Search NASA⌕ Search

SEARCH · Search NASA

Results for “hierarchical 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Graph-Based Modeling and Decomposition of Hierarchical Optimization Problems

We present a graph-theoretic modeling approach for hierarchical optimization that leverages the OptiGraph abstraction implemented in the Julia package Plasmo.jl. We show that the abstraction is flexible and can effectively capture complex hierarchical connectivity that arises from decision-making over multiple spatial and temporal scales (e.g., integration of planning, scheduling, and operations in manufacturing and infrastructures). We also show that the graph abstraction facilitates the conceptualization and implementation of decomposition and approximation schemes. Specifically, we propose a graph-based Benders decomposition (gBD) framework that enables the exploitation of hierarchical (nested) structures and that uses graph aggregation/partitioning procedures to discover such structures. In addition, we provide a Julia implementation of gBD, which we call PlasmoBenders.jl. We illustrate the capabilities using examples arising in the context of energy and power systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A Hierarchical Optimization Method for Electric Vertical Takeoff and Landing Aircraft Network Design

Electric vertical takeoff and landing aircraft (eVTOLs) are expected to serve urban air mobility in a station-to-station configuration, which makes the optimal network design of eVTOL stations a critical question to explore. Existing approaches often face limitations, such as the inability to interact station locations with demand or difficulty in finding the optimal solution for large study regions. Here, this paper first proposes a mathematical model to generate optimal eVTOL station locations while considering associated potential eVTOL demand, and then proposes a heuristic algorithm, Hierarchical Optimization MEthod (HOME), to efficiently solve the model. With a case study of Southern California, HOME was compared to 1) directly solving the original integer linear programming-based network design problem, and 2) employing the widely used genetic algorithm. Results suggest that HOME can find optimal solutions with limited computational resources. The proposed framework powered by HOME provides a computationally efficient way to support urban air mobility planning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Randomized Federated Learning Methods for Nonsmooth, Nonconvex, and Hierarchical Optimization (Final Technical Report)

This final technical report summarizes the outcomes of a DOE-funded project on federated scientific machine learning (FL) under nonsmooth, nonconvex, and hierarchical optimization settings. The project develops new mathematical models, algorithms, and theoretical guarantees for decentralized stochastic, bilevel, and minimax optimization problems arising in DOE mission-relevant applications. A unified framework of randomized and zeroth-order federated optimization methods is introduced, providing provable convergence, communication efficiency, and sample-complexity guarantees. The report documents algorithmic design, theoretical analysis, and empirical validation of the proposed federated learning methods. The project also contributes to workforce development through graduate training and dissemination of results via publications and seminars.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2011

Spectral-Spatial Classification of Hyperspectral Images Using Hierarchical Optimization

A new spectral-spatial method for hyperspectral data classification is proposed. For a given hyperspectral image, probabilistic pixelwise classification is first applied. Then, hierarchical step-wise optimization algorithm is performed, by iteratively merging neighboring regions with the smallest Dissimilarity Criterion (DC) and recomputing class labels for new regions. The DC is computed by comparing region mean vectors, class labels and a number of pixels in the two regions under consideration. The algorithm is converged when all the pixels get involved in the region merging procedure. Experimental results are presented on two remote sensing hyperspectral images acquired by the AVIRIS and ROSIS sensors. The proposed approach improves classification accuracies and provides maps with more homogeneous regions, when compared to previously proposed classification techniques.

Tarabalka, Yuliya↗
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 OSTI2023

Optimizing hierarchical membrane/catalyst systems for oxidative coupling of methane using additive manufacturing

The advantage of a membrane/catalyst system in oxidative coupling of methane (OCM) compared to conventional reactive systems is that by introducing oxygen to the OCM catalytic sites through a membrane, parasitic gas phase reactions of O 2 (g), responsible for lowering product selectivity, can be avoided. The design and fabrication of membrane/catalyst systems has, however, been hampered by low volumetric chemical conversion rates, high capital cost, and difficulties in codesigning membrane and catalyst properties to optimize the performance. We solve these issues by developing a dual-layer additive manufacturing process, based on phase inversion, to design, fabricate and optimize a hollow fiber membrane/catalyst system for OCM. We demonstrate the approach though a case study using BaCe 0.8 Gd 0.2 O 3-δ (BCG) as the basis of both the catalyst and separation layers. We show that by using the manufacturing approach we can codesign the membrane thickness and catalyst surface area so that the flux of oxygen transport through the membrane and methane activation rates in the catalyst layer match each other. Here, we demonstrate that this “rate matching” is critical for maximizing the performance, with the membrane/catalyst system significantly overperforming conventional reactor designs under identical conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Accelerating Bilevel Optimization With Hierarchical Many-Threaded Parallel Differential Evolution

