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Results for “Algorithmic 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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DOE OSTI2025

Performance evaluations of signed and unsigned noisy approximate quantum Fourier arithmetic

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route toward a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor’s algorithm, weighted-sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM’s superconducting-qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands’ superposed integer states. We analyze performance and identify the most effective approximation depths for unsigned quantum addition and quantum multiplication within the given context. We then perform a similar analysis of signed addition and compare to the unsigned results. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges—relevant to signed, unsigned, modular and non-modular versions—that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. Here, we analyze the performance trends in our results and speculate on possible future developments within this computational paradigm.

Computational models↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Planning for Resilient Power Distribution Systems using Risk-Based Quantification and Q-Learning

Grid hardening is one of the most effective approaches that reduce the component failures and restoration efforts thus increasing the resilience of the power systems against extreme events. However, hardening and upgrading the entire system is prohibitively expensive and hence the optimal design of a distribution network is challenging. This paper adopted a reinforcement learning algorithm to identify the optimal hardening strategy to enhance the resilience of power distribution systems. Adopting the Q-learning algorithm as the reinforcement learning technique, we found the sequential optimal action for hardening measures to enhance the grid's resilience for the given budget. To identify the optimal strategy through Q-learning, Conditional Value at Risk (CVaR) is used as a rewarding metric. A study on the IEEE 123-bus test feeder validate the effectiveness of the proposed model and show how to effectively allocate budget limited resources to plan a resilient power distribution network.

Paul, Shuva↗
DOE OSTI2018

Exact and heuristic algorithms for minimizing Tardy/Lost penalties on a single-machine scheduling problem

This paper addresses minimizing Tardy/Lost penalties with common due dates on a single machine. According to this penalty criterion, if tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. The problem is formulated as an integer programming model, and a heuristic algorithm is constructed. Then, using the proposed dominance rules and lower bounds, we develop two dynamic programming algorithms as well as a branch and bound. Experimental results show that the heuristic algorithm has an average optimality gap less than 2 % in all problem sizes. Instances up to 250 jobs with low variety of process times are optimally solved and for high process time varieties, the algorithms solved all instances up to 75 jobs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

SU-E-T-229: Craniospinal Radiotherapy Planning with VMAT, Two First Years Experience

Purpose: To describe how we moved to VMAT in the craniospinal radiotherapy planning process, the actual procedure details, and the results for the patients treated. Methods: Twelve patients underwent craniospinal irradiation with the new procedure, based on the paper by Lee et al. (IJROBP 82, 2012), with some additional modifications. Patients were treated in supine position in Varian Clinac iX linacs with 6 MV RapidArc; prescription doses ranged from 23.4 to 40 Gy (13 to 20 fractions); depending on the PTV length, 2 or 3 isocenters were used, all coordinates being equal except the longitudinal one, setting a few centimeter-long overlapping region; 2 arcs (RA) sharing isocentre for the cranial region, RA1 encompassing cranium and superior spinal region, and RA2 intended to improve conformity, only for cranium; for spine, 1 or 2 isocenters were employed; optimization was performed with Eclipse (V 13.0) using AAA algorithm, establishing sets of optimization parameters to give high conformity while sparing OAR. In pediatric patients, homogeneous irradiation of the vertebrae was also required.Conformity (CI) and heterogeneity (HI) indices (same as Lee et al.), and mean and maximum doses for OAR were calculated. Several pre-treatment verification methods were used: Octavius4D (PTW) for each isocentre, point dose at the junction region, Portal Dosimetry (when possible), and independent MU verification software (Diamond, PTW). Results: CI median value was 1.02 (0.99–1.07) and HI, 1.07 (1.06–1.09); a great reduction was observed for CI and OAR mean doses with respect to Lee et al. data; median maximum eye lens dose was 7.3 Gy (4.0–12.0); mean LungV20Gy was 1.9%; in children, vertebrae were homogeneously irradiated (D95%=20.8 Gy, Dmean= 23.2 Gy).All pre-treatment verifications were found within our action levels except for Portal Dosimetry. Conclusion: A RapidArc planning process for craniospinal axis irradiation has been implemented with significant advantages on conformity, homogeneity, feasibility and efficiency. and increase brain tissue sparing. Variations in volume decrease may be related to shape or location of the tumor.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-T-418: Evaluation of Organs at Risk (OAR) Sparing in Left Breast Irradiation Techniques

