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Results for “mathematical optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Mathematical Optimization of NGCC Solvent-based Carbon Capture Processes to Explore High Capture Designs

For point-source capture, much of the work to date has focused on achieving 90% capture – a somewhat arbitrary target above which parasitic losses to drive carbon capture and compression systems were believed to be too great to be economically justifiable. The recent push for deep decarbonization has caused this target to be revisited, and existing literature is of limited usefulness as most published studies have focused on carbon capture percentages of 90%. In this work, numerous mathematical optimizations were performed between carbon capture targets between 90%-99.8% of a Natural Gas Combined Cycle (NGCC) plant to better understand incremental cost of these systems so they may be compared to other decarbonization technologies, and to inform technical risk associated with targeting higher capture performance for these types of systems.

carbon capture↗
DOE OSTI2021

Predicting Characteristics of the Water Cycle From Scaling Relationships

Over multi-decadal time scales, assuming that changes in subsurface water storage are negligible, the continental precipitative water flux, P, can be divided into two principal components, Q (run-off, including soil infiltration and groundwater recharge) and ET (evapotranspiration). Taking into account a broadly applied Budyko's phenomenology to describe the relationship of ET/P as a function of PET/P, where PET is the potential evapotranspiration, we propose a theoretical framework for predicting characteristics of the water cycle from scaling relationships. In this framework, the ecosystem net primary productivity is expressed in terms of soil formation and vegetation growth, which is mathematically optimized with respect to the water partitioning, generating directly the value ET/P. Here, the mathematical optimization is based on the general ecological principle that dominant ecosystems tend to be those that, for any given conditions, maximize conversion of atmospheric carbon to biomass. It is shown that application of the results of mathematical optimization to water-limited ecosystems is possible by applying the optimization only to a vegetation covered portion of the surface. For energy-limited ecosystems, the optimization can be applied only to a portion of the precipitation equal to PET, assuming that the remaining P simply runs off. We use theoretical and actual values of plant root fractal dimensionalities, d f , to predict ranges of ET/P as a function of PET/P for 0 ≤ PET/P ≤ 1 and compare with annual and multi-decadal means of ET/P. By comparing the developed approach with a large amount of data collected from the literature, we demonstrate its successful applications to both water- and energy-limited systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Physics successfully implements Lagrange multiplier optimization

Optimization is a major part of human effort. While being mathematical, optimization is also built into physics. For example, physics has the Principle of Least Action; the Principle of Minimum Power Dissipation, also called Minimum Entropy Generation; and the Variational Principle. Physics also has Physical Annealing, which, of course, preceded computational Simulated Annealing. Physics has the Adiabatic Principle, which, in its quantum form, is called Quantum Annealing. Thus, physical machines can solve the mathematical problem of optimization, including constraints. Binary constraints can be built into the physical optimization. In that case, the machines are digital in the same sense that a flip–flop is digital. A wide variety of machines have had recent success at optimizing the Ising magnetic energy. We demonstrate in this paper that almost all those machines perform optimization according to the Principle of Minimum Power Dissipation as put forth by Onsager. Further, we show that this optimization is in fact equivalent to Lagrange multiplier optimization for constrained problems. We find that the physical gain coefficients that drive those systems actually play the role of the corresponding Lagrange multipliers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

C3PU:Real-Time Predictive Charge Control Software for Battery Management Systems (Code for Charge Control and Predictive Unit) [SWR-21-48]

C3PU sets up a model predictive control formulation for the optimal charging control of battery packs and can be deployed for real-time operation on an embedded microprocessor. C3PU uses electrochemical and thermal models of battery packs to predict the charging trajectories of the battery pack over a time horizon under different operating conditions. It then selects the optimal charging trajectory such that a pre-defined objective is minimized, which in the present state of the code is to minimize the charging duration of the battery pack. The optimal charging trajectory is obtained by solving an underlying mathematical problem. However, C3PU is flexible to incorporate other charging objectives. The underlying battery models can be swapped as well, as long as they follow certain mathematical properties. Mathematically, optimal control problems (in this case, optimally controlling the charging current of the battery pack) are computationally expensive. C3PU implements advanced numerical techniques, namely pseudo-spectral optimization, to reduce the computational burden of the underlying problem to solve. This allows for the problem to be solved in real-time in an embedded system. Once the optimal charging trajectory is computed over a time horizon, C3PU can package such data and send it out via appropriate communication protocols.

