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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Tutorial for Using an Open-Source Solver for the Regional Energy Deployment System (ReEDS) Model

ReEDS is a publicly available model developed at NREL that can be used to analyze the potential evolution of the U.S. electric power system into the future. ReEDS is formulated as a linear program, written in GAMS, and solved using a linear programming solver (e.g., CPLEX). This tutorial provides context and understanding for the implications of using an open-source solver for ReEDS.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty

The coordination of interconnected elements across the different layers of the supply chain is essential for all industrial processes and the key to optimal decision-making. Yet, the modeling and optimization of such interdependent systems are still burdensome. Here we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. We address the data-driven optimization of this challenging class of problems using the DOMINO framework, which was initially developed to solve single-leader single-follower bi-level optimization problems to guaranteed feasibility. This framework is extended to solve single-leader multi-follower stochastic formulations and its performance is characterized by well-known single and multi-product process scheduling case studies. Through our data-driven algorithmic approach, we present guaranteed feasible solutions to linear and nonlinear mixed-integer bi-level formulations of simultaneous planning and scheduling problems and further characterize the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.

42 ENGINEERING↗
DOE OSTI2019

A scalable stochastic programming approach for the design of flexible systems

We study the problem of designing systems in order to minimize cost while meeting a given flexibility target. Flexibility is attained by enforcing a joint chance constraint, which ensures that the system will exhibit feasible operation with a given target probability level. Unfortunately, joint chance constraints are complicated mathematical objects that often need to be reformulated using mixed-integer programming (MIP) techniques. In this work, we cast the design problem as a conflict resolution problem that seeks to minimize cost while maximizing flexibility. We propose a purely continuous relaxation of this problem that provides a significantly more scalable approach relative to MIP methods and show that the formulation delivers solutions that closely approximate the Pareto set of the original joint chance-constrained problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Topology Optimization for Nonlinear Transient Applications Using a Minimally Invasive Approach (LDRD Final Report)

The purpose of this project was to devise, implement, and demonstrate a method that can use Sandia's existing analysis codes (e.g., Sierra, Alegra, the CTH hydro code) with minimal modification to generate objective function gradients for optimization-based design in transient, non-linear, coupled-physics applications. The approach uses a Moving Least Squares representation of the geometry to substantially reduce the number of geometric degrees of freedom. A Multiple-Program Multiple-Data computing model is then used to compute objective gradients via finite differencing. Details of the formulation and implementation are provided, and example applications are presented that show effectiveness and scalability of the approach.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1983

Aerothermal modeling, phase 1. Volume 1: Model assessment

Phase 1 was conducted as part of the overall NASA Hot Section Technology (HOST) Program. The purpose of this effort was to determine the predictive accuracy of and the deficiencies within the various analytical modules comprising the overall combustor aerothermal model used at General Electric, as well as to formulate recommendations for improvement where needed. This effort involved the assembly of a benchmark quality data base from selected available literature, and from General Electric engine and combustor component test data. This data base was supplemented with additional definitive data obtained from an experimental test program conducted as part of the Phase 1 effort. Using selections from this data base, assessment studies were conducted to evaluate the various modules. Assessment of the internal flow module was conducted using 2-D parabolic and ellipitic, as well as 3-D elliptic internal flow calculations of definitive test data selected from the assembled data base. The 2-D assessment provided methodical examination of the mathematical techniques and the physical submodules, while the 3-D assessment focused on usefulness as a design tool. Calculations of combustor linear metal temperatures, pressure loss performance, and airflow distribution were performed using aerothermal modules which were in general use for many years at General Electric. The results of these assessment provided for the identification of deficiencies within the modules. The deficiencies were addressed in some detail providing a foundation on which to formulate a prioritized list of recommendations for improvement.

Kenworthy, M. J.↗
DOE OSTI2019

A generalized superstructure-based framework for process synthesis

We propose a general framework for the formulation of superstructure-based optimization models for holistic process synthesis. First, we redefine the fundamental problems of reactor, separation, and heat exchanger network synthesis, by presenting generalized problem statements, to make them amenable to seamless integration with each other. Second, we describe the general forms of models that can be developed to address these generalized problems and identify some key characteristics. Notably, for each system, we identify internal variables used only within the system, cost variables used in the objective function, and, importantly, coupling variables for the coupling between systems. Third, we outline some literature models that can be used to address the generalized problems and present new models to couple the three systems. Finally, we show how the individual components (systems and coupling models) can be integrated to formulate a single simultaneous reactor, separation, and heat exchanger network synthesis.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2013