Bilevel optimization is encountered in many relevant real-world applications. The main feature of this type of problem is that an upper-level optimization problem is constrained by a nested lower-level optimization problem. Because of this nested structure, bilevel problems (BLPs) are usually computationally expensive to solve. Differential evolution (DE) has demonstrated promising results in solving BLPs of relatively small scales. As the problem scale increases, the decision space becomes intrinsically larger, requiring a growing number of function evaluations for the method to work properly. In this context, heavy parallelization and high-performance computing techniques are indispensable to enable the resolution of more complex and challenging optimization problems. Hence, we propose a hierarchical many-threaded parallel DE approach for BLPs, where both levels are parallelized. The computational experiments demonstrate that the parallel implementation achieved runtime speeds ranging from 44 to 2559 times faster than the sequential version on a well-known scalable SMD benchmark test problem when executed on an NVIDIA A100 GPU. The findings indicate that the algorithm’s convergence is strongly influenced by the number of both upper- and lower-level generations. Moreover, the success of experiments with large-scale problems is closely linked to the choice of small population sizes.

Dufek, Amanda S↗
NASA NTRS2012

Improved Hierarchical Optimization-Based Classification of Hyperspectral Images Using Shape Analysis

A new spectral-spatial method for classification of hyperspectral images is proposed. The HSegClas method is based on the integration of probabilistic classification and shape analysis within the hierarchical step-wise optimization algorithm. First, probabilistic support vector machines classification is applied. Then, at each iteration two neighboring regions with the smallest Dissimilarity Criterion (DC) are merged, and classification probabilities are recomputed. The important contribution of this work consists in estimating a DC between regions as a function of statistical, classification and geometrical (area and rectangularity) features. Experimental results are presented on a 102-band ROSIS image of the Center of Pavia, Italy. The developed approach yields more accurate classification results when compared to previously proposed methods.

Classification↗
DOE OSTI2022

Hierarchical Distributed Optimal Power Flow of HV and MV Distribution Networks With Continuous and Discrete Devices

With large-scale distributed photovoltaics (PVs) being integrated into distribution networks (DNs), coordinated optimal power flow (OPF) of high voltage (HV) and medium voltage (MV) DNs should be investigated to optimally dispatch the distributed PVs and other network devices. Here, this paper presents a hierarchical distributed OPF method for HV and MV DNs with on-load tap changers, reactive power compensators, feeder switches and distributed PVs. A hierarchical master-slave control architecture is applied to implement coordinated OPF of two-layer DNs. The HV master problem and MV subproblems are transformed into mixed-integer convex problems respectively with second order cone programming and LinDistFlow approximation. Since there is no efficient distributed algorithm to solve such OPF models with integer subproblems, a novel distributed algorithm is proposed in this paper to efficiently solve the hierarchical coordinated OPF model with integer subproblems in a distributed manner. In the proposed algorithm, the coordinated OPF model is solved in a branch-and-bound framework, where in each branch node generalized Benders decomposition (GBD) algorithm is applied to decompose the coordinated OPF model into a master problem and relaxed subproblems and solves them iteratively to get optimal solution. The GBD optimal and feasible cutting planes generated in a branch node are proved to be valid for its descendants. Moreover, three acceleration techniques are introduced into the proposed algorithm to improve computational efficiency. Finally, the effectiveness and accuracy of the proposed method are verified via simulation tests in Jinzhai DNs of China.

42 ENGINEERING↗
DOE OSTI2019

A Highly Efficient Control Framework for Centralized Residential Charging Coordination of Large Electric Vehicle Populations

The potential for widespread adoption of plug-in electric vehicles (PEVs) brings with it the potential for negative impacts on the electric grid from electric vehicle charging. Uncoordinated PEV charging may increase electricity demand during peak hours, which could create concerns for the grid as the number of PEVs increases. Therefore, it is important to coordinate charging to alleviate potential negative impacts. Centralized charging coordination is preferred by grid operator over distributed control strategies because it can systematically allocate energy across a large population of PEVs and achieve global coordination benefits. However, centralized methods presented in the literature to date require prohibitively expensive computational resources and lack realistic PEV charging models. As a result, they cannot achieve the efficiency and accuracy required to implement charging coordination in the real world. This paper introduces a highly efficient receding horizon control framework that enables dynamic charging coordination for large PEV populations. A two-stage hierarchical optimization routine is proposed that aggregates individual PEV charging flexibility to reduce the computational complexity of the optimization process. The control framework is based on high-fidelity, validated charging system models and charging behavior models derived from a real-world data set of residential charging activities collected from thousands of charging stations over multiple years. Case studies illustrate that the proposed charging control framework is capable of effectively coordinating the charging of millions of PEVs using a standard desktop computer.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2021

