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Results for “quadratic 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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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

MO-FG-CAMPUS-TeP2-01: A Graph Form ADMM Algorithm for Constrained Quadratic Radiation Treatment Planning

Purpose: In radiation therapy optimization the constraints can be either hard constraints which must be satisfied or soft constraints which are included but do not need to be satisfied exactly. Currently the voxel dose constraints are viewed as soft constraints and included as a part of the objective function and approximated as an unconstrained problem. However in some treatment planning cases the constraints should be specified as hard constraints and solved by constrained optimization. The goal of this work is to present a computation efficiency graph form alternating direction method of multipliers (ADMM) algorithm for constrained quadratic treatment planning optimization and compare it with several commonly used algorithms/toolbox. Method: ADMM can be viewed as an attempt to blend the benefits of dual decomposition and augmented Lagrangian methods for constrained optimization. Various proximal operators were first constructed as applicable to quadratic IMRT constrained optimization and the problem was formulated in a graph form of ADMM. A pre-iteration operation for the projection of a point to a graph was also proposed to further accelerate the computation. Result: The graph form ADMM algorithm was tested by the Common Optimization for Radiation Therapy (CORT) dataset including TG119, prostate, liver, and head & neck cases. Both unconstrained and constrained optimization problems were formulated for comparison purposes. All optimizations were solved by LBFGS, IPOPT, Matlab built-in toolbox, CVX (implementing SeDuMi) and Mosek solvers. For unconstrained optimization, it was found that LBFGS performs the best, and it was 3–5 times faster than graph form ADMM. However, for constrained optimization, graph form ADMM was 8 – 100 times faster than the other solvers. Conclusion: A graph form ADMM can be applied to constrained quadratic IMRT optimization. It is more computationally efficient than several other commercial and noncommercial optimizers and it also used significantly less computer memory.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

SU-E-T-549: A Combinatorial Optimization Approach to Treatment Planning with Non-Uniform Fractions in Intensity Modulated Proton Therapy

Purpose: Non-uniform fractionation, i.e. delivering distinct dose distributions in two subsequent fractions, can potentially improve outcomes by increasing biological dose to the target without increasing dose to healthy tissues. This is possible if both fractions deliver a similar dose to normal tissues (exploit the fractionation effect) but high single fraction doses to subvolumes of the target (hypofractionation). Optimization of such treatment plans can be formulated using biological equivalent dose (BED), but leads to intractable nonconvex optimization problems. We introduce a novel optimization approach to address this challenge. Methods: We first optimize a reference IMPT plan using standard techniques that delivers a homogeneous target dose in both fractions. The method then divides the pencil beams into two sets, which are assigned to either fraction one or fraction two. The total intensity of each pencil beam, and therefore the physical dose, remains unchanged compared to the reference plan. The objectives are to maximize the mean BED in the target and to minimize the mean BED in normal tissues, which is a quadratic function of the pencil beam weights. The optimal reassignment of pencil beams to one of the two fractions is formulated as a binary quadratic optimization problem. A near-optimal solution to this problem can be obtained by convex relaxation and randomized rounding. Results: The method is demonstrated for a large arteriovenous malformation (AVM) case treated in two fractions. The algorithm yields a treatment plan, which delivers a high dose to parts of the AVM in one of the fractions, but similar doses in both fractions to the normal brain tissue adjacent to the AVM. Using the approach, the mean BED in the target was increased by approximately 10% compared to what would have been possible with a uniform reference plan for the same normal tissue mean BED.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2020

An Optimal Power Control Strategy for Grid-Following Inverters in a Synchronous Frame

This work proposes a power control strategy based on the linear quadratic regulator with optimal reference tracking (LQR-ORT) for a three-phase inverter-based generator (IBG) using an LCL filter. The use of an LQR-ORT controller increases robustness margins and reduces the quadratic value of the power error and control inputs during transient response. A model in a synchronous reference frame that integrates power sharing and voltage–current (V–I) dynamics is also proposed. This model allows for analyzing closed-loop eigenvalue location and robustness margins. The proposed controller was compared against a classical droop approach using proportional-resonant controllers for the inner loops. Mathematical analysis and hardware-in-the-loop (HIL) experiments under variations in the LCL filter components demonstrate fulfillment of robustness and performance bounds of the LQR-ORT controller. Experimental results demonstrate accuracy of the proposed model and the effectiveness of the LQR-ORT controller in improving transient response, robustness, and power decoupling.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1989

