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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A Flexible Quasi-Static Mooring Design Optimization Method for Floating Structures

This paper presents a flexible and efficient design method for optimizing the mooring systems of floating structures. Mooring system optimization is challenging because of the strong nonlinearity of mooring system behavior and the many technical constraints that must be satisfied. Furthermore, different mooring configurations can have very different design spaces. While some successful examples of mooring design optimization exist in the literature, developing an optimization approach that can work across various mooring design problems is a larger challenge. We present such a method based on a flexible parameterization that allows a wide variety of mooring designs to be described by a list of variables, a quasi-static mooring model that provides efficient evaluation of a mooring design without directly considering mooring system dynamics, and an optimization framework that generates, evaluates, and adjusts the mooring design while considering user-specified constraints such as offset limits, strength safety factors, and seabed contact limits. We demonstrate the design optimization framework on four mooring design problems, each for a different type of mooring system. We compare the use of different design modes to simplify the optimization problem, showing that they can reduce the computation time by up to 75%. We also compare different optimization algorithms and find that the resulting computational speed can vary by up to 51 times. We perform a sensitivity study on one design and find that the local sensitivity of anchoring radius to water depth has a positive correlation of 0.29, but the global sensitivity shows large nonlinearities. Lastly, we perform a coupled dynamic analysis on one of the optimized designs and find that the predicted mean platform motions and mooring line tensions are within 1% of dynamic results and the extreme motions and tensions are within 14%. Lastly, we show that a DEA-Chain-Polyester mooring configuration is cost-optimal for the given design problem of the demonstrations, which aligns with general industry practice.

16 TIDAL AND WAVE POWER↗
DOE OSTI2012

Neutronic optimization in high conversion Th-{sup 233}U fuel assembly with simulated annealing

This paper reports on fuel design optimization of a PWR operating in a self sustainable Th-{sup 233}U fuel cycle. Monte Carlo simulated annealing method was used in order to identify the fuel assembly configuration with the most attractive breeding performance. In previous studies, it was shown that breeding may be achieved by employing heterogeneous Seed-Blanket fuel geometry. The arrangement of seed and blanket pins within the assemblies may be determined by varying the designed parameters based on basic reactor physics phenomena which affect breeding. However, the amount of free parameters may still prove to be prohibitively large in order to systematically explore the design space for optimal solution. Therefore, the Monte Carlo annealing algorithm for neutronic optimization is applied in order to identify the most favorable design. The objective of simulated annealing optimization is to find a set of design parameters, which maximizes some given performance function (such as relative period of net breeding) under specified constraints (such as fuel cycle length). The first objective of the study was to demonstrate that the simulated annealing optimization algorithm will lead to the same fuel pins arrangement as was obtained in the previous studies which used only basic physics phenomena as guidance for optimization. In the second part of this work, the simulated annealing method was used to optimize fuel pins arrangement in much larger fuel assembly, where the basic physics intuition does not yield clearly optimal configuration. The simulated annealing method was found to be very efficient in selecting the optimal design in both cases. In the future, this method will be used for optimization of fuel assembly design with larger number of free parameters in order to determine the most favorable trade-off between the breeding performance and core average power density. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2013

Multi-cycle boiling water reactor fuel cycle optimization

In this work a new computer code, BWROPT (Boiling Water Reactor Optimization), is presented. BWROPT uses the Parallel Simulated Annealing (PSA) algorithm to solve the out-of-core optimization problem coupled with an in-core optimization that determines the optimum fuel loading pattern. However it uses a Haling power profile for the depletion instead of optimizing the operating strategy. The result of this optimization is the optimum new fuel inventory and the core loading pattern for the first cycle considered in the optimization. Several changes were made to the optimization algorithm with respect to other nuclear fuel cycle optimization codes that use PSA. Instead of using constant sampling probabilities for the solution perturbation types throughout the optimization as is usually done in PSA optimizations the sampling probabilities are varied to get a better solution and/or decrease runtime. The new fuel types available for use can be sorted into an array based on any number of parameters so that each parameter can be incremented or decremented, which allows for more precise fuel type selection compared to random sampling. Also, the results are sorted by the new fuel inventory of the first cycle for ease of comparing alternative solutions. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Development of Multiresolution Capabilities for the Holistic Energy Resource Optimization Network (HERON) tool A progress update

