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Results for “Derivative-free optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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69 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Incorporating the Min-Max Mesh Optimization Method within the Target-Matrix Paradigm

The Target-Matrix Optimization Paradigm (TMOP) is a method for improving mesh quality via node movement. Through the use of appropriate pre-defined quality metrics and Target-matrices, TMOP provides the ability to define mesh quality in terms of element shape, volume, and edge orientation as a function of position within the mesh, thus facilitating high-level goals such as size-adapted meshing. The Paradigm is developed further in this paper by showing how it can be applied to the problem of improving the mesh in locations where the quality is the worst. Improving the worst quality portions of a mesh was investigated by Freitag, Amenta, and others, who showed that the problem can be formulated as a min-max optimization problem. The Target-paradigm is used to extend the previous work in two important respects. First, by using quality metrics from the Target-paradigm, quality can be user-specified via Target-matrices instead of the quality definition being hard-wired into the quality metric. Second, by making use of the sample point concept in TMOP, one can extend min-max mesh optimization to non-simplicial element types such as quadrilaterals. Numerical experiments were performed to illustrate these extensions and to investigate their utility. A non-gradient solver known as the amoeba was used to numerically compute the optimal solutions. This derivative-free method, in conjunction with the use of barrier metrics from TMOP, enables the solution of the min-max problem without the use of explicit constraints to guarantee that the optimal mesh is non-inverted. The experiments showed that the use of Target-metrics in min-max with triangle (or tetrahedral) element meshes is able to effectively improve the worst quality elements in terms of shape or in terms of size+shape. The experiments also showed that the mesh min-max extension to quadrilateral element meshes can lead to acceptable meshes using barrier metrics from the Target-paradigm, provided that inter-element mesh smoothness is not important. Poor behavior was observed when using non-barrier Target-metrics in min-max with quadrilateral element meshes. For both simplicial and quadrilateral meshes, the min-sum method can be competitive with min-max, however.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. In conclusion, we numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs.

Derivative-free Optimization↗
DOE OSTI2021

Computing the shape gradient of stellarator coil complexity with respect to the plasma boundary

Coil complexity is a critical consideration in stellarator design. The traditional two-step optimization approach, in which the plasma boundary is optimized for physics properties and the coils are subsequently optimized to be consistent with this boundary, can result in plasma shapes which cannot be produced with sufficiently simple coils. To address this challenge, we propose a method to incorporate considerations of coil complexity in the optimization of the plasma boundary. Coil complexity metrics are computed from the current potential solution obtained with the REGCOIL code (Landreman, Nucl. Fusion , vol. 57, 2017, 046003). While such metrics have previously been included in derivative-free fixed-boundary optimization (Drevlak et al. , Nucl. Fusion , vol. 59, 2018, 016010), we compute the local sensitivity of these metrics with respect to perturbations of the plasma boundary using the shape gradient (Landreman & Paul, Nucl. Fusion , vol. 58, 2018, 076023). We extend REGCOIL to compute derivatives of these metrics with respect to parameters describing the plasma boundary. In keeping with previous research on winding surface optimization (Paul et al. , Nucl. Fusion , vol. 58, 2018, 076015), the shape derivatives are computed with a discrete adjoint method. In contrast with the previous work, derivatives are computed with respect to the plasma surface parameters rather than the winding surface parameters. To further reduce the resolution required to compute the shape gradient, we present a more efficient representation of the plasma surface which uses a single Fourier series to describe the radial distance from a coordinate axis and a spectrally condensed poloidal angle. This representation is advantageous over the standard cylindrical representation used in the VMEC code (Hirshman & Whitson, Phys. Fluids , vol. 26, 1983, pp. 3553–3568), as it provides a uniquely defined poloidal angle, eliminating a null space in the optimization of the plasma surface. In comparison with previous spectral condensation methods (Hirshman & Breslau, Phys. Plasmas , vol. 5, 1998, p. 2664), the modified poloidal angle is obtained algebraically rather than through the solution of a nonlinear optimization problem. The resulting shape gradient highlights features of the plasma boundary that are consistent with simple coils and can be used to couple coil and fixed-boundary optimization.

Physics↗
DOE OSTI2016

CONORBIT: constrained optimization by radial basis function interpolation in trust regions

Here, this paper presents CONORBIT (CONstrained Optimization by Radial Basis function Interpolation in Trust regions), a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions, and is an extension of the ORBIT algorithm. It uses a small margin for the RBF constraint models to facilitate the generation of feasible iterates, and extensive numerical tests confirm that such a margin is helpful in improving performance. CONORBIT is compared with other algorithms on 27 test problems, a chemical process optimization problem, and an automotive application. Numerical results show that CONORBIT performs better than COBYLA, a sequential penalty derivative-free method, an augmented Lagrangian method, a direct search method, and another RBF-based algorithm on the test problems and on the automotive application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

