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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Chance-Constrained AC Optimal Power Flow: Reformulations and Efficient Algorithms

Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. Here, in this paper, we adopt a chance-constrained AC optimal power flow formulation, which guarantees that generation, power flows and voltages remain within their bounds with a pre-defined probability. We then discuss different chance-constraint reformulations and solution approaches for the problem. Additionally, we first discuss an analytical reformulation based on partial linearization, which enables us to obtain a tractable representation of the optimization problem. We then provide an efficient algorithm based on an iterative solution scheme which alternates between solving a deterministic AC OPF problem and assessing the impact of uncertainty. This more flexible computational framework enables not only scalable implementations, but also alternative chance-constraint reformulations. In particular, we suggest two sample based reformulations that do not require any approximation or relaxation of the AC power flow equations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Distributed Direction-Optimizing Label Propagation for Community Detection

Designing a scalable algorithm for community detec-tion is challenging due to the tradeoff between the performance and the quality of the result. We propose a new distributed algorithm for community detection —Direction-Optimizing Label Propagation Algorithm, based on a novel Label Propagation Algorithm in community detection. The algorithm is inspired by the direction optimization technique for graph traversal algorithms and relies on the use of frontiers and alternates between label push and label pull operations. This organization creates ?exibility and affords opportunities for balancing the performance and the quality of the solution. We implement our algorithm in distributed memory with an active-message based asynchronous many-task runtime, AM++. We experiment with two seeding strategies for initial seeding stage, namely, random seeding and degree seeding. With the Graph Challenge datasets, our distributed implementation, in conjunction with the runtime support, achieves very good performance and reasonable quality of solution.

Liu, Xu↗
DOE OSTI2023

Diabatic quantum annealing for the frustrated ring model

Abstract Quantum annealing (QA) is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare ground state and a problem Hamiltonian whose ground state encodes solutions to an optimization problem. The standard implementation relies on the evolution being adiabatic: keeping the system in the instantaneous ground state with high probability and requiring a time scale inversely related to the minimum energy gap between the instantaneous ground and excited states. However, adiabatic evolution can lead to evolution times that scale exponentially with the system size, even for computationally simple problems. Here, we study whether non-adiabatic evolutions with optimized annealing schedules can bypass this exponential slowdown for one such class of problems called the frustrated ring model. For sufficiently optimized annealing schedules and system sizes of up to 39 qubits, we provide numerical evidence that we can avoid the exponential slowdown. Our work highlights the potential of highly-controllable QA to circumvent bottlenecks associated with the standard implementation of QA.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Open-source Tools for Solving Grid Optimization Problems: ARPA-e Benchmark Algorithm Overview [Slides]

This document contains the official formulation that will be used for evaluation in Challenge 2 of the Grid Optimization (GO) Competition. Minor changes may occur within the formulation. Entrants will be notified when a new version is released. Changes are not expected to be of a significance that would cause a change in approach for the Entrants. This formulation builds upon the Challenge 1 formulation published in ARPA-E DE-FOA-0001952. Entrants will be judged based on the current official Challenge 2 formulation posted on the GO Competition website (this document, which is subject to change), not the formulation posted in DE-FOA-0001952. Entrants are permitted and encouraged to use any alternative problem formulation and modeling convention within their own software (such as convex relaxation, decoupled power flow formulations, current-voltage formulations, etc.) in an attempt to produce an exact or approximate solution to this particular mathematical program. However, the judging of all submitted approaches must conform to the official formulation presented here.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Dark Energy Survey: Galaxy sample for the baryonic acoustic oscillation measurement from the final dataset

