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At least 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A proximal trust-region method for nonsmooth optimization with inexact function and gradient evaluations

Many applications require minimizing the sum of smooth and nonsmooth functions. For example, basis pursuit denoising problems in data science require minimizing a measure of data misfit plus an $\ell^1$-regularizer. Similar problems arise in the optimal control of partial differential equations (PDEs) when sparsity of the control is desired. Here, we develop a novel trust-region method to minimize the sum of a smooth nonconvex function and a nonsmooth convex function. Our method is unique in that it permits and systematically controls the use of inexact objective function and derivative evaluations. When using a quadratic Taylor model for the trust-region subproblem, our algorithm is an inexact, matrix-free proximal Newton-type method that permits indefinite Hessians. We prove global convergence of our method in Hilbert space and demonstrate its efficacy on three examples from data science and PDE-constrained optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

MO-FG-CAMPUS-TeP2-03: Multi-Criteria Optimization Using Taguchi Method for SRS of Multiple Lesions by Single Isocenter

Purpose: This study utilizes the Taguchi Method to evaluate the VMAT planning parameters of single isocenter treatment plans for multiple brain metastases. An optimization model based on Taguchi and utility concept is employed to optimize the planning parameters including: arc arrangement, calculation grid size, calculation model, and beam energy on multiple performance characteristics namely conformity index and dose to normal brain. Methods: Treatment plans, each with 4 metastatic brain lesions were planned using single isocenter technique. The collimator angles were optimized to avoid open areas. In this analysis four planning parameters (a–d) were considered: (a)-Arc arrangements: set1: Gantry 181cw179 couch0; gantry179ccw0, couch315; and gantry0ccw181, couch45. set2: set1 plus additional arc: Gantry 0cw179, couch270. (b)-Energy: 6-MV; 6MV-FFF (c)-Calculation grid size: 1mm; 1.5mm (d)-Calculation models: AAA; Acuros Treatment planning was performed in Varian Eclipse (ver.11.0.30). A suitable orthogonal array was selected (L8) to perform the experiments. After conducting the experiments with the combinations of planning parameters the conformity index (CI) and the normal brain dose S/N ratio for each parameter was calculated. Optimum levels for the multiple response optimizations were determined. Results: We determined that the factors most affecting the conformity index are arc arrangement and beam energy. These tests were also used to evaluate dose to normal brain. In these evaluations, the significant parameters were grid size and calculation model. Using the utility concept we determined the combination of each of the four factors tested in this study that most significantly influence quality of the resulting treatment plans: (a)-arc arrangement-set2, (b)-6MV, (c)-calc.grid 1mm, (d)-Acuros algorithm. Overall, the dominant significant influences on plan quality are (a)-arcarrangement, and (b)-beamenergy. Conclusion: Results were analyzed using ANOVA and were found to be within the confidence interval. Further investigation using this methodology. Such parameters might include: virtual OAR and optimization criterion such as normal tissue objective.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Systems and methods for energy cost optimization in a building system

Methods and systems to minimize energy cost in response to time-varying energy prices are presented for a variety of different pricing scenarios. A cascaded model predictive control system is disclosed comprising an inner controller and an outer controller. The inner controller controls power use using a derivative of a temperature setpoint and the outer controller controls temperature via a power setpoint or power deferral. An optimization procedure is used to minimize a cost function within a time horizon subject to temperature constraints, equality constraints, and demand charge constraints. Equality constraints are formulated using system model information and system state information whereas demand charge constraints are formulated using system state information and pricing information. A masking procedure is used to invalidate demand charge constraints for inactive pricing periods including peak, partial-peak, off-peak, critical-peak, and real-time.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2017

Development Optimization and Uncertainty Analysis Methods for Oil and Gas Reservoirs

Uncertainty complicates the development optimization of oil and gas exploration and production projects, but methods have been devised to analyze uncertainty and its impact on optimal decision-making. This paper compares two methods for development optimization and uncertainty analysis: Monte Carlo (MC) simulation and stochastic programming. Two example problems for a gas field development and an oilfield development are solved and discussed to elaborate the advantages and disadvantages of each method. Development optimization involves decisions regarding the configuration of initial capital investment and subsequent operational decisions. Uncertainty analysis involves the quantification of the impact of uncertain parameters on the optimum design concept. The gas field development problem is designed to highlight the differences in the implementation of the two methods and to show that both methods yield the exact same optimum design. The results show that both MC optimization and stochastic programming provide unique benefits, and that the choice of method depends on the goal of the analysis. While the MC method generates more useful information, along with the optimum design configuration, the stochastic programming method is more computationally efficient in determining the optimal solution. Reservoirs comprise multiple compartments and layers with multiphase flow of oil, water, and gas. We present a workflow for development optimization under uncertainty for these reservoirs, and solve an example on the design optimization of a multicompartment, multilayer oilfield development.