An analytical sensitivity method for use in integrated aeroservoelastic aircraft design

Interdisciplinary analysis capabilities have been developed for aeroservoelastic aircraft and large flexible spacecraft, but the requisite integrated design methods are only beginning to be developed. One integrated design method which has received attention is based on hierarchal problem decompositions, optimization, and design sensitivity analyses. This paper highlights a design sensitivity analysis method for Linear Quadratic Gaussian (LQG) optimal control laws, enabling the use of LQG techniques in the hierarchal design methodology. The LQG sensitivity analysis method calculates the change in the optimal control law and resulting controlled system responses due to changes in fixed design integration parameters using analytical sensitivity equations. Numerical results of a LQG design sensitivity analysis for a realistic aeroservoelastic aircraft example are presented. In this example, the sensitivity of the optimal control law and aircraft response for various parameters such as wing bending natural frequency is determined. The sensitivity results computed from the analytical expressions are used to estimate changes in response resulting from changes in the parameters. Comparisons of the estimates with exact calculated responses show they are reasonably accurate for + or - 15 percent changes in the parameters. Evaluation of the analytical expressions is computationally faster than equivalent finite difference calculations.

Gilbert, Michael G.↗
NASA NTRS1989

An analytical sensitivity method for use in integrated aeroservoelastic aircraft design

Interdisciplinary analysis capabilities have been developed for aeroservoelastic aircraft and large flexible spacecraft, but the requisite integrated design methods are only beginning to be developed. One integrated design method which has received attention is based on hierarchal problem decompositions, optimization, and design sensitivity analyses. This paper highlights a design sensitivity analysis method for Linear Quadratic Gaussian (LQG) optimal control laws, enabling the use of LQG techniques in the hierarchal design methodology. The LQG sensitivity analysis method calculates the change in the optimal control law and resulting controlled system responses due to changes in fixed design integration parameters using analytical sensitivity equations. Numerical results of an LQG design sensitivity analysis for a realistic aeroservoelastic aircraft example are presented. In this example, the sensitivity of the optimal control law and aircraft response for various parameters such as wing bending natural frequency is determined. The sensitivity results computed from the analytical expressions are used to estimate changes in response resulting from changes in the parameters. Comparisons of the estimates with exact calculated responses show they are reasonably accurate for + or - 15 percent changes in the parameters. Evaluation of the analytical expressions is computationally faster than equivalent finite difference calculations.

Gilbert, Michael G.↗
NASA NTRS1991

Optimal aircraft performance during microburst encounter

The effects of microburst characteristics on the optimal penetration performance of jet transport and general aviation aircraft are presented. The purpose is to determine the best possible performance that can be achieved in a broad range of microbursts. A secondary goal is to illustrate good strategies for dealing with a range of microbursts during takeoff and landing. Over 1100 optimal trajectories were computed for two aircraft types flying through idealized microbursts using a Successive Quadratic Programs trajectory optimization algorithm. Contours of safety metrics are plotted as functions of the length scales, magnitudes, and locations of horizontal wind shears and vertical downdrafts. These performance contours show three length-scale regimes for optimal microburst penetration. At short length scales, hazards usually associated with gustiness predominate (e.g., high normal load factor, rotational upset). At intermediate length scales, a degraded ability to maintain flight path and/or vertical velocity poses the most serious threat. At very long microburst length scales, excessive touchdown velocities may result. The ability to transit a microburst successfully also varies strongly with microburst location. The results show that both aircraft types could penetrate some very severe microbursts if optimal control histories were followed. Nevertheless, these control strategies assume perfect prior knowledge of the wind, and practical limits to successful encounter with real-time control capabilities would be lower. The optimally controlled jet transport can successfully penetrate higher intensity microbursts than can the general aviation aircraft.