An improved hyperbolic embedding algorithm

Because hyperbolic space has properties that make it amenable to graph representations, there is significant interest in scalable hyperbolic-space embedding methods. These embeddings enable constant-time approximation of shortest-path distances, and so are significantly more efficient than full shortest-path computations. In this article, we improve on existing landmark-based hyperbolic embedding algorithms for large-scale graphs. Whereas previous methods compute the embedding by using the derivative-free Nelder–Mead simplex optimization method, our approach uses the limited-memory BFGS (LBFGS) method, which is quasi-Newton optimization, with analytic gradients. Our method is not only significantly faster but also produces higher-quality embeddings. Moreover, we are able to include the hyperbolic curvature as a variable in the optimization. We compare our hyperbolic embedding method implementation in Python (called Hypy) against the best publicly available software, Rigel. Our method is an order of magnitude faster and shows significant improvements in the accuracy of the shortest-path distance calculations. Furthermore, tests are performed on a variety of real-world networks, and we show the scalability of our method by embedding a graph with 1.8 billion edges and 65 million nodes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Scalable computations for nonstationary Gaussian processes

Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with conventional dense linear algebra. In addition, derivative-free or even first-order optimization methods can be very slow to converge when estimating many spatially varying parameters. In this paper, we present a computational framework which couples an algebraic block diagonal plus low-rank covariance matrix approximation with stochastic trace estimation to facilitate the efficient use of second-order solvers for maximum likelihood estimation of Gaussian process models with many parameters. We demonstrate the effectiveness of these methods by simultaneously fitting 192 parameters in the popular nonstationary model of Paciorek and Schervish using 107,600 sea surface temperature anomaly measurements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Adaptive Sampling Trust Region Method for Bi-fidelity Simulation Optimization [SWR-25-166]

Adaptive Sampling Trust Region Method for Bi-fidelity Simulation Optimization aims to demonstrate the effect of adaptive sampling-based bi-fidelity stochastic trust region method (ASTRO-BFDF). ASTRO-BFDF, derived from a derivative-free adaptive sampling trust-region optimization (ASTRO-DF) (Shashaani et al. 2018, Ha and Shashaani 2023), intended to efficiently solve the bi-fidelity simulation optimization.

Mueller, Juliane [National Laboratory of the Rocki↗
NASA NTRS1997

Numerical Optimization Using Computer Experiments

Engineering design optimization often gives rise to problems in which expensive objective functions are minimized by derivative-free methods. We propose a method for solving such problems that synthesizes ideas from the numerical optimization and computer experiment literatures. Our approach relies on kriging known function values to construct a sequence of surrogate models of the objective function that are used to guide a grid search for a minimizer. Results from numerical experiments on a standard test problem are presented.

Trosset, Michael W.↗
DOE OSTI2020

Black-Box Optimization for Design of Concentrating Solar Power and Photovoltaic Hybrid Systems with Optimal Dispatch Decisions

The hybridization of concentrating solar power (CSP) and photovoltaics (PV) can enable dispatchable renewable electricity generation at a lower price than current stand-alone CSP systems. However, designing a CSP-PV hybrid system can be challenging because of the many degrees of freedom in design that affect the internal and external system interactions and trade-offs. We develop a methodology to determine optimal designs for CSP-PV hybrids by implementing NLopt's derivative-free, or “black-box,” algorithms around pre-existing CSP-PV hybrid simulation software that utilizes the National Renewable Energy Laboratory’s System Advisor Model (SAM); we then employ a dispatch optimization model to determine operational decisions that maximize a plant’s profits. We present optimal designs for CSP-PV hybrid systems dispatching against four time-of-delivery (ToD) pricing structures. NLopt’s algorithms can improve the base case design’s power purchase agreement (PPA) price by 15% to 21%, depending on the ToD pricing structure. In addition, we present the resulting optimal CSP-PV hybrid design’s annual performance metrics, which tend to have capacity factors between 50% and 62%, but are able to generate electricity during the year’s highest-valued periods about 90% of the time. Lastly, we investigate the trade-offs between capacity factor and PPA price using Pareto fronts and demonstrate that, for some ToD pricing structures, the system capacity factor can increase by 20% but at the expense of a 2% increase in PPA price.

black-box↗
DOE OSTI2021

Manifold Sampling for Optimizing Nonsmooth Nonconvex Compositions

Here we propose a manifold sampling algorithm for minimizing a nonsmooth composition $f= h\circ F$, where we assume $h$ is nonsmooth and may be inexpensively computed in closed form and $F$ is smooth but its Jacobian may not be available. We additionally assume that the composition $h\circ F$ defines a continuous selection. Manifold sampling algorithms can be classified as model-based derivative-free methods, in that models of $F$ are combined with particularly sampled information about $h$ to yield local models for use within a trust-region framework. We demonstrate that cluster points of the sequence of iterates generated by the manifold sampling algorithm are Clarke stationary. We consider the tractability of three particular subproblems generated by the manifold sampling algorithm and the extent to which inexact solutions to these subproblems may be tolerated. Numerical results demonstrate that manifold sampling as a derivative-free algorithm is competitive with state-of-the-art algorithms for nonsmooth optimization that utilize first-order information about $f$.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Enabling Scale-Up Through Multi-Fidelity Adaptive Computing