02 PETROLEUM↗
DOE OSTI2021

Tuning Multigrid Methods with Robust Optimization and Local Fourier Analysis

Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier analysis is that it can be used to minimize an estimate of the spectral radius of a stationary iteration, or the condition number of a preconditioned system, in terms of a symbol representation of the algorithm. In practice, this is a “minimax” problem, minimizing with respect to solver parameters the appropriate measure of work, which involves maximizing over the Fourier frequency. Often, several algorithmic parameters may be determined by local Fourier analysis in order to obtain efficient algorithms. Analytical solutions to minimax problems are rarely possible beyond simple problems; the status quo in local Fourier analysis involves grid sampling, which is prohibitively expensive in high dimensions. In this paper, we propose and explore optimization algorithms to solve these problems efficiently. Finally, several examples, with known and unknown analytical solutions, are presented to show the effectiveness of these approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Local convergence analysis of an inexact trust-region method for nonsmooth optimization

In Baraldi, we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function in Hilbert space—a class of problems that is ubiquitous in data science, learning, optimal control, and inverse problems. Furthermore, this algorithm has demonstrated excellent performance and scalability with problem size. In this paper, we enrich the convergence analysis for this algorithm, proving strong convergence of the iterates with guaranteed rates. In particular, we demonstrate that the trust-region algorithm recovers superlinear, even quadratic, convergence rates when using a second-order Taylor approximation of the smooth objective function term.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

HyKKT: a hybrid direct-iterative method for solving KKT linear systems

Here, we propose a solution strategy for the large indefinite linear systems arising in interior methods for nonlinear optimization. The method is suitable for implementation on hardware accelerators such as graphical processing units (GPUs). The current gold standard for sparse indefinite systems is the LBLT factorization where L is a lower triangular matrix and B is 1×1 or 2×2 block diagonal. However, this requires pivoting, which substantially increases communication cost and degrades performance on GPUs. Our approach solves a large indefinite system by solving multiple smaller positive definite systems, using an iterative solver on the Schur complement and an inner direct solve (via Cholesky factorization) within each iteration. Cholesky is stable without pivoting, thereby reducing communication and allowing reuse of the symbolic factorization. We demonstrate the practicality of our approach on large optimal power flow problems and show that it can efficiently utilize GPUs and outperform LBL T factorization of the full system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Lagrangian–Eulerian multidensity topology optimization with the material point method

Abstract In this paper, a hybrid Lagrangian–Eulerian topology optimization (LETO) method is proposed to solve the elastic force equilibrium with the Material Point Method (MPM). LETO transfers density information from freely movable Lagrangian carrier particles to a fixed set of Eulerian quadrature points. This transfer is based on a smooth radial kernel involved in the compliance objective to avoid the artificial checkerboard pattern. The quadrature points act as MPM particles embedded in a lower‐resolution grid and enable a subcell multidensity resolution of intricate structures with a reduced computational cost. A quadrature‐level connectivity graph‐based method is adopted to avoid the artificial checkerboard issues commonly existing in multiresolution topology optimization methods. Numerical experiments are provided to demonstrate the efficacy of the proposed approach.

Li, Yue↗
DOE OSTI2020

A general-purpose method for Pareto optimal placement of flow rate and concentration sensors in networked systems – With application to wastewater treatment plants

The advent of affordable computing, low-cost sensor hardware, and high-speed and reliable communications have spurred installation of ubiquitous sensors in complex engineered systems. However, ensuring reliable data quality remains a challenge. Exploitation of redundancy among sensor signals can help improving the precision of measured variables, detecting the presence of gross errors, and identifying faulty sensors. The cost of sensor ownership, maintenance efforts in particular, can still be cost-prohibitive however. Maximizing the ability to assess and control data quality while minimizing the cost of ownership thus requires a careful sensor placement. To solve this challenge, in this work we develop a generally applicable method to solve the multi-objective sensor placement problem in systems governed by linear and bilinear balance equations. Importantly, the method computes all Pareto-optimal sensor layouts with conventional computational resources and requires no information about the expected sensor quality.