INL researchers work on technoeconomic analyses for integrated energy systems (IES) using the Framework for Optimization of ResourCes and Economics (FORCE). Within FORCE, researchers use the Holistic Energy Resource Optimization Network (HERON) tool to conduct optimization of grid portfolios under uncertain market conditions. These optimizations determine optimal capacities for all IES components and strategies for resource dispatch which maximize some economic metric (e.g., net present value). Resource dispatch occurs on finer timescales (typically hours) and thus are asked to respond to a given time series (e.g. hourly load demand profiles for a grid, or pre-determined electricity prices). Volatile and complex bidding dynamics as well as poorly forecasted weather events within deregulated markets add uncertainty to the time series; FORCE can address this uncertainty by training a reduced order model on historical time series and generate unique synthetic time series which represent individual scenarios or realizations of the market. The IES configuration can be simulated under these different sampled realizations and a stochastic optimization is conducted which optimizes the expected value of the desired economic metric. The training of a synthetic time series generator is limited by the chosen time resolution; dynamics can occur on different time scales. Seasonal demand trends can dominate faster dynamical events (such as power outages from certain sectors or severe weather events) which might not get captured correctly by the trained model. In this report, we investigate different ways of addressing the training and generation of time series on multiple time scales using three main algorithms: wavelet decomposition, dynamic mode decomposition, and generative adversarial networks for time series. We demonstrate a time series analysis that yields information on not just the frequency space but also temporal space: where a fast Fourier transform can provide what frequencies dominate, the new algorithms can provide when the frequencies dominate as well. These analyses can help improve IES optimization by allowing researchers to couple simulations at different timescales when it is most needed - seasonal, day-ahead, and real time optimization - with greater computational efficiency. Future work will include implementation of a subset of the proposed algorithms into the FORCE toolset and application of these analyses into multiple timescale optimization.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Sampling Size Optimization for Bioburden Density Estimation in Planetary Protection

Planetary protection (PP) is a discipline that focuses on minimizing the biological contamination of spacecraft to ensure compliance with international policy. Precise estimation of bioburden - the total number of microbes in or on spacecraft hardware – and the bioburden density are of utmost importance for PP. Such estimation is the way concordance with requirements is demonstrated, and it is critical for quantifying the potential risk of inadvertently contaminating other planetary bodies. Although a suite of molecular techniques have been used to thoroughly characterize and profile the microbiome of various cleanroom environments and spacecraft, the gold standard remains the physical enumeration of microbes via culturing of samples directly taken from spacecraft and associated surfaces. However, due to technical, budgetary, and programmatic constraints, only a manageable portion (around 10%) of the entire spacecraft surface is directly sampled with cotton swabs or wipes. To generate the bioburden current best estimate (CBE) for components not directly verifiable, the accepted approach is to apply a NASA-defined bioburden estimate based on the components’ manufacturing or assembly environment. This approach utilizes a prespecified bioburden density estimation that applies a maximum value across the total surface area of the specified component. For hardware components that underwent similar assembly processes, an implied bioburden is adopted for all components, based on a direct verification of a representative component within the same lot. Once all components have a CBE, the bioburden estimates are generated. In previous publication [ 1], we have shown that statistical risks quantifying the accuracy of the estimates for sampled, prespecified, and implied components can be derived and ranked. For mean squared error (MSE) function, the risks are available analytically and hence a cost function can be obtained to optimize the risks with respect to the sampling area and sampling cost. Since the sampling area and sampling cost are two complimentary variables, their sum will have a well-defined minimum. This paper presents the multivariate optimization of the integrated risk of an empirical Bayes estimator to determine the optimal sampling schedule for a given number of components. It is assumed that given a number of components, N, the bioburden density for each component can either be sampled, implied, or prespecified. The multivariate optimization searches through different options to sample, imply or prespecify the bioburden density for a component, and account for the component’s surface area and cost of sampling. The idea of the optimization is based on the observation that the statistical risk of using an estimator is a monotonically decreasing function of the sampled area. The larger the sampled area, the lower the risk of using the estimator as the estimator becomes more and more accurate as the sampling area increases. On the other hand, the cost of sampling is monotonically increasing as the sampled surface grows. This makes the risk and total cost of sampling complimentary variables which can be counterbalanced to achieve an optimal overall value with respect to the sampled surface. In this paper, the integrated risk has been used to quantify the accuracy of the estimator. This risk has been selected because it depends on neither the true value of the parameter nor on the collected data. The cost of each sample was also available to obtain the total cost of sampling of N components. The paper will present the results based on computer-simulated data as well as the data collected during the InSight mission. The computer-simulated data have N components with randomly generated total areas and each component assigned to one of the three categories according to the method of estimating of bioburden density: sampled, implied, or prespecified. The cost of sampling is also available. The cost of sampling is estimated based on a cost model provided by the planetary protection group at JPL. For this paper, the overall cost was assumed to be a linear function of exposure. The optimization process finds the allocation of the components to the three categories that minimizes the tradeoff between integrated risk and total cost. For the InSight data, a set of components is selected representing all three categories, and optimization is performed to determine if the performed allocation was optimal or if a better allocation could have been obtained. To the best of our knowledge, this work is the first attempt not only perform an accurate estimation of bioburden density but also do it in an optimal way.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fast yaw optimization for wind plant wake steering using Boolean yaw angles