In this paper, we present and validate the galaxy sample used for the analysis of the baryon acoustic oscillation (BAO) signal in the Dark Energy Survey (DES) Y6 data. The definition is based on a color and redshift-dependent magnitude cut optimized to select galaxies at redshifts higher than 0.6, while ensuring a high-quality photo- z determination. The optimization is performed using a Fisher forecast algorithm, finding the optimal i -magnitude cut to be given by i < 19.64 + 2.894 z ph . For the optimal sample, we forecast an increase in precision in the BAO measurement of ∼ 25 % with respect to the Y3 analysis. Our BAO sample has a total of 15,937,556 galaxies in the redshift range 0.6 < z ph < 1.2 , and its angular mask covers 4 , 273.42 deg 2 to a depth of i = 22.5 . We validate its redshift distributions with three different methods: directional neighborhood fitting algorithm (DNF), which is our primary photo- z estimation; direct calibration with spectroscopic redshifts from VIPERS, which is a spectroscopic galaxy sample that overlaps with our BAO sample and is complete within our selection cuts; and clustering redshift using SDSS galaxies. The fiducial redshift distribution is a combination of these three techniques performed by modifying the mean and width of the DNF distributions to match those of VIPERS and clustering redshift. In this paper, we also describe the methodology used to mitigate the effect of observational systematics, which is analogous to the one used in the Y3 analysis. This paper is one of the two dedicated to the analysis of the BAO signal in DES Y6. In its companion paper, we present the angular diameter distance constraints obtained through the fitting to the BAO scale.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Hierarchical Optimal Power Flow with Improved Gradient Evaluation

Existing algorithms to solve alternating-current optimal power flow (AC-OPF) often exploit linear approximations to simplify system models and accelerate computations. In this paper, we improve a recent hierarchical OPF algorithm, which rested on primal-dual gradients evaluated in a linearized distribution power flow model. Specifically, we identify a risk of voltage violation arising from the model linearization, and propose a more accurate gradient evaluation method to eliminate that risk. We further develop a hierarchical primal-dual algorithm to solve OPF based on the proposed gradient evaluation method. Numerical results on IEEE networks show that our algorithm can enhance voltage safety with satisfactory computational efficiency.

distributed algorithm↗
DOE OSTI2014

Deformable image registration based automatic CT-to-CT contour propagation for head and neck adaptive radiotherapy in the routine clinical setting

Purpose: To evaluate the clinical potential of deformable image registration (DIR)-based automatic propagation of physician-drawn contours from a planning CT to midtreatment CT images for head and neck (H and N) adaptive radiotherapy. Methods: Ten H and N patients, each with a planning CT (CT1) and a subsequent CT (CT2) taken approximately 3–4 week into treatment, were considered retrospectively. Clinically relevant organs and targets were manually delineated by a radiation oncologist on both sets of images. Four commercial DIR algorithms, two B-spline-based and two Demons-based, were used to deform CT1 and the relevant contour sets onto corresponding CT2 images. Agreement of the propagated contours with manually drawn contours on CT2 was visually rated by four radiation oncologists in a scale from 1 to 5, the volume overlap was quantified using Dice coefficients, and a distance analysis was done using center of mass (CoM) displacements and Hausdorff distances (HDs). Performance of these four commercial algorithms was validated using a parameter-optimized Elastix DIR algorithm. Results: All algorithms attained Dice coefficients of >0.85 for organs with clear boundaries and those with volumes >9 cm{sup 3}. Organs with volumes <3 cm{sup 3} and/or those with poorly defined boundaries showed Dice coefficients of ∼0.5–0.6. For the propagation of small organs (<3 cm{sup 3}), the B-spline-based algorithms showed higher mean Dice values (Dice = 0.60) than the Demons-based algorithms (Dice = 0.54). For the gross and planning target volumes, the respective mean Dice coefficients were 0.8 and 0.9. There was no statistically significant difference in the Dice coefficients, CoM, or HD among investigated DIR algorithms. The mean radiation oncologist visual scores of the four algorithms ranged from 3.2 to 3.8, which indicated that the quality of transferred contours was “clinically acceptable with minor modification or major modification in a small number of contours.” Conclusions: Use of DIR-based contour propagation in the routine clinical setting is expected to increase the efficiency of H and N replanning, reducing the amount of time needed for manual target and organ delineations.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Manifold Sampling for Optimizing Nonsmooth Nonconvex Compositions