Psiaki, Mark L.↗
DOE OSTI2024

Connected Traffic Signal Coordination Optimization Framework through Network-Wide Adaptive Linear Quadratic Regulator–Based Control Strategy

Traffic congestion in metropolitan areas causes several significant challenges, such as longer travel times, decreased productivity, increased fuel consumption and vehicle emissions, and even severe injuries during crashes. Traffic signal control is a management approach to reduce traffic congestion and allocate the appropriate right of way for safety and mobility efficiency, both in temporal and spatial domains. Here, this study proposes a network-wide adaptive signal control coordination optimization framework based on the linear quadratic regulator algorithm. The traffic flow conditions driven by signal control inputs are formulated based on their network-wide state-space representation. After modeling traffic control regulation constraints, an adaptive linear quadratic regulator algorithm is designed to maximize the network-wide total throughput under the current conditions. Optimal signal control split time durations for multiple intersections in the network are derived by solving the algebraic Riccati equation. Furthermore, the recursive least square parameter estimation method is employed to quantify dynamic traffic condition changes. To verify the effectiveness of this proposed signal control framework, both simulation and real-world experimental tests are conducted for multiple intersections in downtown Chattanooga, Tennessee, United States. In preparation for real-world experimental tests, pipelines for real-time data processing implementation and historical traffic flow data analysis are conducted. The test results demonstrate that the proposed control framework achieves a decrease in travel time by up to 19.4%, total time spent (TTS) by up to 11.9%, and relative queue balance (RQB) by up to 15.6%. The research findings indicate that the proposed signal control framework can be generalized to handle large scale signal control optimization network-wide.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Comparing three generations of D-Wave quantum annealers for minor embedded combinatorial optimization problems

Abstract Quantum annealing (QA) is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. QA in the transverse Ising model, implemented on D-Wave quantum processing units, are available as cloud computing resources. In this study we report concise benchmarks across three generations of D-Wave quantum annealers, consisting of four different devices, for the NP-hard discrete combinatorial optimization problems unweighted maximum clique and unweighted maximum cut on random graphs. The Ising, or equivalently quadratic unconstrained binary optimization, formulation of these problems do not require auxiliary variables for order reduction, and their overall structure and weights are not highly variable, which makes these problems simple test cases to understand the sampling capability of current D-Wave quantum annealers. All-to-all minor embeddings of size 52, with relatively uniform chain lengths, are used for a direct comparison across the Chimera, Pegasus, and Zephyr device topologies. A grid-search over annealing times and the minor embedding chain strengths is performed in order to determine the level of reasonable performance for each device and problem type. Experiment metrics that are reported are approximation ratios for non-broken chain samples, chain break proportions, and time-to-solution for the maximum clique problem instances. How fairly the quantum annealers sample optimal maximum cliques, for instances which contain multiple maximum cliques, is quantified using entropy of the measured ground state distributions. The newest generation of quantum annealing hardware, which has a Zephyr hardware connectivity, performed the best overall with respect to approximation ratios and chain break frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Coramin v. 0.1 Beta

Coramin is a package that provides tools for developing tailored algorithms for mixed-integer nonlinear programming problems. This software includes the ability to: - Generate convex or piecewise relaxations of nonlinear optimization problems, addressing bilinear, quadratic, and convex/concave univariate functions - Perform optimization-based bounds tightening on all or subsets of the problem variables - Generate polyhedral envelopes for multi-linear functions

Bynum, Michael↗
NASA NTRS2008

Optimized Non-Obstructive Particle Damping (NOPD) Treatment for Composite Honeycomb Structures

Non-Obstructive Particle Damping (NOPD) technology is a passive vibration damping approach whereby metallic or non-metallic particles in spherical or irregular shapes, of heavy or light consistency, and even liquid particles are placed inside cavities or attached to structures by an appropriate means at strategic locations, to absorb vibration energy. The objective of the work described herein is the development of a design optimization procedure and discussion of test results for such a NOPD treatment on honeycomb (HC) composite structures, based on finite element modeling (FEM) analyses, optimization and tests. Modeling and predictions were performed and tests were carried out to correlate the test data with the FEM. The optimization procedure consisted of defining a global objective function, using finite difference methods, to determine the optimal values of the design variables through quadratic linear programming. The optimization process was carried out by targeting the highest dynamic displacements of several vibration modes of the structure and finding an optimal treatment configuration that will minimize them. An optimal design was thus derived and laboratory tests were conducted to evaluate its performance under different vibration environments. Three honeycomb composite beams, with Nomex core and aluminum face sheets, empty (untreated), uniformly treated with NOPD, and optimally treated with NOPD, according to the analytically predicted optimal design configuration, were tested in the laboratory. It is shown that the beam with optimal treatment has the lowest response amplitude. Described below are results of modal vibration tests and FEM analyses from predictions of the modal characteristics of honeycomb beams under zero, 50% uniform treatment and an optimal NOPD treatment design configuration and verification with test data.