Abstract. In wind plants, turbines can be yawed into the wind to steer their wakes away from downstream turbines and achieve an overall increase in plant power. Mathematical optimization is typically used to determine the best yaw angles at which to operate the turbines in a plant. In this paper, we present a new heuristic to rapidly determine the yaw angles in a wind plant. In this method, we define the turbine yaw angles as Boolean – either yawed at a predefined angle or nonyawed – as opposed to the typical methods of defining yaw angles as continuous or with fine discretizations. We then optimize which turbines should be yawed with an algorithm that sweeps through the turbines from the most upstream to the most downstream. We demonstrate that our new Boolean optimization method can find turbine yaw angles that perform well compared to a traditionally used gradient-based optimizer for which the yaw angles are defined as continuous. There is less than 0.6 % difference in the optimized power between the two optimization methods for randomly placed turbine layouts and less than a 0.6 % difference in the optimal annual energy production between the two optimization methods for a real wind farm. Additionally, we show that our new method is much more computationally efficient than the traditional method. For plants with nonzero optimal yaw angles, our new method is generally able to solve for the turbine yaw angles 50–150 times faster, and in some extreme cases up to 500 times faster, than the traditional method.

17 WIND ENERGY↗
DOE OSTI2021

The impacts of convex piecewise linear cost formulations on AC optimal power flow

Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is the treatment of power generation cost functions, where nonlinear network optimization has largely used polynomial representations and market optimization has adopted piecewise linear encodings. This work combines state-of-the-art results from both lines of research to understand the best mathematical formulations of the nonlinear AC optimal power flow problem with piecewise linear generation cost functions. An extensive numerical analysis of non-convex models, linear approximations, and convex relaxations across fifty-four realistic test cases illustrates that nonlinear optimization methods are surprisingly sensitive to the mathematical formulation of piecewise linear functions. The results indicate that a poor formulation choice can slow down algorithm performance by a factor of ten, increasing the runtime from seconds to minutes. Furthermore, these results provide valuable insights into the best formulations of nonlinear optimal power flow problems with piecewise linear cost functions, an important step towards building a new generation of energy markets that incorporate the nonlinear AC power flow model.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2017

Deterministic direct aperture optimization using multiphase piecewise constant segmentation