We present ideas from our ongoing work in adaptive computing - an optimization framework that allows us to strategically deploy various fidelity level experiments and simulations to guide decision making. The framework aims to enable uncertainty quantified scale-up of simulations and experiments, which causes increased complexity. A key feature of the framework is the integration of user-specified local model trustworthiness estimates. Adaptive sampling strategies allow us to optimally exploit the multiple fidelity level information and trustworthiness measures to arrive at the best decisions within a highly limited budget of objective function evaluations.

adaptive sampling↗
DOE OSTI2016

iTOUGH2 v7.1

iTOUGH2 (inverse TOUGH2) provides inverse modeling capabilities for TOUGH2, a simulator for multi-dimensional, multi-phase, multi-component, non-isothermal flow and transport in fractured porous media. iTOUGH2 performs sensitivity analyses, data-worth analyses, parameter estimation, and uncertainty propagation analyses in geosciences and reservoir engineering and other application areas. iTOUGH2 supports a number of different combinations of fluids and components (equation-of-state (EOS) modules). In addition, the optimization routines implemented in iTOUGH2 can also be used for sensitivity analysis, automatic model calibration, and uncertainty quantification of any external code that uses text-based input and output files using the PEST protocol. iTOUGH2 solves the inverse problem by minimizing a non-linear objective function of the weighted differences between model output and the corresponding observations. Multiple minimization algorithms (derivative-free, gradient-based, and second-order; local and global) are available. iTOUGH2 also performs Latin Hypercube Monte Carlo simulations for uncertainty propagation analyses. A detailed residual and error analysis is provided. This upgrade includes (a) global sensitivity analysis methods, (b) dynamic memory allocation (c) additional input features and output analyses, (d) increased forward simulation capabilities, (e) parallel execution on multicore PCs and Linux clusters, and (f) bug fixes.

Finsterle, Stefan↗
DOE OSTI2021

Physics-Informed Evolutionary Strategy Based Control for Mitigating Delayed Voltage Recovery

Here, in this work we propose a novel data-driven, real-time power system voltage stability control method based on the physics-informed guided meta evolutionary strategy (ES). The main objective is to quickly provide an adaptive control strategy to secure system voltage stability. The problem is challenging due to the high-dimensional feature of the power system model and the fast-changing and uncertain nature of power system operation scenarios. To this end, a model-free and derivative-free guided ES method is applied. The method is further combined with a meta-learning strategy to make the learnt control policy automatically adapted to unseen operation conditions and fault scenarios, which is highly desired for real-time emergency control. Last but not least, physical knowledge is embedded in the above method through a trainable action mask technique to rule out unnecessary load shedding actions for better learning and control performance. Case studies on the IEEE 300-bus system and comparisons with other state-of-the-art benchmark methods verify the superiority of the proposed physics-informed guided meta ES method in realizing fast and adaptive power system voltage stability control.

42 ENGINEERING↗
DOE OSTI2025

HFBTHO-AD: Differentiation of a nuclear energy density functional code

The HFBTHO code implements a nuclear energy density functional solver to model the structure of atomic nuclei. HFBTHO has previously been used to calibrate energy functionals and perform sensitivity analysis by using derivative-free methods. To enable derivative-based optimization and uncertainty quantification approaches, we must compute the derivatives of HFBTHO outputs with respect to the parameters of the energy functional, which are a subset of all input parameters of the code. Here, we use the algorithmic/automatic differentiation (AD) tool Tapenade to differentiate HFBTHO. We compare the derivatives obtained using AD against finite-difference approximation and examine the performance of the derivative computation.

Algorithmic differentiation↗
DOE OSTI2018

Accurate, rapid identification of dislocation lines in coherent diffractive imaging via a min-max optimization formulation

Defects such as dislocations impact materials properties and their response during external stimuli. Imaging these defects in their native operating conditions to establish the structure-function relationship and, ultimately, to improve performance via defect engineering has remained a considerable challenge for both electron-based and x-ray-based imaging techniques. While Bragg coherent x-ray diffractive imaging (BCDI) is successful in many cases, nuances in identifying the dislocations has left manual identification as the preferred method. Derivative-based methods are also used, but they can be inaccurate and are computationally inefficient. Here we demonstrate a derivative-free method that is both more accurate and more computationally efficient than either derivative-or human-based methods for identifying 3D dislocation lines in nanocrystal images produced by BCDI. We formulate the problem as a min-max optimization problem and show exceptional accuracy for experimental images. We demonstrate a 227x speedup for a typical experimental dataset with higher accuracy over current methods. We discuss the possibility of using this algorithm as part of a sparsity-based phase retrieval process. Here, we also provide MATLAB code for use by other researchers.

47 OTHER INSTRUMENTATION↗