42 ENGINEERING↗
DOE OSTI2016

Method of generating features optimal to a dataset and classifier

A method of generating features optimal to a particular dataset and classifier is disclosed. A dataset of messages is inputted and a classifier is selected. An algebra of features is encoded. Computable features that are capable of describing the dataset from the algebra of features are selected. Irredundant features that are optimal for the classifier and the dataset are selected.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Interaction–Deletion: A Composite Energy Method for the Optimization of Molecular Systems Selectively Removing Specific Nonbonded Interactions

The complex interactions between different portions of a large molecule can be challenging to analyze through traditional electronic structure calculations. Moreover, standard methods cannot easily quantify the physical consequences of individual pairwise interactions inside a molecule. By creating a set of molecular fragments, we propose a composite energy method to explore changes in a molecule caused by removing selected nonbonded interactions between different molecular portions. Energies and forces are easily obtained with this composite approach, allowing geometry optimizations that lead to chemically meaningful structures that describe how the omitted interactions contribute to changes in the local geometrical minima. We illustrate the application of our new hybrid scheme by computing the influence of intramolecular hydrogen-bonding interactions in two small molecules: 1,6-(tG + G + TG + G + g – )-hexanediol and a cyclic analogue, cis-1,4-cyclohexanediol. The resulting structural and energetic changes are interpreted to yield key physical insights and quantify concepts such as “preparation energy” or “reorganization energy”. We demonstrate that the composite method can be extended to larger molecular systems by showing its application on a Si(100) surface model containing interactions between dissociated ammonia molecules on adjacent surface dimers. The scheme’s efficacy is also tested by applying it to systems having multiple intramolecular interactions, viz., 310-polyglycine and H+GPGG. Furthermore, the cooperative nature of intramolecular hydrogen bonds is explored by using interaction–deletion in 2-nitrobenzene-1,3-diol.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Linear shaped-charge jet optimization using machine learning methods

Linear shaped charges are used to focus energy into rapidly creating a deep linear incision. The general design of a shaped charge involves detonating a confined mass of high explosive (HE) with a metal-lined concave cavity on one side to produce a high velocity jet for the purpose of striking and penetrating a given material target. This jetting effect occurs due to the interaction of the detonation wave with the cavity geometry, which produces an unstable fluid phenomenon known as the Richtmyer–Meshkov instability and results in the rapid growth of a long narrow jet. We apply machine learning and optimization methods to hydrodynamics simulations of linear shaped charges to improve the simulated jet characteristics. The designs that we propose and investigate in this work generally involve modifying the behavior of the detonation waves prior to interaction with the liner material. These designs include the placement of multiple detonators and the use of metal inclusions within the HE. In conclusion, we are able to produce a linear shaped-charge design with a higher penetration depth than the baseline case that we consider and accomplish this using the same amount of or less HE.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Personalized learning via task load optimization

A method for providing task load-optimized computer-generated training experiences to a user of a training system that includes: a display, a training simulator, a prediction program (ML1), and a training optimization program (ML2). In response to receiving a predicted optimal task load, ML2 provides a first training experience recommendation related to the training content and/or training conditions that, if utilized in providing a training experience to the user, is predicted to result in the predicted actual task load of the user equaling the predicted optimal task load. In response to receiving biometric information or performance metric information, ML1 determines the predicted actual task load. If the predicted actual task load does not match the predicted optimal task load, ML2 provides a second training experience recommendation and a second training experience is provided where at least one of the training content or the training conditions is changed.

Bertolli, Michael G.↗
DOE OSTI2025

A simple introduction to the SiMPL method for density-based topology optimization

We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent variable (SiMPL). The SiMPL method (pronounced as “the simple method”) optimizes a design using only first-order derivative information of the objective function. The bound constraints on the density field are enforced with the help of the (negative) Fermi–Dirac entropy, which is also used to define a non-symmetric distance function called a Bregman divergence on the set of admissible designs. This Bregman divergence leads to a simple update rule that is further simplified with the help of a so-called latent variable. Because the SiMPL method involves discretizing the latent variable, it produces a sequence of pointwise-feasible iterates, even when high-order finite elements are used in the discretization. Numerical experiments demonstrate that the method outperforms other popular first-order optimization algorithms. In conclusion, to outline the general applicability of the technique, we include examples with (self-load) compliance minimization and compliant mechanism optimization problems.