Purpose Direct aperture optimization (DAO) attempts to incorporate machine constraints in the inverse optimization to eliminate the post‐processing steps in fluence map optimization (FMO) that degrade plan quality. Current commercial DAO methods utilize a stochastic or greedy approach to search a small aperture solution space. In this study, we propose a novel deterministic direct aperture optimization that integrates the segmentation of fluence map in the optimization problem using the multiphase piecewise constant Mumford‐Shah formulation. Methods The Mumford‐Shah based direct aperture optimization problem was formulated to include an L2‐norm dose fidelity term to penalize differences between the projected dose and the prescribed dose, an anisotropic total variation term to promote piecewise continuity in the fluence maps, and the multiphase piecewise constant Mumford‐Shah function to partition the fluence into pairwise discrete segments. A proximal‐class, first‐order primal‐dual solver was implemented to solve the large scale optimization problem, and an alternating module strategy was implemented to update fluence and delivery segments. Three patients of varying complexity—one glioblastoma multiforme (GBM) patient, one lung (LNG) patient, and one bilateral head and neck (H&N) patient with 3 PTVs—were selected to test the new DAO method. For each patient, 20 non‐coplanar beams were first selected using column generation, followed by the Mumford‐Shah based DAO (DAO MS ). For comparison, a popular and successful approach to DAO known as simulated annealing—a stochastic approach—was replicated. The simulated annealing DAO (DAO SA ) plans were then created using the same beam angles and maximum number of segments per beam. PTV coverage, PTV homogeneity , and OAR sparing were assessed for each plan. In addition, high dose spillage, defined as the 50% isodose volume divided by the tumor volume, as well as conformity, defined as the van't Riet conformation number, were evaluated. Results DAO MS achieved essentially the same OAR doses compared with the DAO SA plans for the GBM case. The average difference of OAR D max and D mean between the two plans were within 0.05% of the plan prescription dose. The lung case showed slightly improved critical structure sparing using the DAO MS approach, where the average OAR D max and D mean were reduced by 3.67% and 1.08%, respectively, of the prescription dose. The DAO MS plan substantially improved OAR dose sparing for the H&N patient, where the average OAR D max and D mean were reduced by over 10% of the prescription dose. The DAO MS and DAO SA plans were comparable for the GBM and LNG PTV coverage, while the DAO MS plan substantially improved the H&N PTV coverage, increasing D99 by 6.98% of the prescription dose. For the GBM and LNG patients, the DAO MS and DAO SA plans had comparable high dose spillage but slightly worse conformity with the DAO MS approach. For the H&N plan, DAO MS was considerably superior in high dose spillage and conformity to the DAO SA . The deterministic approach is able to solve the DAO problem substantially faster than the simulated annealing approach, with a 9.5‐ to 40‐fold decrease in total solve time, depending on the patient case. Conclusions A novel deterministic direct aperture optimization formulation was developed and evaluated. It combines fluence map optimization and the multiphase piecewise constant Mumford‐Shah segmentation into a unified framework, and the resulting optimization problem can be solved efficiently. Compared to the widely and commercially used simulated annealing DAO approach, it showed comparable dosimetry behavior for simple plans, and substantially improved OAR sparing, PTV coverage, PTV homogeneity, high dose spillage, and conformity for the more complex head and neck plan.

Nguyen, Dan↗
DOE OSTI2014

Progressive construction of a parametric reduced‐order model for PDE‐constrained optimization

Summary An adaptive approach to using reduced‐order models (ROMs) as surrogates in partial differential equations (PDE)‐constrained optimization is introduced that breaks the traditional offline‐online framework of model order reduction. A sequence of optimization problems constrained by a given ROM is defined with the goal of converging to the solution of a given PDE‐constrained optimization problem. For each reduced optimization problem, the constraining ROM is trained from sampling the high‐dimensional model (HDM) at the solution of some of the previous problems in the sequence. The reduced optimization problems are equipped with a nonlinear trust‐region based on a residual error indicator to keep the optimization trajectory in a region of the parameter space where the ROM is accurate. A technique for incorporating sensitivities into a reduced‐order basis is also presented, along with a methodology for computing sensitivities of the ROM that minimizes the distance to the corresponding HDM sensitivity, in a suitable norm. The proposed reduced optimization framework is applied to subsonic aerodynamic shape optimization and shown to reduce the number of queries to the HDM by a factor of 4‐5, compared with the optimization problem solved using only the HDM, with errors in the optimal solution far less than 0.1%. Copyright © 2014 John Wiley & Sons, Ltd.