Purpose: To compare dose to organs at risk (OAR) for left sided breast radiation therapy with comparable planning target volume (PTV) coverage in three techniques; free breathing in supine position (FB), deep inspirational breath hold in supine (DIBH) and free breathing in prone position (PP). Methods: Ten left sided breast cancer patients suitable for this study underwent a CT scan in three techniques e.g. supine, FB and DIBH and prone position (PP). One radiation oncologist contoured the PTV and OAR (cardiac components) based on RTOG guidelines. Treatment plans were optimized using field-in-field technique with AAA algorithm. Each plan was optimized to provide identical coverage to PTV such that a reasonable comparison in OAR dosimetry can be evaluated. The prescribed dose to PTV were 42.56 Gy; 2.66 Gy in 16 fractions. Results: Average lung dose parameters; Dmean, V10, V20 and V30 were 0.5 Gy, 0.6%, 0.2%, and 0.1% respectively in PP which is significantly lower than FB (5.9 Gy, 14.2%, 10.7 %, and 8.4%) and DIBH (5.8 Gy, 14.3%, 10.2%, 7.8%). Similarly average heart Dmean, V2.5, V5, V10, and V20 were much lower in PP (1.2Gy, 9.1%, 2.1%, 0.8%, and 0.4%), and in DIBH (1.2 Gy, 10.6%, 1.7%, 0.5%, and 0.1%) compared to FB (2.6 Gy, 21%, 7.2%, 4.4% and 3.3%) respectively. Similar findings were also noted in the heart component left anterior descending artery (LAD) and Left ventricle (LV) which are correlated to radiation related toxicity. Conclusion: Based on the calculated dose, FB technique provides highest heart and lung dose. Prone has lowest lung dose, and DIBH has lowest LAD dose. It is found that PP is always superior for heart, LV, LAD and lung as compared to FB. This conclusion is in contrast to some published study concluding that prone position has no benefit for heart sparing.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Efficient Parallel Discrete Event Simulation on Cloud/Virtual Machine Platforms

Cloud and Virtual machine (VM) technologies present new challenges with respect to performance and monetary cost in executing parallel discrete event simulation (PDES) applications. Due to the introduction of overall cost as a metric, the traditional use of the highest-end computing configuration is no longer the most obvious choice. Moreover, the unique runtime dynamics and configuration choices of Cloud and VM platforms introduce new design considerations and runtime characteristics specific to PDES over Cloud/VMs. Here, an empirical study is presented to guide an understanding of the dynamics, trends, and trade-offs in executing PDES on Cloud/VM platforms. Performance and cost measures obtained from multiple PDES applications executed on the Amazon EC2 Cloud and on a high-end VM host machine reveal new, counterintuitive VM--PDES dynamics and guidelines. One of the critical aspects uncovered is the fundamental mismatch in hypervisor scheduler policies designed for general cloud workloads versus the virtual time ordering needed for PDES workloads. This insight is supported by experimental data revealing the gross deterioration in PDES performance traceable to VM scheduling policy. To overcome this fundamental problem, the design and implementation of a new deadlock-free scheduler algorithm are presented, optimized specifically for PDES applications on VMs. The scalability of our scheduler has been tested up to 128 VMs multiplexed on 32 cores, showing significant improvement in the runtime relative to the default Cloud/VM scheduler. The observations, algorithmic design, and results are timely for emerging cloud/VM-based installations, highlighting the need for PDES-specific support in high performance discrete event simulations on Cloud/VM platforms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Pilot Point Optimization of Mining Boundaries for Lateritic Metal Deposits: Finding the Trade-off Between Dilution and Ore Loss