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

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

BROOD: Bilevel and Robust Optimization and Outlier Detection for Efficient Tuning of High-Energy Physics Event Generators

The parameters in Monte Carlo (MC) event generators are tuned on experimental measurements by evaluating the goodness of fit between the data and the MC predictions. The relative importance of each measurement is adjusted manually in an often time-consuming, iterative process to meet different experimental needs. In this work, we introduce several optimization formulations and algorithms with new decision criteria for streamlining and automating this process. These algorithms are designed for two formulations: bilevel optimization and robust optimization. Both formulations are applied to the datasets used in the ATLAS A14 tune and to the dedicated hadronization datasets generated by the SHERPA generator, respectively. The corresponding tuned generator parameters are compared using three metrics. We compare the quality of our automatic tunes to the published ATLAS A14 tune. Moreover, we analyze the impact of a pre-processing step that excludes data that cannot be described by the physics models used in the MC event generators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Autonomous and dynamic precursor selection for solid-state materials synthesis

Abstract Solid-state synthesis plays an important role in the development of new materials and technologies. While in situ characterization and ab-initio computations have advanced our understanding of materials synthesis, experiments targeting new compounds often still require many different precursors and conditions to be tested. Here we introduce an algorithm (ARROWS 3 ) designed to automate the selection of optimal precursors for solid-state materials synthesis. This algorithm actively learns from experimental outcomes to determine which precursors lead to unfavorable reactions that form highly stable intermediates, preventing the target material’s formation. Based on this information, ARROWS 3 proposes new experiments using precursors it predicts to avoid such intermediates, thereby retaining a larger thermodynamic driving force to form the target. We validate this approach on three experimental datasets, containing results from over 200 synthesis procedures. In comparison to black-box optimization, ARROWS 3 identifies effective precursor sets for each target while requiring substantially fewer experimental iterations. These findings highlight the importance of domain knowledge in optimization algorithms for materials synthesis, which are critical for the development of fully autonomous research platforms.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Online Stochastic Optimization of Networked Distributed Energy Resources

Our work investigates distributed control and incentive mechanisms to coordinate distributed energy resources (DERs) with both continuous and discrete decision variables as well as device dynamics in distribution grids. We formulate a multi-period social welfare maximization problem, and based on its convex relaxation propose a distributed stochastic dual gradient algorithm for managing DERs. Moreover, we extend it to an online realtime setting with time-varying operating conditions, asynchronous updates by devices, and feedback being leveraged to account for nonlinear power flows as well as reduce communication overhead. The resulting algorithm provides a general online stochastic optimization algorithm for coordinating networked DERs with discrete power setpoints and dynamics to meet operational and economic objectives and constraints. We characterize the convergence of the algorithm analytically and evaluate its performance numerically.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Optimization and Evaluation of Energy Savings for Connected and Autonomous Off-Road Vehicles