Panossian, H.↗
DOE OSTI2019

D-Wave for High Energy Physics

aWe analyze different problems in high-energy physics where quantum computing, and namely quantum annealers, may be able to provide an edge in coming years: 1) The training of Restricted Boltzmann Machines (RBM) is a natural problem for quantum annealers. We explore RBM trained on a D-Wave machine for classification of galaxy morphologies, including a discussion of how to obtain a Boltzmann distribution from the annealer. 2) For this study, we cast the problem of explaining and predicting the production of particles in high energy collisions (color recombination) as an optimization problem and employ classical and quantum computing techniques to find solutions. In particular, we present a quadratic unconstrained binary optimization (QUBO) formulation for quantum annealers. In parallel to these efforts, we also present the cross-platform XACC package for quantum compilation and execution.

Caldeira, J.↗
NASA NTRSDate not supplied

A Multilevel Approach For SolvingLarge-Scale QUBO Problems With Noisy Hybrid Quantum Approximate Optimization

Quantum approximate optimization is one ofthe promising candidates for useful quantum computation,particularly in the context of finding approximate solutionsto Quadratic Unconstrained Binary Optimization (QUBO)problems. However, the existing quantum processing units(QPUs) are of relatively small size, and canonical mappingsof QUBO via the Ising model require one qubit per vari-able, rendering direct large-scale optimization infeasible.In classical optimization, a general strategy for addressingmany large-scale problems is via multilevel/multigrid meth-ods, where the large target problem is iteratively coarsenedand the global solution is constructed from multiple small-scale optimization runs. In this work, we experimentallytest how existing QPUs perform when used as a sub-solverwithin such a multilevel strategy. To this aim, we com-bine and extend (via additional classical processing steps)the recently proposed Noise-Directed Adaptive Remapping(NDAR) and Quantum Relax&Round (QRR) algorithms.We first demonstrate the effectiveness of our heuristicextensions on Rigetti’s superconducting transmon deviceAnkaa-2. We find approximate solutions to10instances offully connected82-qubit Sherrington-Kirkpatrick graphswith random integer-valued coefficients obtaining normal-ized approximation ratios (ARs) in the range∼0.98−1.0,and the same class with real-valued coefficients (ARs∼0.94−1.0). Then, we implement the extended NDAR andQRR algorithms as subsolvers in the multilevel algorithmfor6large-scale graphs with at most∼27,000variables.In practice, the QPU (with classical post-processing steps)is used to find approximate solutions to dozens of at most82-qubit problems, which are iteratively used to constructthe global solution. We observe that quantum optimizationresults are competitive in terms of the quality of solutionswhen compared to classical heuristics used as subsolverswithin the multilevel approach.Reproducibility: source code and data are available at[TBA upon acceptance]

quantum computing↗
DOE OSTI2020

Inferring the Dynamics of the State Evolution During Quantum Annealing

To solve an optimization problem using a commercial quantum annealer, one has to represent the problem of interest as an Ising or a quadratic unconstrained binary optimization (QUBO) problem and submit its coefficients to the annealer, which then returns a user-specified number of low-energy solutions. It would be useful to know what happens in the quantum processor during the anneal process so that one could design better algorithms or suggest improvements to the hardware. However, existing quantum annealers are not able to directly extract such information from the processor. Hence, in this work we propose to use advanced features of D-Wave 2000Q to indirectly infer information about the dynamics of the state evolution during the anneal process. Specifically, D-Wave 2000Q allows the user to customize the anneal schedule, that is, the schedule with which the anneal fraction is changed from the start to the end of the anneal. Furthermore, using this feature, we design a set of modified anneal schedules whose outputs can be used to generate information about the states of the system at user-defined time points during a standard anneal. With this process, called "slicing", we obtain approximate distributions of lowest-energy anneal solutions as the anneal time evolves. We use our technique to obtain a variety of insights into the annealer, such as the state evolution during annealing, when individual bits in an evolving solution flip during the anneal process and when they stabilize, and we introduce a technique to estimate the freeze-out point of both the system as well as of individual qubits.