Mishra, Partha↗
DOE OSTI2021

Efficient kinetic thermal inverse modeling for organic material decomposition

The prevalent use of organic materials in manufacturing is a fire safety concern, and motivates the need for predictive thermal decomposition models. A critical component of predictive modeling is numerical inference of kinetic parameters from bench scale data. Currently, an active area of computational pyrolysis research focuses on identifying efficient, robust methods for optimization. This paper demonstrates that kinetic parameter calibration problems can successfully be solved using classical gradient-based optimization. We explore calibration examples that exhibit characteristics of concern: high nonlinearity, high dimensionality, complicated schemes, overlapping reactions, noisy data, and poor initial guesses. The examples demonstrate that a simple, non-invasive change to the problem formulation can simultaneously avoid local minima, avoid computation of derivative matrices, achieve a computational efficiency speedup of 10x, and make optimization robust to perturbations of parameter components. Techniques from the mathematical optimization and inverse problem communities are employed. By re-examining gradient-based algorithms, we highlight opportunities to develop kinetic parameter calibration methods that should outperform current methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

PRIMO – The Oil & Gas Well Plugging Optimizer

This work presents PRIMO’s main capabilities and introduces the PRIMO web application, an intuitive user interface that leverages our sophisticated mathematical optimization model to rigorously optimize P&A priorities and plugging campaign efficiency. The web app simplifies user interaction, provides a powerful data management framework, and supports a broad user base (e.g., state agencies, well owners/operators, and plugging companies) to use PRIMO for decision-making. Specifically, we provide a demonstration of how to input the information on candidate wells, plugging campaign budget, user-defined priority and efficiency criteria to PRIMO. A real-world case study that consists of 1411 oil and gas wells and impact and efficiency priorities (e.g., well age, well proximity to schools/hospitals, well accessibility, distance between wells in projects) is presented to showcase PRIMO’s core capabilities: (i) ranking a candidate well population based on priorities, (ii) recommending high-impact and high-efficiency P&A projects, and (iii) assigning impact and efficiency scores to projects allowing for rigorous quantitative comparison among them.

02 PETROLEUM↗
DOE OSTI2022

Pareto Optimal and Dual-Objective Geometric and Structural Design of an Underwater Kite for Closed-Loop Flight Performance

This paper presents the formulation and results for a control-aware optimization of the combined geometric and structural design of an energy-harvesting underwater kite. Because kite-based energy-harvesting systems, both airborne and underwater, possess strong coupling between closed-loop flight control, geometric design, and structural design, consideration of all three facets of the design within a single codesign framework is highly desirable. However, while prior literature has addressed one or two attributes of the design at a time, this work constitutes the first comprehensive effort aimed at addressing all three. In particular, focusing on the goals of power maximization and mass minimization, we present a codesign formulation that fuses a geometric optimization tool, structural optimization tool, and closed-loop flight efficiency map. The resulting integrated codesign tool is used to address two mathematical optimization formulations that exhibit subtle differences: a Pareto optimal formulation and a dual-objective formulation that focuses on a weighted power-to-mass ratio as the techno-economic metric of merit. Further, based on the resulting geometric and structural designs, using a mediumfidelity closed-loop simulation tool, the proposed formulation is shown to achieve more than three times the powerto-mass ratio of a previously published, unoptimized benchmark design.

42 ENGINEERING↗
DOE OSTI2024

GO Competition Challenge 1 Benchmark Approach and Validation Support

At the outset ARPA-e’s grid optimization competition sought to test a hypothesis that modern nonlinear optimization methods had reached a level of performance and reliability necessary to optimize energy grids using nonlinear power flow equations. The results demonstrated by this project and the other participants in the grid optimization competition have demonstrated beyond any shadow of doubt that this hypothesis is true. This result suggest that the mathematical optimization technology now exists to produce a revolution in power grid optimization software, which would improve the efficiency of energy grid operations to the broad benefit of society.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Droning on to Delivery: Examining the Energy Impacts of Using Drones for Moving Goods