Off-road vehicles, such as wheel loaders, excavators, and harvesters, are extensively utilized across a wide range of industries, including construction, agriculture, and mining. These machines have become indispensable in supporting the day-to-day operational needs of a nation, playing a critical role in various sectors' infrastructure and productivity. However, despite their utility, off-road vehicles are significant consumers of fossil fuels, resulting in substantial emissions that contribute to environmental degradation. This highlights the pressing need for research and technological advancements aimed at improving their energy efficiency and reducing their carbon footprint. There are, however, two primary challenges that must be addressed to achieve these goals. First, off-road vehicles typically perform both driving and working tasks simultaneously, which introduces a high level of complexity into their overall dynamic systems. Analysis the interactions between these functions is challenging. Second, research into off-road vehicles is inherently interdisciplinary, demanding expertise across several domains such as fluid power systems, vehicle dynamics, control theory, optimization techniques, and real-world implementation. Recognizing these challenges, we proposed the project titled "Optimization and Evaluation of Energy Savings for Connected and Autonomous Off-Road Vehicles" as a comprehensive solution to enhance fuel efficiency while simultaneously improving productivity. This project specifically focuses on autonomous off-road vehicles, with particular attention to wheel loaders, and seeks to develop novel methods to optimize energy consumption without sacrificing operational performance. The project integrates real-time control algorithms, vehicle dynamics modeling, and co-optimization of powertrain system and vehicle system to achieve these goals. Our optimization strategy dynamically co-optimizes critical parameters at both the powertrain and vehicle levels, including vehicle speed, working tool movements, powertrain dynamics, and engine operations in real-time. To streamline this optimization process, we developed a vehicle model that captures the key dynamics while significantly enhancing computational efficiency. This allows the system to intelligently minimize fuel consumption, all while maintaining or even improving productivity through real-time calculations during various off-road operations. To validate the effectiveness of this energy optimization method, we introduced a state-of-the-art Hardware-in-the-Loop (HIL) testbed. This reconfigurable testbed seamlessly integrates the actual engine with virtual models of the wheel loader's subsystems, allowing for accurate emulation of real-world operational loads and environments. By simulating these conditions, the HIL testbed enables us to evaluate the wheel loader’s performance under diverse working scenarios, ensuring the developed solution is applicable in real-world operations. This testbed proved to be instrumental in validating the optimization algorithms and demonstrating the system's practical effectiveness. During the evaluation and testing phase, we employed the HIL testbed to rigorously assess the energy savings and productivity improvements generated by the optimized system. The results were highly encouraging, revealing that the automated wheel loader achieved over 30% fuel savings compared to traditional, human-operated cycles, with comparable or even enhanced levels of productivity. The insights gained from this HIL-based testing provided critical validation of our approach and highlighted the potential for deploying these optimized autonomous technologies in real-world off-road vehicles.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

A Hybrid Bulk Algorithm to Predict Turbulent Fluxes over Dry and Wet Bare Soils

Measurements made in the Columbia River basin (Oregon) in an area of irregular terrain during the second Wind Forecast Improvement Project (WFIP2) field campaign are used to develop an optimized hybrid bulk algorithm to predict the surface turbulent fluxes from readily measured or modeled quantities over dry and wet bare or lightly vegetated soil surfaces. The hybrid (synthetic) algorithm combines (i) an aerodynamic method for turbulent flow, which is based on the transfer coefficients (drag coefficient and Stanton number), roughness lengths, and Monin–Obukhov similarity; and (ii) a modified Priestley–Taylor (P-T) algorithm with physically based ecophysiological constraints, which is essentially based on the surface energy budget (SEB) equation. Soil heat flux in the latter case was estimated from measurements of soil temperature and soil moisture. In the framework of the hybrid algorithm, bulk estimates of the momentum flux and the sensible heat flux are derived from a traditional aerodynamic approach, whereas the latent heat flux (or moisture flux) is evaluated from a modified P-T model. Direct measurements of the surface fluxes (turbulent and radiative) and other ancillary atmospheric/soil parameters made during WFIP2 for different soil conditions (dry and wet) are used to optimize and tune the hybrid bulk algorithm. The bulk flux estimates are validated against the measured eddy-covariance fluxes. We also discuss the SEB closure over dry and wet surfaces at various time scales based on the modeled and measured fluxes. Although this bulk flux algorithm is optimized for the data collected during the WFIP2, a hybrid approach can be used for similar flux-tower sites and field campaigns.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Synchronization-Avoiding Graph Algorithms