Mixed Integer Programming and Heuristic Scheduling for Space Communication

Optimal planning and scheduling for a communication network was created where the nodes within the network are communicating at the highest possible rates while meeting the mission requirements and operational constraints. The planning and scheduling problem was formulated in the framework of Mixed Integer Programming (MIP) to introduce a special penalty function to convert the MIP problem into a continuous optimization problem, and to solve the constrained optimization problem using heuristic optimization. The communication network consists of space and ground assets with the link dynamics between any two assets varying with respect to time, distance, and telecom configurations. One asset could be communicating with another at very high data rates at one time, and at other times, communication is impossible, as the asset could be inaccessible from the network due to planetary occultation. Based on the network's geometric dynamics and link capabilities, the start time, end time, and link configuration of each view period are selected to maximize the communication efficiency within the network. Mathematical formulations for the constrained mixed integer optimization problem were derived, and efficient analytical and numerical techniques were developed to find the optimal solution. By setting up the problem using MIP, the search space for the optimization problem is reduced significantly, thereby speeding up the solution process. The ratio of the dimension of the traditional method over the proposed formulation is approximately an order N (single) to 2*N (arraying), where N is the number of receiving antennas of a node. By introducing a special penalty function, the MIP problem with non-differentiable cost function and nonlinear constraints can be converted into a continuous variable problem, whose solution is possible.

Lee, Charles H.↗
NASA NTRS1979

High speed cylindrical rolling element bearing analysis 'CYBEAN' - Analytic formulation

This paper documents the analytic foundation and software architecture for the computerized mathematical simulation of high speed cylindrical rolling element bearing behavior. The software, CYBEAN (CYlindrical BEaring ANalysis), considers a flexible, variable geometry outer ring, EHD films, roller centrifugal and quasidynamic loads, roller tilt and skew, mounting fits, cage and flange interactions. The representation includes both steady state and time transient simulation of thermal interactions internal to and coupled with the surroundings of the bearing. A sample problem illustrating program use is presented.

Kleckner, R. J.↗
DOE OSTI2024

A mixed integer linear programming approach for the design of chemical process families

Tackling climate change goals requires widespread deployment of process technology variants across many decentralized sites with different geographical, environmental, and operational requirements. Conventional engineering approaches focus on unique designs for each installation (process variant), while missing opportunities for manufacturing standardization. Here, instead we seek to optimize a process platform of common unit designs while simultaneously designing an entire family of process variants that make use of that platform. This reduces engineering effort, deployment timelines, and manufacturing costs. We propose a nonlinear generalized disjunctive programming formulation and convert this to an efficient mixed-integer linear programming (MILP) formulation through discretization of the design space. We formulate our optimization in Pyomo with costing from IDAES, and we demonstrate the computational performance and solution quality on a water treatment desalination system from the PARETO framework and a carbon capture system built in Aspen Plus as part of CCSI2.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Optimal decision trees for categorical data via integer programming

Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if allowed to grow large, they lose interpretability. In this paper, we present a mixed integer programming formulation to construct optimal decision trees of a prespecified size. We take the special structure of categorical features into account and allow combinatorial decisions (based on subsets of values of features) at each node. Our approach can also handle numerical features via thresholding. Here we show that very good accuracy can be achieved with small trees using moderately-sized training sets. The optimization problems we solve are tractable with modern solvers.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2011

Systems, methods and apparatus for modeling, specifying and deploying policies in autonomous and autonomic systems using agent-oriented software engineering

Systems, methods and apparatus are provided through which in some embodiments, an agent-oriented specification modeled with MaCMAS, is analyzed, flaws in the agent-oriented specification modeled with MaCMAS are corrected, and an implementation is derived from the corrected agent-oriented specification. Described herein are systems, method and apparatus that produce fully (mathematically) tractable development of agent-oriented specification(s) modeled with methodology fragment for analyzing complex multiagent systems (MaCMAS) and policies for autonomic systems from requirements through to code generation. The systems, method and apparatus described herein are illustrated through an example showing how user formulated policies can be translated into a formal mode which can then be converted to code. The requirements-based programming systems, method and apparatus described herein may provide faster, higher quality development and maintenance of autonomic systems based on user formulation of policies.

