A Python surrogate modeling framework with derivatives

Bouhlel, Mohamed Amine; Hwang, John T.; Bartoli, Nathalie; Lafage, Rémi; Morlier, Joseph; Martins, Joaquim R. R. A.

doi:10.1016/j.advengsoft.2019.03.005

Cited by 278 publications

(145 citation statements)

References 31 publications

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“…We use MOE with KPLS(+K) surrogate models as the experts and implemented these methods in the Surrogate Modeling Toolbox [61]. MOE relies on the expectation-maximization algorithm for Gaussian mixture models [62].…”

Section: Mixture Of Expertsmentioning

confidence: 99%

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Adaptive modeling strategy for constrained global optimization with application to aerodynamic wing design

Bartoli

Lefèbvre

Dubreuil

et al. 2019

Aerospace Science and Technology

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Surrogate models are often used to reduce the cost of design optimization problems that involve computationally costly models, such as computational fluid dynamics simulations. However, the number of evaluations required by surrogate models usually scales poorly with the number of design variables, and there is a need for both better constraint formulations and multimodal function handling. To address this issue, we developed a surrogate-based gradient-free optimization algorithm that can handle cases where the function evaluations are expensive, the computational budget is limited, the functions are multimodal, and the optimization problem includes nonlinear equality or inequality constraints. The proposed algorithm-super efficient global optimization coupled with mixture of experts (SEGOMOE)can tackle complex constrained design optimization problems through the use of an enrichment strategy based on a mixture of experts coupled with adaptive surrogate models. The performance of this approach was evaluated for analytic constrained and unconstrained problems, as well as for a multimodal aerodynamic shape optimization problem with 17 design variables and an equality constraint. Our results showed that the method is efficient and that the optimum is much less dependent on the starting point than the conventional gradient-based optimization.

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Section: Mixture Of Expertsmentioning

confidence: 99%

“…As a consequence, in the following, the SEGOMOE framework is used with the automatic cluster number approach already presented by Bartoli et al [49]. The algorithm is implemented within the NASA OpenMDAO framework [64] and, additionally, can use surrogates available within the Surrogate Modeling Toolbox [61].…”

Section: The Segomoe Algorithmmentioning

confidence: 99%

Adaptive modeling strategy for constrained global optimization with application to aerodynamic wing design

Bartoli

Lefèbvre

Dubreuil

et al. 2019

Aerospace Science and Technology

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“…M represents the number of training data patterns, which can be determined from the sample size formula with a finite population correction factor. The framework of RMTS is displayed in Figure 1 [21] and the general model of RMTS can be stated formally as below.…”

Section: Metamodel Constructionmentioning

confidence: 99%

“…RMTS solves an energy minimization function where the splines pass through the training points to obtain the coefficients i  of the splines. The energy minimization function (9) comprises three terms, the second derivatives of the splines, regularization and approximation error related to the training points [21].…”

Section: Metamodel Constructionmentioning

confidence: 99%

Coupling Elephant Herding with Ordinal Optimization for Solving the Stochastic Inequality Constrained Optimization Problems

Horng

Lin

2020

Applied Sciences

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The stochastic inequality constrained optimization problems (SICOPs) consider the problems of optimizing an objective function involving stochastic inequality constraints. The SICOPs belong to a category of NP-hard problems in terms of computational complexity. The ordinal optimization (OO) method offers an efficient framework for solving NP-hard problems. Even though the OO method is helpful to solve NP-hard problems, the stochastic inequality constraints will drastically reduce the efficiency and competitiveness. In this paper, a heuristic method coupling elephant herding optimization (EHO) with ordinal optimization (OO), abbreviated as EHOO, is presented to solve the SICOPs with large solution space. The EHOO approach has three parts, which are metamodel construction, diversification and intensification. First, the regularized minimal-energy tensor-product splines is adopted as a metamodel to approximately evaluate fitness of a solution. Next, an improved elephant herding optimization is developed to find N significant solutions from the entire solution space. Finally, an accelerated optimal computing budget allocation is utilized to select a superb solution from the N significant solutions. The EHOO approach is tested on a one-period multi-skill call center for minimizing the staffing cost, which is formulated as a SICOP. Simulation results obtained by the EHOO are compared with three optimization methods. Experimental results demonstrate that the EHOO approach obtains a superb solution of higher quality as well as a higher computational efficiency than three optimization methods.

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“…A Python implementation of multi-fidelity co-kriging based on Le Gratiet's work can be found in the open source Surrogate Modeling Toolbox [18] (SMT). *…”

Section: Kriging and Multi-fidelity Co-kriging Descriptionmentioning

confidence: 99%

Multi-fidelity efficient global optimization: Methodology and application to airfoil shape design

Meliani

Bartoli²,

Lefèbvre³

et al. 2019

AIAA Aviation 2019 Forum

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A Python surrogate modeling framework with derivatives

Cited by 278 publications

References 31 publications

Adaptive modeling strategy for constrained global optimization with application to aerodynamic wing design

Adaptive modeling strategy for constrained global optimization with application to aerodynamic wing design

Coupling Elephant Herding with Ordinal Optimization for Solving the Stochastic Inequality Constrained Optimization Problems

Multi-fidelity efficient global optimization: Methodology and application to airfoil shape design

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