GOSAC: global optimization with surrogate approximation of constraints

Müller, Juliane; Woodbury, J.

doi:10.1007/s10898-017-0496-y

Cited by 34 publications

(21 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Müller and Woodbury (2017) develop a method for addressing computationally inexpensive objectives while satisfying computationally expensive constraints. Their two-phase method first seeks feasibility by solving a multi-objective optimization problem (a problem class that is the subject of Section 8.4) in which the constraint violations are minimized simultaneously; the second phase seeks to reduce the objective subject to constraints derived from cubic RBF models of the constraint functions.…”

Section: Methods For Constrained Optimizationmentioning

confidence: 99%

“…Tröltzsch [2016] uses linear models of the constraint functions and quadratic models of the objective function, with these models replacing c and f in the augmented Lagrangian merit function in (77). Step acceptance uses a merit function (an exact penalty function). Müller and Woodbury [2017] develop a method for addressing computationally inexpensive objectives while satisfying computationally expensive constraints. Their two-phase method first seeks feasibility by solving a multi-objective optimization problem (a problem class that is the subject of Section 8.4) in which the constraint violations are minimized simultaneously; the second phase seeks to reduce the objective subject to constraints derived from cubic RBF models of the constraint functions.…”

Section: Simulation-based Constraintsmentioning

confidence: 99%

See 1 more Smart Citation

Derivative-free optimization methods

2019

View full text Add to dashboard Cite

Dedicated to the memory of Andrew R. Conn for his inspiring enthusiasm and his many contributions to the renaissance of derivative-free optimization methods. AbstractIn many optimization problems arising from scientific, engineering and artificial intelligence applications, objective and constraint functions are available only as the output of a black-box or simulation oracle that does not provide derivative information. Such settings necessitate the use of methods for derivative-free, or zeroth-order, optimization. We provide a review and perspectives on developments in these methods, with an emphasis on highlighting recent developments and on unifying treatment of such problems in the non-linear optimization and machine learning literature. We categorize methods based on assumed properties of the black-box functions, as well as features of the methods. We first overview the primary setting of deterministic methods applied to unconstrained, non-convex optimization problems where the objective function is defined by a deterministic black-box oracle. We then discuss developments in randomized methods, methods that assume some additional structure about the objective (including convexity, separability and general non-smooth compositions), methods for problems where the output of the black-box oracle is stochastic, and methods for handling different types of constraints.

show abstract

Section: Methods For Constrained Optimizationmentioning

confidence: 99%

Section: Simulation-based Constraintsmentioning

confidence: 99%

Derivative-free optimization methods

2019

View full text Add to dashboard Cite

show abstract

“…Durantin et al (2016) discusses a rocket motor design. Müller and Woodbury (2017) discusses the agricultural management of a speci…c watershed to minimize the costs of reducing the phosphorus load to a given threshold by retiring agricultural lands with high nutrient runo¤. Chaiyotha and Krityakierne (2020) compares several EGO-based methods for solving a pressure vessel design optimization problem.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

“…Several more methods are discussed in Bagheri et al (2017b), Cheng et al (2018), Durantin et al (2016), Dzahini et al (2020), Habib et al (2016), Friese et al (2020), Haftka et al (2016), Müller and Woodbury (2017), Parnianifard, et al (2020), Passos et al (2019), Lee (2021), Su et al (2020), and Ungredda and Branke (2021).…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

Constrained optimization in simulation: efficient global optimization and Karush-Kuhn-Tucker conditions

Kleijnen

Nieuwenhuyse²,

Beers³

2021

SSRN Journal

View full text Add to dashboard Cite

“…Interpolation approximation models such as radial basis functions (RBFs; Powell, ) have been used in many optimization algorithms (Müller et al, ; Regis & Shoemaker, , ) and applied to a variety of science problems, for example, watershed management (Müller & Woodbury, ), methane transport in the community land model (Müller et al, ), and the multiobjective design of airfoils (Müller, ). Closely related to using surrogate models for optimization purposes are Gaussian process emulation approaches that have been used to quantify the uncertainty of microphysical parameters (Johnson et al, ; Lee et al, ).…”

Section: Introductionmentioning

confidence: 99%

Optimization of the Eddy‐Diffusivity/Mass‐Flux Shallow Cumulus and Boundary‐Layer Parameterization Using Surrogate Models

Langhans

Mueller

Collins

2019

J Adv Model Earth Syst

Self Cite

View full text Add to dashboard Cite

Physical parameterizations in global atmospheric and ocean models typically include free parameters that are not theoretically or empirically constrained. New methods are required to determine the optimal parameter combinations for such models in an objective, exhaustive, yet computationally feasible manner. Here we propose to apply computationally inexpensive radial basis function (RBF) surrogate models to minimize a "cost," or error, function of an atmospheric model or a physical parameterization. The RBF is iteratively updated as more input-output pairs are obtained during the optimization. The approach is used to optimize the eddy-diffusivity/mass-flux boundary-layer parameterization of the convective boundary-layer in a single-column model framework. The optimization based on surrogate models is able to identify parameter combinations that reduce the error of the untuned default setting by 41%. The probability to detect a low-error solution increases rapidly especially over the first tens of single-column model evaluations. In comparison, a quadratic polynomial model only yields an error reduction of 17% since (a) high-order parameter interactions are not accounted for and (b) the construction of the polynomial is not based on an iterative sampling approach. The RBF surrogate models achieve this 17% error reduction for 40% of the polynomial model's cost. Interestingly, one of the emerging optimal settings describes a pure mass flux parameterization without eddy-diffusivity component. A second optimal solution is characterized by a plume fractional area of 20-30% and an eddy-mixing time scale of ∼700 s. Key Points:• Radial basis function (RBF) surrogate models provide an efficient framework to optimize physics parameterizations such as EDMF • The RBF surrogate models detect solutions much better than those provided by a commonly used quadratic polynomial model and are less costly • A multiplume model without eddy-diffusivity flux emerges as one of the optimal settings for the cloud-free and cloud-topped convective PBL

show abstract

GOSAC: global optimization with surrogate approximation of constraints

Cited by 34 publications

References 35 publications

Derivative-free optimization methods

Derivative-free optimization methods

Constrained optimization in simulation: efficient global optimization and Karush-Kuhn-Tucker conditions

Optimization of the Eddy‐Diffusivity/Mass‐Flux Shallow Cumulus and Boundary‐Layer Parameterization Using Surrogate Models

Contact Info

Product

Resources

About