An active subspace method for accelerating convergence in Delaunay-based optimization via dimension reduction

Zhao, Muhan; Alimo, Shahrouz Ryan; Bewley, Thomas

doi:10.1109/cdc.2018.8619219

Cited by 7 publications

(6 citation statements)

References 14 publications

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“…This algorithm is called optimization by moving ridge functions (OMoRF), as it leverages local ridge function approximations that move through the function domain. Although other optimization algorithms have used subspaces to reduce the problem dimension (Wang et al 2016;Zhao, Alimo, and Bewley 2018;Kozak et al 2019), OMoRF differs from these in some key aspects. First, it is completely derivative-free.…”

Section: Introductionmentioning

confidence: 99%

“…Although the VRSSD algorithm does not require full gradient calculations, it still requires directional derivatives to be computed. Similarly, the Delaunay-based derivative-free optimization via global surrogates with active subspace method ( -DOGS with ASM) proposed by Zhao, Alimo, and Bewley (2018) requires an initial sample of gradient evaluations to determine the dimensionreducing subspace. Second, the subspaces computed by OMoRF correspond to the directions of strongest variability of the objective function.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, OMoRF does not assume a global dimension-reducing subspace. Many similar algorithms that use ridge functions for optimization purposes (Lukaczyk et al 2014;Zhao, Alimo, and Bewley 2018;Gross, Seshadri, and Parks 2020) assume that the function f varies primarily along a constant linear subspace U throughout the entire domain D. This assumption may limit the application of ridge functions to a few special cases. Although adaptive sampling approaches have been applied previously for stochastic optimization with active subspaces (Choromanski et al 2019), to the best of the authors' knowledge, OMoRF is the first model-based optimization algorithm to propose the use of local ridge functions.…”

Section: Introductionmentioning

confidence: 99%

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Optimization by moving ridge functions: derivative-free optimization for computationally intensive functions

Gross

Parks

2021

Engineering Optimization

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A novel derivative-free algorithm, called optimization by moving ridge functions (OMoRF), for unconstrained and bound-constrained optimization is presented. This algorithm couples trust region methodologies with output-based dimension reduction to accelerate convergence of model-based optimization strategies. The dimension-reducing subspace is updated as the trust region moves through the function domain, allowing OMoRF to be applied to functions with no known global low-dimensional structure. Furthermore, its low computational requirement allows it to make rapid progress when optimizing high-dimensional functions. Its performance is examined on a set of test problems of moderate to high dimension and a high-dimensional design optimization problem. The results show that OMoRF compares favourably with other common derivative-free optimization methods, even for functions in which no underlying global low-dimensional structure is known.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimization by moving ridge functions: derivative-free optimization for computationally intensive functions

Gross

Parks

2021

Engineering Optimization

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“…9 However, their use in optimisation has been rather limited. 4,10,11 Given the opportunities these ridge function approximations afford, a closer examination of ridge functions in the context of optimisation is necessary.…”

Section: Introductionmentioning

confidence: 99%

“…Although their research was focused on using ridge functions for preliminary design optimisation studies, they did not address the possibility of using such ridge approximations for greater refinement during optimisation. Zhao et al 10 demonstrated that such optimisation refinement studies were possible by using ridge function surrogates in a Delaunay-based optimisation via global surrogates (∆-DOGS) method. This approach sought to approximately solve the bound-constrained optimisation problem…”

Section: Introductionmentioning

confidence: 99%

Optimisation with Intrinsic Dimension Reduction: A Ridge Informed Trust-Region Method

Gross

Seshadri

Parks

2020

AIAA Scitech 2020 Forum

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High-dimensional design optimisation continues to present many challenges for engineers. Traditional model-based optimisation strategies can be difficult to implement for high-dimensional problems, as surrogate models often require sample sizes which are exponential in the number in number of variables. In this paper, we present an algorithm which combines ideas from ridge function approximations and trust-region methods to perform optimisation on high-dimensional functions with underlying low-dimensional structure. This approach allows us to efficiently explore the design space by focusing on the few directions in which the objective varies the most. By slowly increasing the problem dimension, this algorithm also can further explore regions of interest in detail. This allows for more accurate solutions than previous approaches which have used ridge functions during optimisation. We test this algorithm against a number of common model-based optimisation methods, and it is shown to be effective for a class of high-dimensional problems. In particular, we apply the method to a NACA 0012 aerofoil to obtain an optimal design with respect to drag. During this study, we demonstrate how ridge functions can be vital tools for design space exploration, and, with our algorithm, how they can be used for optimisation refinement.

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A derivative-free optimization algorithm for the efficient minimization of functions obtained via statistical averaging

2020

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This paper considers the efficient minimization of the infinite time average of a stationary ergodic process in the space of a handful of design parameters which affect it. Problems of this class, derived from physical or numerical experiments which are sometimes expensive to perform, are ubiquitous in engineering applications. In such problems, any given function evaluation, determined with finite sampling, is associated with a quantifiable amount of uncertainty, which may be reduced via additional sampling. The present paper proposes a new optimization algorithm to adjust the amount of sampling associated with each function evaluation, making function evaluations more accurate (and, thus, more expensive), as required, as convergence is approached. The work builds on our algorithm for Delaunay-based Derivative-free Optimization via Global Surrogates (∆-DOGS, see JOGO

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An active subspace method for accelerating convergence in Delaunay-based optimization via dimension reduction

Cited by 7 publications

References 14 publications

Optimization by moving ridge functions: derivative-free optimization for computationally intensive functions

Optimization by moving ridge functions: derivative-free optimization for computationally intensive functions

Optimisation with Intrinsic Dimension Reduction: A Ridge Informed Trust-Region Method

A derivative-free optimization algorithm for the efficient minimization of functions obtained via statistical averaging

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