Hinchey, Michael G.↗
DOE OSTI2021

Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

In this paper, we address the aircraft conflict resolution problem in air traffic control. We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions. We first examine the two-dimensional aircraft conflict resolution problem with speed and heading control represented as continuous decision variables. We show that the proposed disjunctive linear separation conditions are equivalent to the classical nonlinear conditions for aircraft separation. Further, we characterise conflict-free trajectories based on aircraft velocity bounds and propose a simple pre-processing algorithm to identify aircraft pairs which are either always conflict-free, or which cannot be separated using speed and heading control only. We then incorporate altitude control and propose a lexicographic optimisation formulation that aims to minimise the number of flight level changes before resolving outstanding conflicts via two-dimensional velocity control. The proposed mixed-integer programming formulations are nonconvex, and we propose convex relaxations, decomposition methods and constraint generation algorithms to solve the two-dimensional and lexicographic optimisation formulations to guaranteed optimality. Numerical experiments on four types of conflict resolution benchmarking instances are conducted to test the performance of the proposed mixed-integer formulations. Further, the proposed method is compared against two benchmarks based on state-of-the-art approaches for the aircraft conflict resolution problem. Our numerical results show that the proposed method largely outperforms both benchmarks in terms of runtime and is able to solve significantly more instances to global optimality.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Solving equilibrium problems using extended mathematical programming

We introduce an extended mathematical programming framework for specifying equilibrium problems and their variational representations, such as generalized Nash equilibrium, multiple optimization problems with equilibrium constraints, and (quasi-) variational inequalities, and computing solutions of them from modeling languages. We define a new set of constructs with which users annotate variables and equations of the model to describe equilibrium and variational problems. Our constructs enable a natural translation of the model from one formulation to another more computationally tractable form without requiring the modeler to supply derivatives. In the context of many independent agents in the equilibrium, we facilitate expression of sophisticated structures such as shared constraints and additional constraints on their solutions. We define shared variables and demonstrate their uses for sparse reformulation, economic equilibrium problems sharing economic states, mixed pricing behavior of agents, and so on. We give some equilibrium and variational examples from the literature and describe how to formulate them using our framework. Experimental results comparing performance of various complementarity formulations for shared variables are provided. Our framework has been implemented and is available within GAMS/EMP.

Equilibrium programming↗
NASA NTRS1995

A Variational Formulation for the Finite Element Analysis of Sound Wave Propagation in a Spherical Shell

Development of design tools to furnish optimal acoustic environments for lightweight aircraft demands the ability to simulate the acoustic system on a workstation. In order to form an effective mathematical model of the phenomena at hand, we have begun by studying the propagation of acoustic waves inside closed spherical shells. Using a fully-coupled fluid-structure interaction model based upon variational principles, we have written a finite element analysis program and are in the process of examining several test cases. Future investigations are planned to increase model accuracy by incorporating non-linear and viscous effects.

Lebiedzik, Catherine↗
NASA NTRS1986

The mathematical modeling of rapid solidification processing

The detailed formulation of and the results obtained from a continuum mechanics-based mathematical model of the planar flow melt spinning (PFMS) rapid solidification system are presented and discussed. The numerical algorithm proposed is capable of computing the cooling and freezing rates as well as the fluid flow and capillary phenomena which take place inside the molten puddle formed in the PFMS process. The FORTRAN listings of some of the most useful computer programs and a collection of appendices describing the basic equations used for the modeling are included.

Gutierrez-Miravete, E.↗
DOE OSTI2021

FLASSH 1.0: Full Law Analysis Scattering System Hub

Nuclear technologies, such as thermal reactors and critical systems, are driven by reaction rates which are directly dependent on thermal neutrons. The ability to calculate reaction rates is directly linked to the capability to predict and understand the cross sections. For atoms bound within a material structure, the available modes of energy exchange are captured in the Thermal Scattering Law (TSL, i.e. S(α,β)). The TSL is fundamentally a material property and can be defined explicitly to account for the excitation and deexcitation of the lattice energy states. This work describes the development of the Full Law Analysis Scattering System Hub (FLASSH) which calculates the TSL and cross sections. FLASSH is a modern code which has been designed to produce accurate TSL evaluations, remove historical approximations, and improve formulations while making advance physics accessible and simple to use.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Convex Programs for Minimal-Area Problems

The minimal-area problem that defines string diagrams in closed string field theory asks for the metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2π. This is an extremal length problem in conformal geometry as well as a problem in systolic geometry. Here, we consider the analogous minimal-area problem for homology classes of curves and, with the aid of calibrations and the max flow-min cut theorem, formulate it as a local convex program. We derive an equivalent dual program involving maximization of a concave functional. These two programs give new insights into the form of the minimal-area metric and are amenable to numerical solution. We explain how the homology problem can be modified to provide the solution to the original homotopy problem.

97 MATHEMATICS AND COMPUTING↗