Zahr, Matthew J.↗
DOE OSTI2017

Co-optimization of CO 2 -EOR and Storage Processes under Geological Uncertainty

This paper presents an integrated numerical framework to co-optimize EOR and CO 2 storage performance in the Farnsworth field unit (FWU), Ochiltree County, Texas. The framework includes a field-scale compositional reservoir flow model, an uncertainty quantification model and a neural network optimization process. The reservoir flow model has been constructed based on the field geophysical, geological, and engineering data. A laboratory fluid analysis was tuned to an equation of state and subsequently used to predict the thermodynamic minimum miscible pressure (MMP). A history match of primary and secondary recovery processes was conducted to estimate the reservoir and multiphase flow parameters as the baseline case for analyzing the effect of recycling produced gas, infill drilling and water alternating gas (WAG) cycles on oil recovery and CO 2 storage. A multi-objective optimization model was defined for maximizing both oil recovery and CO 2 storage. The uncertainty quantification model comprising the Latin Hypercube sampling, Monte Carlo simulation, and sensitivity analysis, was used to study the effects of uncertain variables on the defined objective functions. Uncertain variables such as bottom hole injection pressure, WAG cycle, injection and production group rates, and gas-oil ratio among others were selected. The most significant variables were selected as control variables to be used for the optimization process. A neural network optimization algorithm was utilized to optimize the objective function both with and without geological uncertainty. The vertical permeability anisotropy (Kv/Kh) was selected as one of the uncertain parameters in the optimization process. The simulation results were compared to a scenario baseline case that predicted CO 2 storage of 74%. The results showed an improved approach for optimizing oil recovery and CO 2 storage in the FWU. The optimization process predicted more than 94% of CO 2 storage and most importantly about 28% of incremental oil recovery. The sensitivity analysis reduced the number of control variables to decrease computational time. A risk aversion factor was used to represent results at various confidence levels to assist management in the decision-making process. The defined objective functions were proved to be a robust approach to co-optimize oil recovery and CO 2 storage. The Farnsworth CO 2 project will serve as a benchmark for future CO 2 –EOR or CCUS projects in the Anadarko basin or geologically similar basins throughout the world.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

NEXTorch: A Design and Bayesian Optimization Toolkit for Chemical Sciences and Engineering

Automation and optimization of chemical systems require well-informed decisions on what experiments to run to reduce time, materials, and/or computations. Data-driven active learning algorithms have emerged as valuable tools to solve such tasks. Bayesian optimization, a sequential global optimization approach, is a popular active-learning framework. Past studies have demonstrated its efficiency in solving chemistry and engineering problems. Here we introduce NEXTorch, a library in Python/PyTorch, to facilitate laboratory or computational design using Bayesian optimization. NEXTorch offers fast predictive modeling, flexible optimization loops, visualization capabilities, easy interfacing with legacy software, and multiple types of parameters and data type conversions. It provides GPU acceleration, parallelization, and state-of-the-art Bayesian optimization algorithms and supports both automated an d human-in-the-loop optimization. The comprehensive online documentation introduces Bayesian optimization theory and several examples from catalyst synthesis, reaction condition optimization, parameter estimation, and reactor geometry optimization. NEXTorch is open-source and available on GitHub

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Comparison of tungsten versus molybdenum for double shell capsules using machine learning design optimization

Double shell targets are an alternative ignition platform for inertial confinement fusion. One design consideration for double shell targets is the choice of inner shell material to help trap radiation emitted by the hot fuel to aid ignition. Materials such as molybdenum and tungsten are of interest for the inner shell layer of the targets. While molybdenum has a lower density that could inhibit instability growth and allow for radiography and code benchmarking, tungsten has a higher density that could provide more compression and confinement. These tradeoffs have been explored using optimized designs for each material. Our previous work [Vazirani et al., “Coupling 1D xRAGE simulations with machine learning for graded inner shell design optimization in double shell capsules,” Phys. Plasmas 28, 122709 (2021); Vazirani et al., “Coupling multi-fidelity xRAGE with machine learning for graded inner shell design optimization in double shell capsules,” Phys. Plasmas 30, 062704 (2023); and Vazirani et al., “Bayesian batch optimization for molybdenum versus tungsten inertial confinement fusion double shell target design,” Stat. Anal. Data Min. 17, e11698 (2024)] resulted in a multi-fidelity Bayesian optimization framework to find yield-optimized double shell target geometries. By leveraging simulations of varying fidelities (one-dimensional and two-dimensional) to inform one another, the multi-fidelity optimization was able to optimize a design in the highest fidelity with significantly fewer simulations than would be used in a systematic parameter scan. In this work, we apply the multi-fidelity Bayesian optimization to explore the optimized designs of double shell targets with molybdenum and tungsten inner shells as well as the physics producing the high performing implosions. A physics exploration of all the simulations used in this study shows trends in designs that contribute to high yields, ion temperatures, and fuel areal densities. Comparison of molybdenum and tungsten simulations shows that they can produce similar implosion conditions with different geometries, which would be important to study in experiments. Graded density layers produce varying performances with the two materials but continue to be of interest for future studies along with studies of doped inner shell materials and applied surface roughness.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Evaluating Optimization Strategies for Engine Simulations Using Machine Learning Emulators