Geological contacts in lateritic metal deposits (footwall topographies) often delineate the orebody boundaries. Spatial variations seen in such contacts are frequently higher than those for the metal grades of the deposit. Therefore, borehole spacing chosen based on the grade variations cannot adequately capture the geological contact variability. Consequently, models created using such boreholes cause high volumetric uncertainties in the actual and targeted ore extraction volumes, which, in turn, lead to high unplanned dilution and ore losses. In this paper, a method to design optimum ore/mining boundaries for lateritic metal deposits is presented. The proposed approach minimizes the dilution/ore losses and comprises two main steps. First, the uncertainty on the orebody boundary is represented using a set of stochastic realizations generated with a multiple-point statistics algorithm. Then, the optimal orebody boundary is determined using an optimization technique inspired by a model calibration method called Pilot Points. The pilot points represent synthetic elevation values, and they are used to construct smooth mining boundaries using the multilevel B-spline technique. The performance of a generated surface is evaluated using the expected sum of losses in each of the stochastic realizations. The simulated annealing algorithm is used to iteratively determine the pilot point values which minimize the expected losses. The results show a significant reduction in the dilution volume as compared to those obtained from the actual mining operation.

58 GEOSCIENCES↗
DOE OSTI2019

Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing

We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state |x⟩ that is proportional to the solution of the system of linear equations $A\overrightarrow{x} = \overrightarrow{b}$. The time complexities of our algorithms are O(κ 2 log(κ)/ε) and O(κ log(κ)/ε), where κ is the condition number of A and ε is the precision. Both algorithms are constructed using families of Hamiltonians that are linear combinations of products of A, the projector onto the initial state |b⟩, and single-qubit Pauli operators. The algorithms are conceptually simple and easy to implement. They are not obtained from equivalences between the gate model and adiabatic quantum computing. They do not use phase estimation or variable-time amplitude amplification, and do not require large ancillary systems. We discuss a gate-based implementation via Hamiltonian simulation and prove that our second algorithm is almost optimal in terms of κ. Like previous methods, our techniques yield an exponential quantum speed-up under some assumptions. Our results emphasize the role of Hamiltonian-based models of quantum computing for the discovery of important algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Classical optimization with imaginary-time block encoding on quantum computers: The MaxCut problem

Optimization problems in finance, physics, and computer science are typically very hard to tackle in classical computing; quantum computing could help speed up computations and provide efficient methods for tackling large problems. Typically, to treat a problem with a quantum computer, the optimal solution is cast as the ground state of a diagonal Hamiltonian. Here, we develop a method, called imaginary-time evolution block encoding (ITE-BE), based on a recent imaginary-time algorithm, which requires no variational parameter optimization, as all parameters can be derived analytically from the target Hamiltonian. We also demonstrate that our method can be successfully combined with other quantum algorithms such as the quantum approximate optimization algorithm (QAOA). For illustration, here we study the MaxCut problem. We find that the QAOA ansatz increases the postselection success of ITE-BE, and shallow QAOA circuits, when boosted with ITE-BE, achieve better performance than deeper QAOA circuits. For the special case of the transverse initial state, we adapt our block-encoding scheme to allow for a deterministic application of the first layer of the circuit.

Zhong, Dawei [University of Southern California, L↗
DOE OSTI2023

ALESQP: An Augmented Lagrangian Equality-Constrained SQP Method for Optimization with General Constraints

Here we present a new algorithm for infinite-dimensional optimization with general constraints, called ALESQP. In short, ALESQP is an augmented Lagrangian method that penalizes inequality constraints and solves equality-constrained nonlinear optimization subproblems at every iteration. The subproblems are solved using a matrix-free trust-region sequential quadratic programming (SQP) method that takes advantage of iterative, i.e., inexact linear solvers, and is suitable for large-scale applications. A key feature of ALESQP is a constraint decomposition strategy that allows it to exploit problem-specific variable scalings and inner products. We analyze convergence of ALESQP under different assumptions. We show that strong accumulation points are stationary. Consequently, in finite dimensions ALESQP converges to a stationary point. In infinite dimensions we establish that weak accumulation points are feasible in many practical situations. Under additional assumptions we show that weak accumulation points are stationary. We present several infinite-dimensional examples where ALESQP shows remarkable discretization-independent performance in all of its iterative components, requiring a modest number of iterations to meet constraint tolerances at the level of machine precision. Also, we demonstrate a fully matrix-free solution of an infinite-dimensional problem with nonlinear inequality constraints.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

DiaMonD: An Integrated Multifaceted Approach to Mathematics at the Interfaces of Data, Models, and Decisions