EMOS (Energy Management Optimization System) [SWR-21-46]

EMOS software performs a real-time hierarchal optimal control for energy systems like multi-port electric vehicles charging site with distributed energy resources (DERs) and energy storage systems (ESSs). It gathers information in real-time from electric vehicles, power grid, and DERs, solves a multi-objective energy management optimization problem, and output setpoint for chargers, ESS converters, DERs converters, and grid converters. The software incorporates a novel integration of two control tasks: a) An Energy Management Optimization (EMO), which is the brain of EMOS controller that gathers information in real-time from EVs [e.g., battery size, state-of-charge (SOC), desired SOC, and charge acceptance curve], grid (e.g., electricity price, allowed feeder capacity, ramp rate limit, and reactive power), and DERs (e.g., prediction for solar generation for PV systems). It solves a control optimization problem in real-time to find optimal setpoint for ESSs power dispatch, EVs charging rate, and grid inverters. The objectives are to (1) minimize the charging cost considering grid energy, demand charges, and battery energy, (2) minimize charging time to meet fast charging criterion, (3) keep high energy level on ESSs at the end of an operating period, while satisfying constraints related to grid, EVs, and power converters. b) Real-Time Energy Management System (RT-EMS) is a rule-based algorithm that has faster response than EMO. It receives optimal setpoint from EMO and actual measurements from the system and modify the setpoint to compensate for any fast disturbance in the system, until a new optimum solution is received. Fast disturbances may include vehicle connect/disconnect, unpredicted variation in DERs profiles, variation in grid voltage, errors in PV generation prediction, and others. In addition, RT-EMS regulates voltage at point of common coupling (PCC) by managing reactive power of grid converters.

Mohamed, Ahmed↗
DOE OSTI2018

On Per-Phase Topology Control and Switching in Emerging Distribution Systems

This paper presents a new concept and approach for topology control and switching in distribution systems by extending the traditional circuit switching to laterals and single-phase loads. Voltage unbalance and other key performance indicators including voltage magnitudes, line loading, and energy losses are used to characterize and demonstrate the technical value of optimizing system topology on a per-phase basis in response to feeder conditions. The near-optimal per-phase topology control is defined as a series of hierarchical optimization problems. The proposed approach is respectively applied to IEEE 13-bus and 123-bus test systems for demonstration, which included the impact of integrating electric vehicles (EVs) in the test circuit. It is concluded that the proposed approach can be effectively leveraged to improve voltage profiles with electric vehicles, the extent of which depends upon the performance of the base case without EVs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Optimizing checkpoint data placement with guaranteed burst buffer endurance in large-scale hierarchical storage systems

Non-volatile devices, such as SSDs, will be an integral part of the deepening storage hierarchy on large-scale HPC systems. These devices can be on the compute nodes as part of a distributed burst buffer service or they can be external. Wherever they are located in the hierarchy, one critical design issue is the SSD endurance under the write-heavy workloads, such as the checkpoint I/O for scientific applications. For these environments, it is widely assumed that checkpoint operations can occur once every 60 min and for each checkpoint step as much as half of the system memory can be written out. Unfortunately, for large-scale HPC applications, the burst buffer SSDs can be worn out much more quickly given the extensive amount of data written at every checkpoint step. One possible solution is to control the amount of data written by reducing the checkpoint frequency. However, a direct effect caused by reduced checkpoint frequency is the increased vulnerability window of system failures and therefore potentially wasted computation time, especially for large-scale compute jobs.

Computer Science↗
DOE OSTI2017

Bio-inspired Murray materials for mass transfer and activity

Both plants and animals possess analogous tissues containing hierarchical networks of pores, with pore size ratios that have evolved to maximize mass transport and rates of reactions. The underlying physical principles of this optimized hierarchical design are embodied in Murray’s law. However, we are yet to realize the benefit of mimicking nature’s Murray networks in synthetic materials due to the challenges in fabricating vascularized structures. Here we emulate optimum natural systems following Murray’s law using a bottom-up approach. Such bio-inspired materials, whose pore sizes decrease across multiple scales and finally terminate in size-invariant units like plant stems, leaf veins and vascular and respiratory systems provide hierarchical branching and precise diameter ratios for connecting multi-scale pores from macro to micro levels. Our Murray material mimics enable highly enhanced mass exchange and transfer in liquid–solid, gas–solid and electrochemical reactions and exhibit enhanced performance in photocatalysis, gas sensing and as Li-ion battery electrodes.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