This work evaluates different optimization algorithms for computational fluid dynamics (CFD) simulations of engine combustion. Due to the computational expense of CFD simulations, emulators built with machine learning algorithms were used as surrogates for the optimizers. Two types of emulators were used: a Gaussian process (GP) and a weighted variety of machine learning methods called SuperLearner (SL). The emulators were trained using a dataset of 2048 CFD simulations that were run concurrently on a supercomputer. The design of experiments (DOE) for the CFD runs was obtained by perturbing nine input parameters using a Monte-Carlo method. The CFD simulations were of a heavy duty engine running with a low octane gasoline-like fuel at a partially premixed compression ignition mode. Ten optimization algorithms were tested, including types typically used in research applications. Each optimizer was allowed 800 function evaluations and was randomly tested 100 times. The optimizers were evaluated for the median, minimum, and maximum merits obtained in the 100 attempts. Some optimizers required more sequential evaluations, thereby resulting in longer wall clock times to reach an optimum. The best performing optimization methods were particle swarm optimization (PSO), differential evolution (DE), GENOUD (an evolutionary algorithm), and micro-genetic algorithm (GA). These methods found a high median optimum as well as a reasonable minimum optimum of the 100 trials. Moreover, all of these methods were able to operate with less than 100 successive iterations, which reduced the wall clock time required in practice. Two methods were found to be effective but required a much larger number of successive iterations: the DIRECT and MALSCHAINS algorithms. A random search method that completed in a single iteration performed poorly in finding optimum designs but was included to illustrate the limitation of highly concurrent search methods. The last three methods, Nelder–Mead, bound optimization by quadratic approximation (BOBYQA), and constrained optimization by linear approximation (COBYLA), did not perform as well.

Probst, Daniel M.↗
DOE OSTI2014

Beamlet based direct aperture optimization for MERT using a photon MLC

Purpose: A beamlet based direct aperture optimization (DAO) for modulated electron radiotherapy (MERT) using photon multileaf collimator (pMLC) shaped electron fields is developed and investigated. Methods: The Swiss Monte Carlo Plan (SMCP) allows the calculation of dose distributions for pMLC shaped electron beams. SMCP is interfaced with the Eclipse TPS (Varian Medical Systems, Palo Alto, CA) which can thus be included into the inverse treatment planning process for MERT. This process starts with the import of a CT-scan into Eclipse, the contouring of the target and the organs at risk (OARs), and the choice of the initial electron beam directions. For each electron beam, the number of apertures, their energy, and initial shape are defined. Furthermore, the DAO requires dose–volume constraints for the structures contoured. In order to carry out the DAO efficiently, the initial electron beams are divided into a grid of beamlets. For each of those, the dose distribution is precalculated using a modified electron beam model, resulting in a dose list for each beamlet and energy. Then the DAO is carried out, leading to a set of optimal apertures and corresponding weights. These optimal apertures are now converted into pMLC shaped segments and the dose calculation for each segment is performed. For these dose distributions, a weight optimization process is launched in order to minimize the differences between the dose distribution using the optimal apertures and the pMLC segments. Finally, a deliverable dose distribution for the MERT plan is obtained and loaded back into Eclipse for evaluation. For an idealized water phantom geometry, a MERT treatment plan is created and compared to the plan obtained using a previously developed forward planning strategy. Further, MERT treatment plans for three clinical situations (breast, chest wall, and parotid metastasis of a squamous cell skin carcinoma) are created using the developed inverse planning strategy. The MERT plans are compared to clinical standard treatment plans using photon beams and the differences between the optimal and the deliverable dose distributions are determined. Results: For the idealized water phantom geometry, the inversely optimized MERT plan is able to obtain the same PTV coverage, but with an improved OAR sparing compared to the forwardly optimized plan. Regarding the right-sided breast case, the MERT plan is able to reduce the lung volume receiving more than 30% of the prescribed dose and the mean lung dose compared to the standard plan. However, the standard plan leads to a better homogeneity within the CTV. The results for the left-sided thorax wall are similar but also the dose to the heart is reduced comparing MERT to the standard treatment plan. For the parotid case, MERT leads to lower doses for almost all OARs but to a less homogeneous dose distribution for the PTV when compared to a standard plan. For all cases, the weight optimization successfully minimized the differences between the optimal and the deliverable dose distribution. Conclusions: A beamlet based DAO using multiple beam angles is implemented and successfully tested for an idealized water phantom geometry and clinical situations.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Red-QAOA: Efficient Variational Optimization through Circuit Reduction