Calculus of Variations and Optimization↗
DOE OSTI2020

The Convolutional Multiple Whole Profile (CMWP) Fitting Method, a Global Optimization Procedure for Microstructure Determination

The analysis of line broadening in X-ray and neutron diffraction patterns using profile functions constructed on the basis of well-established physical principles and TEM observations of lattice defects has proven to be a powerful tool for characterizing microstructures in crystalline materials. These principles are applied in the convolutional multiple-whole-profile (CMWP) procedure to determine dislocation densities, crystallite size, stacking fault and twin boundary densities, and intergranular strains. The different lattice defect contributions to line broadening are separated by considering the hkl dependence of strain anisotropy, planar defect broadening and peak shifts, and the defect dependent profile shapes. The Levenberg–Marquardt (LM) peak fitting procedure can be used successfully to determine crystal defect types and densities as long as the diffraction patterns are relatively simple. However, in more complicated cases like hexagonal materials or multiple-phase patterns, using the LM procedure alone may cause uncertainties. Here, we extended the CMWP procedure by including a Monte Carlo statistical method where the LM and a Monte Carlo algorithm were combined in an alternating manner. The updated CMWP procedure eliminated uncertainties and provided global optimized parameters of the microstructure in good correlation with electron microscopy methods.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Optimization of Molecular Methods for Detecting Duckweed-Associated Bacteria

The bacterial colonization dynamics of plants can differ between phylogenetically similar bacterial strains and in the context of complex bacterial communities. Quantitative methods that can resolve closely related bacteria within complex communities can lead to a better understanding of plant–microbe interactions. However, current methods often lack the specificity to differentiate phylogenetically similar bacterial strains. In this study, we describe molecular strategies to study duckweed–associated bacteria. We first systematically optimized a bead-beating protocol to co-isolate nucleic acids simultaneously from duckweed and bacteria. We then developed a generic fingerprinting assay to detect bacteria present in duckweed samples. To detect specific duckweed–bacterium associations, we developed a genomics-based computational pipeline to generate bacterial strain-specific primers. These strain-specific primers differentiated bacterial strains from the same genus and enabled the detection of specific duckweed–bacterium associations present in a community context. Moreover, we used these strain-specific primers to quantify the bacterial colonization of duckweed by normalization to a plant reference gene and revealed differences in colonization levels between strains from the same genus. Lastly, confocal microscopy of inoculated duckweed further supported our PCR results and showed bacterial colonization of the duckweed root–frond interface and root interior. The molecular methods introduced in this work should enable the tracking and quantification of specific plant-microbe associations within plant-microbial communities.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Model-Free Primal-Dual Methods for Network Optimization with Application to Real-Time Optimal Power Flow: Preprint

This paper examines the problem of real-time optimization of networked systems and develops online algorithms that steer the system towards the optimal trajectory without explicit knowledge of the system model. The problem is modeled as a dynamic optimization problem with time-varying performance objectives and engineering constraints. The design of the algorithms leverages the online zero-order primal-dual projected-gradient method. In particular, the primal step that involves the gradient of the objective function (and hence requires networked systems model) is replaced by its zero-order approximation with two function evaluations using a deterministic perturbation signal. The evaluations are performed using the measurements of the system output, hence giving rise to a feedback interconnection, with the optimization algorithm serving as a feedback controller. The paper provides some insights on the stability and tracking properties of this interconnection. Finally, the paper applies this methodology to a real-time optimal power flow problem in power systems, and shows its efficacy on the IEEE 37-node distribution test feeder for reference power tracking and voltage regulation.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

Optimal lattice-structured materials

This paper describes a method for optimizing the mesostructure of lattice-structured materials. These materials are periodic arrays of slender members resembling efficient, lightweight macroscale structures like bridges and frame buildings. Current additive manufacturing technologies can assemble lattice structures with length scales ranging from nanometers to millimeters. Previous work demonstrates that lattice materials have excellent stiffness- and strength-to-weight scaling, outperforming natural materials. However, there are currently no methods for producing optimal mesostructures that consider the full space of possible 3D lattice topologies. The inverse homogenization approach for optimizing the periodic structure of lattice materials requires a parameterized, homogenized material model describing the response of an arbitrary structure. This work develops such a model, starting with a method for describing the long-wavelength, macroscale deformation of an arbitrary lattice. The work combines the homogenized model with a parameterized description of the total design space to generate a parameterized model. Finally, the work describes an optimization method capable of producing optimal mesostructures. Several examples demonstrate the optimization method. One of these examples produces an elastically isotropic, maximally stiff structure, here called the isotruss, that arguably outperforms the anisotropic octet truss topology.

36 MATERIALS SCIENCE↗