Because they were developed for optimal sequential complexity, classical graph algorithms as found in textbooks have strictly-defined orders of operations. Enforcing a prescribed order of operations, or even an approximate order, in a distributed memory setting requires significant amounts of synchronization, which in turn can severely limit scalability. As a result, new algorithms are typically required to achieve scalable performance, even for solving well-known graph problems. Yet, even in these cases, parallel graph algorithms are written according to parallel programming models that evolved for, e.g., scientific computing, and that still have inherent, and scalability-limiting, amounts of synchronization. In this paper we present a new approach to parallel graph algorithms: synchronization-avoiding algorithms. To eliminate synchronization and its associated overhead, synchronization-avoiding algorithms perform work in an unordered and fully asynchronous fashion in such a way that the result is constantly refined toward its final state. “Wasted” work is minimized by locally prioritizing tasks using problem-dependent task utility metrics. We classify algorithms for graph applications into two broad categories: algorithms with monotonic updates (which evince global synchronization) and algorithms with nonmonotonic updates (which evince vertex-centric synchronization). We apply our approach to both classes and develop novel, synchronization-avoiding algorithms for solving exemplar problems: SSSP and connected components for the former, graph coloring for the latter. We demonstrate that eliminating synchronization in conjunction with effective scheduling policies and optimizations in the runtime results in improved scalability for both classes of algorithms.

Firoz, Jesun S.↗
DOE OSTI2015

SU-E-T-446: Group-Sparsity Based Angle Generation Method for Beam Angle Optimization

Purpose: This work is to develop the effective algorithm for beam angle optimization (BAO), with the emphasis on enabling further improvement from existing treatment-dependent templates based on clinical knowledge and experience. Methods: The proposed BAO algorithm utilizes a priori beam angle templates as the initial guess, and iteratively generates angular updates for this initial set, namely angle generation method, with improved dose conformality that is quantitatively measured by the objective function. That is, during each iteration, we select “the test angle” in the initial set, and use group-sparsity based fluence map optimization to identify “the candidate angle” for updating “the test angle”, for which all the angles in the initial set except “the test angle”, namely “the fixed set”, are set free, i.e., with no group-sparsity penalty, and the rest of angles including “the test angle” during this iteration are in “the working set”. And then “the candidate angle” is selected with the smallest objective function value from the angles in “the working set” with locally maximal group sparsity, and replaces “the test angle” if “the fixed set” with “the candidate angle” has a smaller objective function value by solving the standard fluence map optimization (with no group-sparsity regularization). Similarly other angles in the initial set are in turn selected as “the test angle” for angular updates and this chain of updates is iterated until no further new angular update is identified for a full loop. Results: The tests using the MGH public prostate dataset demonstrated the effectiveness of the proposed BAO algorithm. For example, the optimized angular set from the proposed BAO algorithm was better the MGH template. Conclusion: A new BAO algorithm is proposed based on the angle generation method via group sparsity, with improved dose conformality from the given template. Hao Gao was partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500)

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Joint Optimization of Well Completions and Controls for CO 2 Enhanced Oil Recovery and Storage

CO 2 storage through CO 2 enhanced oil recovery (EOR) is considered as one of the technologies to help promote larger scale deployment of CO 2 storage because of associated economic benefits through oil recovery, 45Q tax credits and the utilization of existing infrastructure. The objective of this study is to demonstrate how optimal reservoir management and operation strategies (including well completions and controls) can be used to optimize both CO 2 storage and oil recovery. The optimization problem was focused on jointly estimating the well completions (i.e., fraction of injection/production well perforations in each reservoir layer) and CO 2 injection/oil production controls that maximize the net present value (NPV) in a CO 2 EOR and storage operation. We utilized the newly developed StoSAG algorithm, one of the most efficient optimization algorithms in the reservoir management community, to solve the optimization problem. The performance of joint optimization approach was compared with the performance of well control only optimization approach. In addition, the performance of co-optimization of CO 2 storage and oil recovery approach was compared with the performances of maximization of only CO 2 storage and maximization of only oil recovery approaches. The optimization results showed that a joint optimization of well completions and well controls can achieve an 8.84% higher final NPV than the one obtained from the optimization of only well controls. It was observed that the NPV incremental for joint optimization is mainly due to the fact that the optimal well completions and controls approach results in efficient CO 2 storage and oil production from different reservoir layers depending on the differences in individual layer properties. Comparison of co-optimization (i.e., maximization of NPV) and maximization of only CO 2 storage or only oil recovery showed that the co-optimization and maximization of only oil recovery result in significantly higher final NPV than that obtained through maximization of only CO 2 storage approach while maximization of only CO 2 storage can achieve significantly higher CO 2 storage in the reservoir compared to the other two scenarios. The similar results for co-optimization and maximization of oil production are obtained because of the difference in oil revenue compared to CO 2 storage tax credit. To the best of our knowledge, this is the first study in oil/gas industry and CO 2 storage community to perform joint optimization of well completions and well controls in the fields. We expect that the proposed optimization framework will be a useful and efficient tool for field engineers to optimally manage CO 2 EOR projects to maximize revenue through oil recovery as well as CO 2 storage by taking advantage of the new 45Q tax law.