The Quantum Approximate Optimization Algorithm (QAOA) provides a quantum solution for combinatorial optimization problems. However, the optimal parameter searching process of QAOA is greatly affected by noise, leading to non-optimal solutions. This paper introduces a novel approach to optimize QAOA by exploiting the energy landscape concentration of similar instances via graph reduction, thus addressing the effect of noise. We formalize the notion of similar instances in QAOA and develop a Simulated Annealing-based graph reduction algorithm, called Red-QAOA, to identify the most similar subgraph for efficient parameter optimization. Red-QAOA outperforms state-of-the-art Graph Neural Network (GNN) based graph pooling techniques in performance and demonstrates effectiveness on a diverse set of real-world optimization problems encompassing 3200 graphs. Red-QAOA reduced the node counts and edge counts by 28% and 37%, respectively, while maintaining a low mean square error of 2%. These enable the identification of an optimal parameter set that is closer to the ideal true optimal solution in the presence of noise. By substantially streamlining the search for QAOA parameters, our approach sets the stage for the practical application of quantum algorithms in solving complex optimization problems.

Wang, Meng↗
DOE OSTI2019

Fast, Dynamic, and Scalable Algorithms for Large-Scale Constrained Optimization

Scientists and engineers constantly aim to optimize an objective subject to physical, environmental, and/or resource constraints. The technique of using mathematical models to formulate and find real solutions of such problems is known as mathematical optimization, a process that has become invaluable for design and discovery in numerous scientific fields. This project has focused on the design, analysis, and implementation of high-performance computing algorithms for solving cutting-edge optimization problems. These include problems that involve (1) data uncertainties, such as those in the future supply, demand, and capacity of a given power system, (2) extreme numbers of alternatives, such as in the design of electrical power grids to avoid network vulnerabilities, and (3) real-time decisions, such as in the control of chemical reactors. The key features of the new algorithms are that they are fast, dynamic, and scalable to meet the computational requirements of scientists and researchers working to optimize large-scale, complex systems. The algorithms that have been designed, analyzed, and tested as part of the project can be characterized based on the types of optimization problems they have been designed to solve. Much of the work has focused on algorithms for solving large-scale constrained optimization problems. Contributions have also been made in the design of algorithms for unconstrained optimization, with some specialized methods for solving problems that have inherent nonsmoothness. Contributions have also been made in areas that have grown to prominence in the field over the five-year award period. These include the design of algorithms for solving large-scale stochastic optimization problems, such as those that arise in large-scale machine learning, and in complexity analyses for solving nonconvex problems, which has been a focal point of much recent work in continuous optimization. Overall, the project has supported work that has led to almost 30 articles that have been published or accepted to top journals in the field of mathematical optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Impact of K-Optimization on Trap Concentration in (Ag,Cu)(In,Ga)Se 2 Solar Cells