For many problems in computational science and engineering, the so-called forward problem-solution of the underlying mathematical model to yield output quantities of interest, given input parameters--is difficult enough for frontier complex models, which are often characterized by coupled multiphysics and possibly stochastic behavior over a wide range of length and time scales. However, we face the need to move beyond the forward problem, to address what is often the ultimate goal of CS&E: decision-making. This requires us to tackle a spectrum of mathematical problems that subsume, and are thus even more difficult than, the forward problem. First, given experimental data, we wish to estimate unknown parameters characterizing a model of a natural or engineered system by solving an inverse problem. Second, we seek the optimal con figuration of the system (or experiments) by solving an optimal design problem. Third, the optimal operation of the system must be determined by solving an optimal control problem. And fourth, we must quantify uncertainties as they propagate through all of the preceding problems, from data to model inference to prediction and finally to optimal design and control. Optimal mathematical methods and algorithms for such end-to-end, data-to-decisions modeling and simulation of complex problems--requiring integrated solution of forward, inverse, optimization, and UQ problems for large, multiphysics, multiscale models--entails challenges of the highest order, while also presenting great opportunities for applied mathematics research. Unfortunately, research on forward, inverse, optimization, and UQ problems has all-too-often progressed in isolation. This has led to mathematical methods that perform well when considering the forward simulation in isolation, but are prohibitive or suboptimal or unstable when combined with other methods within the framework of inversion, optimization, or UQ. The reverse is also true: general-purpose methods developed within the inversion, optimization, and UQ fields often become prohibitive when applied to complex CS&E problems since they do not exploit their structure. DiaMonD is a multi-institutional DOE MMICC effort that aims to address the challenges of end-to-end, data-to-decisions modeling and simulation for complex CS&E problems in a unifi ed, systematic, and integrated fashion. Institutions involved are Colorado State, Florida State, Los Alamos, MIT, Oak Ridge, Stanford, and UT-Austin. The goals of DiaMonD are (1) to develop advanced mathematical methods and analysis for multimodel, multiphysics, multiscale model problems driven by frontier DOE applications, including those in subsurface energy and environmental flows, materials for energy storage and conversion, and ice sheet dynamics; (2) to create theory and algorithms for integrated inversion, optimization, and uncertainty quantification for these complex problems; and (3) to disseminate the philosophy of an integrated end-to-end, data-to-decisions approach to modeling and simulation of complex problems to the broader applied math and computational science communities through workshops and other outreach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Improving the FLORIS wind plant model for compatibility with gradient-based optimization

The FLORIS (FLOw Redirection and Induction in Steady-state) model, a parametric wind turbine wake model that predicts steady-state wake characteristics based on wind turbine position and yaw angle, was developed for optimization of control settings and turbine locations. This article provides details on changes made to the FLORIS model to make the model more suitable for gradient-based optimization. Changes to the FLORIS model were made to remove discontinuities and add curvature to regions of non-physical zero gradient. Exact gradients for the FLORIS model were obtained using algorithmic differentiation. A set of three case studies demonstrate that using exact gradients with gradient-based optimization reduces the number of function calls by several orders of magnitude. The case studies also show that adding curvature improves convergence behavior, allowing gradient-based optimization algorithms used with the FLORIS model to more reliably find better solutions to wind farm optimization problems.

17 WIND ENERGY↗
DOE OSTI2026

Computing an Optimal Entanglement Path with Throughput and Fidelity Considerations

Entanglement distribution is a core function of quantum networks essential for operations including teleportation, distributed quantum sensing, and multisite computation. Entanglement throughput and fidelity are two critical performance measures that depend on the quantum transmission along the links and swapping operations at the repeaters along the path. We study the problem of computing a end-to-end entanglement path that satisfies both fidelity and throughput requirements, leveraging qubit buffers at the nodes and considering the sequential swapping order. We show that the general problem of simultaneously satisfying both metrics to be NP-hard, and develop an algorithm to maximize throughput subject to a given fidelity threshold. We introduce the concepts of entanglement probability distribution and path domination and exploit them in the design of our algorithm. Extensive numerical results show that our algorithm can find optimal solutions in networks with thousands of nodes in less than a second. We also describe practical and possible implementation aspects of this algorithm in terms of devices and architecture support.

Xue, Guoliang [Arizona State University]↗