Artificial intelligence↗
DOE OSTI2025

RLMolLM: Reinforcement Learning-Enhanced Language Model Framework for Inverse Molecular Design

Inverse molecular design faces significant challenges due to vast chemical space and complex property requirements. While language models show promise for molecular generation, they struggle with validity, multi-property optimization, and structural constraints. This work presents RLMolLM, a reinforcement learning framework combining Proximal Policy Optimization (PPO) with genetic algorithms to address these limitations. Our approach optimizes multiple user-specified properties including quantitative estimates of drug-likeness (QED), synthetic accessibility (SA), and ADMET (absorption, distribution, metabolism, excretion, and toxicity) endpoints without requiring complete model retraining, while maintaining capability for scaffold-constrained generation where specific substructures must be preserved. We outperform state-of-the-art methods for molecular optimization, achieving best QED scores across GDB13, Moses, and Zinc datasets with up to 31% improvement over previous methods while maintaining excellent validity, uniqueness, and novelty metrics. For simultaneous multi-property optimization, our framework achieves substantial improvements in ADMET properties including 4.5-fold reduction in hERG toxicity and enhanced Caco-2 permeability compared to Moses dataset. Under structural constraints, the framework significantly improves molecular validity while preserving scaffolds and effectively optimizing properties. In conclusion, this versatile solution advances pharmaceutical and materials molecular design through effective integration of reinforcement learning and genetic algorithms with multi-property optimization and scaffold preservation.

Genetic algorithms↗
DOE OSTI2023

CATS: The Hubble Constant from Standardized TRGB and Type Ia Supernova Measurements

The tip of the red giant branch (TRGB) provides a luminous standard candle for constructing distance ladders to measure the Hubble constant. In practice, its measurements via edge-detection response (EDR) are complicated by the apparent fuzziness of the tip and the multipeak landscape of the EDR. Previously, we optimized an unsupervised algorithm, Comparative Analysis of TRGBs, to minimize the variance among multiple halo fields per host without relying on individualized choices, achieving state-of-the-art ~<0.05 mag distance measures for optimal data. Here we apply this algorithm to an expanded sample of SN Ia hosts to standardize these to multiple fields in the geometric anchor, NGC 4258. In concert with the Pantheon+ SN Ia sample, this analysis produces a (baseline) result of H 0 = 73.22 ± 2.06 km s -1 Mpc -1 . The largest difference in H 0 between this and similar studies employing the TRGB derives from corrections for SN survey differences and local flows used in the most recent SN Ia compilations that were absent in earlier studies. The SN-related differences total ~2.0 km s -1 Mpc -1 . A smaller share, ~1.4 km s -1 Mpc -1 , results from the inhomogeneity of the TRGB calibration across the distance ladder. We employ a grid of 108 variants around the optimal TRGB algorithm and find that the median of the variants is 72.94 ± 1.98 km s -1 Mpc -1 with an additional uncertainty due to algorithm choices of 0.83 km s -1 Mpc -1 . None of these TRGB variants result in an H 0 of less than 71.6 km s -1 Mpc -1 .

79 ASTRONOMY AND ASTROPHYSICS↗