Recent progress has been made in improving efficiency in Cu(In,Ga)Se 2 (CIGS) absorbers with steady increases in peak efficiency. One way this has been achieved is by adding Ag to CIGS (ACIGS) to achieve higher V OC . However, these efficiencies are still well below the Shockley-Queisser efficiency limit, and traps acting as recombination centers and compensating centers are one thing limiting the solar efficiency. Past research in CIGS has shown that alkali treatment can improve the efficiency and metastability problems in CIGS, but less is understood about the role of alkali treatments in ACIGS. Here, we investigate the impact of potassium in ACIGS through its impact on trap incorporation and minority carrier lifetime. The samples in this study were grown in a roll-to-roll coater with Mo, ACIGS, CdS, and ZnO structure. Both cells were grown identically except the second (K-optimized) cell was grown with increased K-doping of the Mo contact and was more Cu-poor near the surface to optimize the K profile. This resulted in an efficiency increase from 16.8% to 18.7% for the K-optimized cell, which was mostly due to a 65 mV V OC increase. The doping profile showed a 2X increase in acceptor concentration of the K-optimized cell (2.5×10 15 cm -3 ) which suggests that the K was better incorporated into the ACIGS after these optimizations. To characterize the traps in these cells, deep level transient and optical spectroscopy were used. The DLOS measurements showed an EV+0.98 eV trap whose concentration was reduced 10X in the K-optimized cell (4×10 14 cm -3 ). This is consistent with previous results from the alkali treatment in CIGS, which also showed a decrease in near-conduction band trap concentration [1], but the reduction was larger than previous studies possibly indicating the combination of K and Cu-poor surface may both have aided in reducing the EV+0.98 eV trap concentration. The other primary trap is the mid-gap trap (EV+0.58 eV), which was quantified using DLTS. Its concentration decreased from 9×10 13 cm -3 to 4×10 13 cm -3 in the K-optimized sample, which is a 2X reduction. Previous studies have shown this trap is likely an efficient recombination center [2], which makes sense because it is near mid-gap. This trap has also been associated with V OC instability and reduction, so reducing this trap concentration is essential to achieve high V OC and cell efficiency. To help confirm this association, time-resolved photoluminescence measurements have shown in this sample set and a previous study that the minority carrier lifetime (19 ns baseline to 56 ns K-optimized) and this EV+0.56 eV trap concentration are inversely proportional, which would be expected for a recombination-limited carrier lifetime. The K optimization of ACIGS results in significantly improved cell efficiency and reduced trap concentrations that correlate with the improved material and electrical properties. We will report on this and the impact of the K optimization on the cell metastability.

14 SOLAR ENERGY↗
DOE OSTI2021

Model-based Design Optimization to Achieve the Performance Goals (16.0 SEER/9.5 HSPF), Developing Heat Pump by Using Low-GWP Refrigerants and 5 mm Diameter Tubes

Usage of low-GWP refrigerants can reduce the Green House Gas (GHG) emission of HVAC systems. Our research in previous milestone report has shown that using heat exchangers with 5 mm diameter tubes instead of 9 mm diameter tubes is a promising solution to meet the performance goals of heat pump using low-GWP refrigerants. In addition, the 5mm tube heat exchangers can lead to lower system refrigerant charge and as a result, reduce environmental impact further. However, shifting to small tube diameters requires in-depth heat exchanger design optimization to adapt to the transition to low-GWP refrigerants. In the 2nd quarter of FY21, we conducted multi-objective optimizations using Particle Swarm Optimization algorithm on a residential 5-ton air source heat pump to investigate the potential system performance improvements and material savings. 4 low-GWP refrigerants, ARM20A, ARM20B, R454A and R454C are investigated in this study. The objectives of the optimization are to minimize the heat pump material cost and to maximize the system performance simultaneously. As a result, the HXs material cost is reduced by up to 77% according to the copper and aluminum material price in current market. Under heating mode operation, the smart 4-way valve guarantees that the optimal low-GWP systems maintain or outperform the heating performance of the R410A baseline system. The model-based design optimization yields 18.3-18.9 SEER and 10.6-11.9 HSPF for optimal systems using different low-GWP refrigerants. The initial performance goals (16.0 SEER/9.5 HSPF) are achieved. Furthermore, up to 50% system refrigerant charge reduction is possible in the optimized low-GWP heat pump system using ARM20B. And 91%-95% predicted life-time direct CO 2 emission reduction is achieved by using the optimal 5mm tube low-GWP heat pumps. The significant material saving, charge reduction and direct CO 2 emission reduction help in reducing the environmental impacts of heat pump systems. The optimal heat exchangers resulting from this research can fit into the original baseline indoor and outdoor fan-coil unit. This can reduce the retrofitting effort by minimizing the change in manufacturing and installation of the heat pumps and guarantee the compatibility with end-users’ house structure. Finally, the new products can be easily accepted by manufacturers and end-users.

42 ENGINEERING↗