIRECT algorithm is adopted.…”

Section: Active Learning Kriging Model Combining With Random‐set Basementioning

confidence: 99%

Unified reliability analysis by active learning Kriging model combining with random‐set based Monte Carlo simulation method

Yuan

Numerical Meth Engineering

Gao

2016

Summary Reliability analysis with both aleatory and epistemic uncertainties is investigated in this paper. The aleatory uncertainties are described with random variables, and epistemic uncertainties are tackled with evidence theory. To estimate the bounds of failure probability, several methods have been proposed. However, the existing methods suffer the dimensionality challenge of epistemic variables. To get rid of this challenge, a so‐called random‐set based Monte Carlo simulation (RS‐MCS) method derived from the theory of random sets is offered. Nevertheless, RS‐MCS is also computational expensive. So an active learning Kriging (ALK) model that only rightly predicts the sign of performance function is introduced and closely integrated with RS‐MCS. The proposed method is termed as ALK‐RS‐MCS. ALK‐RS‐MCS accurately predicts the bounds of failure probability using as few function calls as possible. Moreover, in ALK‐RS‐MCS, an optimization method based on Karush–Kuhn–Tucker conditions is proposed to make the estimation of failure probability interval more efficient based on the Kriging model. The efficiency and accuracy of the proposed approach are demonstrated with four examples. Copyright © 2016 John Wiley & Sons, Ltd.