42 ENGINEERING↗
NASA NTRS2023

Quantum Image Denoising: A Framework via Boltzmann Machines, QUBO, and Quantum Annealing

We investigate a framework for binary image denoising via restricted Boltzmann machines (RBMs) that introduces a denoising objective in quadratic unconstrained binary optimization (QUBO) form and is well-suited for quantum annealing. The denoising objective is attained by balancing the distribution learned by a trained RBM with a penalty term for derivations from the noisy image. We derive the statistically optimal choice of the penalty parameter assuming the target distribution has been well-approximated, and further suggest an empirically supported modification to make the method robust to that idealistic assumption. We also show under additional assumptions that the denoised images attained by our method are, in expectation, strictly closer to the noise-free images than the noisy images are. While we frame the model as an image denoising model, it can be applied to any binary data. As the QUBO formulation is well-suited for implementation on quantum annealers, we test the model on a D-Wave Advantage machine, and also test on data too large for current quantum annealers by approximating QUBO solutions through classical heuristics.

restricted Boltzmann machine↗
NASA NTRS1996

Comparative Evaluation of Different Optimization Algorithms for Structural Design Applications

Non-linear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Centre, a project was initiated to assess the performance of eight different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using the eight different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems, however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with Sequential Unconstrained Minimizations Technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.

Patnaik, Surya N.↗
NASA NTRS1996

Performance Trend of Different Algorithms for Structural Design Optimization

Nonlinear programming algorithms play an important role in structural design optimization. Fortunately, several algorithms with computer codes are available. At NASA Lewis Research Center, a project was initiated to assess performance of different optimizers through the development of a computer code CometBoards. This paper summarizes the conclusions of that research. CometBoards was employed to solve sets of small, medium and large structural problems, using different optimizers on a Cray-YMP8E/8128 computer. The reliability and efficiency of the optimizers were determined from the performance of these problems. For small problems, the performance of most of the optimizers could be considered adequate. For large problems however, three optimizers (two sequential quadratic programming routines, DNCONG of IMSL and SQP of IDESIGN, along with the sequential unconstrained minimizations technique SUMT) outperformed others. At optimum, most optimizers captured an identical number of active displacement and frequency constraints but the number of active stress constraints differed among the optimizers. This discrepancy can be attributed to singularity conditions in the optimization and the alleviation of this discrepancy can improve the efficiency of optimizers.

Patnaik, Surya N.↗
DOE OSTI2021

Machine learning framework for quantum sampling of highly constrained, continuous optimization problems

In recent years, there is growing interest in using quantum computers for solving combinatorial optimization problems. In this work, we developed a generic, machine learning-based framework for mapping continuous-space inverse design problems into surrogate quadratic unconstrained binary optimization (QUBO) problems by employing a binary variational autoencoder and a factorization machine. The factorization machine is trained as a low-dimensional, binary surrogate model for the continuous design space and sampled using various QUBO samplers. Using the D-Wave Advantage hybrid sampler and simulated annealing, we demonstrate that by repeated resampling and retraining of the factorization machine, our framework finds designs that exhibit figures of merit exceeding those of its training set. We showcase the framework’s performance on two inverse design problems by optimizing (i) thermal emitter topologies for thermophotovoltaic applications and (ii) diffractive meta-gratings for highly efficient beam steering. This technique can be further scaled to leverage future developments in quantum optimization to solve advanced inverse design problems for science and engineering applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1974

Application of modern control theory to scheduling and path-stretching maneuvers of aircraft in the near terminal area

A design concept of the dynamic control of aircraft in the near terminal area is discussed. An arbitrary set of nominal air routes, with possible multiple merging points, all leading to a single runway, is considered. The system allows for the automated determination of acceleration/deceleration of aircraft along the nominal air routes, as well as for the automated determination of path-stretching delay maneuvers. In addition to normal operating conditions, the system accommodates: (1) variable commanded separations over the outer marker to allow for takeoffs and between successive landings and (2) emergency conditions under which aircraft in distress have priority. The system design is based on a combination of three distinct optimal control problems involving a standard linear-quadratic problem, a parameter optimization problem, and a minimum-time rendezvous problem.

Athans, M.↗