The demand for fast, localized delivery has grown significantly in recent years. Whether for cheesy snacks, prepared food, medical solutions, or business deliveries, fast and efficient delivery is increasingly a demand and differentiator. Drone delivery in the freight sector offers to revolutionize last-mile logistics and improve services. This research analyzes the impacts of drone energy for delivery operations, aiming to compare various types of drones (large and small, rotary and VTOL) and various types of business methods. The project executes novel open-air and laboratory-based testing to look at the impacts of weights, operations, temperatures and weather conditions. The study combines this real-world experimental data with fleet optimization mathematical models to assess energy consumption of different scenarios as well as examine the minimum fleet size and additional battery requirements. These fleet optimization models compare energy between types of deployments with existing delivery methods. The model was also extended to look at mixed fleets of aerial drones and ground vehicles to accommodate different restrictions on drones or when weather prohibits their use. The analysis provided insights into factors such as drone design, payload weight, flight distance, weather conditions and operational parameters and impacts of each. It showed how to combine different types of vehicles to reduce energy and improve services. And it showed that drone speed, routing restrictions, and unfavorable weather significantly influence energy consumption. Our open experiment data and optimization models can assist stakeholders and industry in understanding drone package delivery and offers keys to improving deployment.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Integration of discrete-event dynamics and machining dynamics for machine tool: Modeling, analysis and algorithms

Machining dynamics research lays a solid foundation for machining operations by providing stable combinations of spindle speed and depth of cut. Furthermore, machine learning has been applied to predict tool life as a function of cutting speed. However, the existing research does not consider the discrete-event dynamics in machine shop, i.e., the machine tool needs to process a series of parts in queue under various practical production requirements. This paper addresses the integration of discrete-event dynamics and machining dynamics to achieve cost savings in machining. A learning-based cost function is first proposed for the studied integrated optimization problem of machine tool. The proposed cost function utilizes the predicted tool life under different stable cutting speeds for further optimizing speed selection of machine tool to deal with the discrete-event dynamics in machine shop. Then, according to the practical production requirements, effective mathematical optimization models are developed for the related integrated optimization problems with the consideration of cost, makespan and due date, respectively. Numerical results show the effectiveness of our proposed methods and also the potential to be used in practice.

Ma, Mason↗
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 OSTI2022

ADAM: A web platform for graph-based modeling and optimization of supply chains

Modeling and optimization are essential tasks that arise in the analysis and design of supply chains (SCs). SC models are essential for understanding emergent behavior such as transactions between participants, inherent value of products exchanged, as well as impact of externalities (e.g., policy and climate) and of constraints. Unfortunately, most users of SC models have limited expertise in mathematical optimization, and this hinders the adoption of advanced decision-making tools. Here, in this work, we present ADAM, a web platform that enables the modeling and optimization of SCs. ADAM facilitates modeling by leveraging intuitive and compact graph-based abstractions that allow the user to express dependencies between locations, products, and participants. ADAM model objects serve as repositories of experimental, technology, and socio-economic data; moreover, the graph abstractions facilitate the organization and exchange of models and provides a natural framework for education and outreach. Here, we discuss the graph abstractions and software design principles behind ADAM, its key functional features and workflows, and application examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Implementing a unified solver for nonlinearly constrained optimization

SQP and interior-point methods (also referred to as Lagrange-Newton methods) typically share key algorithmic components, such as strategies for computing descent directions and mechanisms that promote global convergence. Building on this insight, we introduce a unifying framework with eight building blocks that abstracts the workflows of Lagrange-Newton methods. We then present Uno, a modular C++ solver that implements our unifying framework and allows the automatic combination of a wide range of strategies with no programming effort from the user. Uno is meant to (1) organize mathematical optimization strategies into a coherent hierarchy; (2) offer a wide range of efficient and robust methods that can be compared for a given instance; (3) enable researchers to experiment with novel optimization strategies; and (4) reduce the cost of development and maintenance of multiple optimization solvers. Uno’s software design allows user to compose new customized solvers for emerging optimization areas such as robust optimization or optimization problems with complementarity constraints, while building on reliable nonlinear optimization techniques. We demonstrate that Uno is highly competitive against state-of-the-art solvers filterSQP, IPOPT, SNOPT, MINOS, LANCELOT, LOQO, and CONOPT on a subset of 429 small problems from the CUTE collection. Uno is available as open-source software under the MIT license at https://github.com/cvanaret/Uno and via its C, Julia, Python, Fortran, and AMPL interfaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Quantum Optimization: Potential, Challenges, and the Path Forward

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization being one of the most pronounced domains. Across computer science and physics, there are a number of algorithmic approaches, often with little linkage. This is further complicated by the fragmented nature of the field of mathematical optimization, where major classes of optimization problems, such as combinatorial optimization, convex optimization, non-convex optimization, and stochastic extensions, have devoted communities. With these aspects in mind, this work draws on multiple approaches to study quantum optimization. Provably exact versus heuristic settings are first explained using computational complexity theory — highlighting where quantum advantage is possible in each context. Then, the core building blocks for quantum optimization algorithms are outlined to subsequently define prominent problem classes and identify key open questions that, if answered, will advance the field. The effects of scaling relevant problems on noisy quantum devices are also outlined in detail, alongside meaningful benchmarking problems. We underscore the importance of benchmarking by proposing clear metrics to conduct appropriate comparisons with classical optimization techniques. Lastly, we highlight two domains – finance and sustainability – as rich sources of optimization problems that could be used to benchmark, and eventually validate, the potential real-world impact of quantum optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Predictive modeling of a subcritical pulverized-coal power plant for optimization: Parameter estimation, validation, and application

As renewable power generation deployment increases, fossil fuel plants are increasingly required to operate more flexibly. Many coal-fired power plants were originally designed to operate at base load and do not operate optimally at partial load. Predictive first-principles plant-wide models can be employed to identify opportunities for flexibility improvements and diagnose low-load operating issues. This paper describes the application of the Institute for the Design of Advanced Energy Systems Integrated Platform (IDAES) to model and optimize flexible power plant operations. The key benefits of using IDAES are that it provides an open-source, fully equation-oriented modeling framework for efficient modular model construction, reuse, and customization, together with a mathematical optimization framework leveraging powerful, state-of-the-art solvers. The process systems engineering workflow from predictive process simulation to parameter estimation, model validation, and plant optimization is applicable to a variety of existing and next-generation energy systems as well as other chemical and environmental processes. Here, to demonstrate this capability, a physics-based, steady-state model was developed to improve full- and part-load performance of the Escalante Generating Station, a 245 MWe (net) subcritical pulverized coal-fired power plant owned and operated by Tri-State Generation and Transmission Association. Specifically, sixty-nine model parameters were simultaneously estimated from several months of operating data enabling prediction of flow rates, temperatures, pressures, and steam quality throughout the plant. The validated model was leveraged by Escalante to reduce the minimum operating load from 90 MW to 50 MW by diagnosing a low-load water-hammer issue, enabling coal usage and emissions reductions during periods of low power demand. Additionally, opportunities for heat rate reduction (i.e., efficiency improvement) through a steeper sliding-pressure approach to load-following and optimization of other boiler operating variables were also identified and quantified. For example, a potential efficiency improvement of 0.7 percentage points was observed at half-load operation.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2025

LLGOMAX: Enhancing Industry-Standard Tools for AC Optimal Unit Commitment (CRADA Final Report)

This was a collaborative effort between Lawrence Livermore National Security, LLC ("LLNS"), as manager and operator of Lawrence Livermore National Laboratory ("LLNL") and ECCO International Inc. ("Participant"). The team designed and implemented a new approach for the Security-Constrained Alternating-Current Unit Commitment (SCACUC) problem. The SCACUC problem is a mathematical optimization problem that decides which generating units should be online and how much power should be produced (and consumed) at each point of the power grid. The decisions are made so as to minimize the total cost of supplying electricity while respecting technical constraints of the power grid, both under normal and emergency conditions. The team developed a solution for SCACUC as specified in the ARPA-E Grid Optimization Competition (GOC) Challenge 3, which put forth a forward-looking version of the problem, which many features not present in today’s electricity market specifications for SCACUC.

24 POWER TRANSMISSION AND DISTRIBUTION↗