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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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Parameter extraction and transistor models

Using specified mathematical models of the MOSFET device, the optimal values of the model-dependent parameters were extracted from data provided by the Jet Propulsion Laboratory (JPL). Three MOSFET models, all one-dimensional were used. One of the models took into account diffusion (as well as convection) currents. The sensitivity of the models was assessed for variations of the parameters from their optimal values. Lines of future inquiry are suggested on the basis of the behavior of the devices, of the limitations of the proposed models, and of the complexity of the required numerical investigations.

Rykken, Charles↗
NASA NTRS1988

Analysis procedures and subjective flight results of a simulator validation and cue fidelity experiment

A joint experiment to investigate simulator validation and cue fidelity was conducted by the Dryden Flight Research Facility of NASA Ames Research Center (Ames-Dryden) and NASA Langley Research Center. The primary objective was to validate the use of a closed-loop pilot-vehicle mathematical model as an analytical tool for optimizing the tradeoff between simulator fidelity requirements and simulator cost. The validation process includes comparing model predictions with simulation and flight test results to evaluate various hypotheses for differences in motion and visual cues and information transfer. A group of five pilots flew air-to-air tracking maneuvers in the Langley differential maneuvering simulator and visual motion simulator and in an F-14 aircraft at Ames-Dryden. The simulators used motion and visual cueing devices including a g-seat, a helmet loader, wide field-of-view horizon, and a motion base platform.

Carr, Peter C.↗
NASA NTRS1993

A new sensitivity analysis for structural optimization of composite rotor blades

This paper presents a detailed mathematical derivation of the sensitivity derivatives for the structural dynamic, aeroelastic stability and response characteristics of a rotor blade in hover and forward flight. The formulation is denoted by the term semianalytical approach, because certain derivatives have to be evaluated by a finite difference scheme. Using the present formulation, sensitivity derivatives for the structural dynamic and aeroelastic stability characteristics, were evaluated for both isotropic and composite rotor blades. Based on the results, useful conclusions are obtained regarding the relative merits of the semi-analytical approach, for calculating sensitivity derivatives, when compared to a pure finite difference approach.

Venkatesan, C.↗
NASA NTRS2018

Information Theory Applied to Decision Making Structures

Decision making structures, such as control boards, process information on many topics as they select options for the system and project. The decisions are based on the information known to the board members and presenters (subject matter experts) and shared at the board during discussion. This information flow through this process can be modelled using information theory. Information theory provides a mathematical basis to understand the flow of information through the decision making process and the information needed for a particular decision. Information theory also provides the mathematical relationships on which to base the optimal decision making structure for a specific system development and organizational structure. Since decision making bodies provide control for the system or project, control theory can be used to construct a decision making model. This provides a starting point for adding cognitive science models. Information processing by each individual board participant can be represented through cognitive processes which are integrated across the board participants through information theory relationship. The set theory view of information theory provides a structure in which to look at the relationships between the participants in a decision making structure.

Watson, Michael D.↗
NASA NTRS2018

Information Theory Applied to Decision Making Structures

Decision making structures, such as control boards, process information on many topics as they select options for the system and project. The decisions are based on the information known to the board members and presenters (subject matter experts) and shared at the board during discussion. This information flow through this process can be modelled using information theory. Information theory provides a mathematical basis to understand the flow of information through the decision making process and the information needed for a particular decision. Information theory also provides the mathematical relationships on which to base the optimal decision making structure for a specific system development and organizational structure. Since decision making bodies provide control for the system or project, control theory can be used to construct a decision making model. This provides a starting point for adding cognitive science models. Information processing by each individual board participant can be represented through cognitive processes which are integrated across the board participants through information theory relationship. The set theory view of information theory provides a structure in which to look at the relationships between the participants in a decision making structure.

Watson, Michael D.↗
DOE OSTI2024

A survey on checkpointing strategies: Should we always checkpoint à la Young/Daly?

The Young/Daly formula provides an approximation of the optimal checkpointing period for a parallel application executing on a supercomputing platform. It was originally designed to handle fail-stop errors for preemptible tightly-coupled applications, but has been extended to other application and resilience frameworks. Here, we provide some background and survey various scenarios to assess the usefulness and limitations of the formula, both for preemptible applications and workflow applications represented as a graph of tasks. We also discuss scenarios with uncertainties, and extend the study to silent errors. We exhibit cases where the optimal period is of a different order than that dictated by the Young/Daly formula, and finally we explain how checkpointing can be further combined with replication.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Bayesian Optimization for Reactor Design Optimization

This study present a test case in which the Bayesian Optimization method is applied to a simulation-based reactor core design optimization problem. The test case aims to showcase the potential of an automated design optimization algorithm for reactor designs by streamlining the reactor core design workflow, given the high computational cost of simulations. The contributions of this work are threefold. First, the existing HTGR model is converted into a simulation-based design optimization test case by developing a pipeline that enables modification of key design parameters and evaluates design performance based on simulation outputs. Second, Bayesian Optimization is implemented and adapted to demonstrate the feasibility of automatic design optimization for nuclear reactor core. Proposed approach leverages Gaussian Process models to characterize the relationship between design variables and performance metrics, while incorporating novel acquisition functions that balance exploration of the design space with exploitation of promising configurations. This implementation lays the foundation for the future developments of reactor design optimization algorithms.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1995

Multidisciplinary aerospace design optimization: Survey of recent developments

The increasing complexity of engineering systems has sparked increasing interest in multidisciplinary optimization (MDO). This paper presents a survey of recent publications in the field of aerospace where interest in MDO has been particularly intense. The two main challenges of MDO are computational expense and organizational complexity. Accordingly the survey is focussed on various ways different researchers use to deal with these challenges. The survey is organized by a breakdown of MDO into its conceptual components. Accordingly, the survey includes sections on Mathematical Modeling, Design-oriented Analysis, Approximation Concepts, Optimization Procedures, System Sensitivity, and Human Interface. With the authors' main expertise being in the structures area, the bulk of the references focus on the interaction of the structures discipline with other disciplines. In particular, two sections at the end focus on two such interactions that have recently been pursued with a particular vigor: Simultaneous Optimization of Structures and Aerodynamics, and Simultaneous Optimization of Structures Combined With Active Control.

Sobieszczanski-Sobieski, Jaroslaw↗
NASA NTRS1997

Execution of Multidisciplinary Design Optimization Approaches on Common Test Problems

A class of synthetic problems for testing multidisciplinary design optimization (MDO) approaches is presented. These test problems are easy to reproduce because all functions are given as closed-form mathematical expressions. They are constructed in such a way that the optimal value of all variables and the objective is unity. The test problems involve three disciplines and allow the user to specify the number of design variables, state variables, coupling functions, design constraints, controlling design constraints, and the strength of coupling. Several MDO approaches were executed on two sample synthetic test problems. These approaches included single-level optimization approaches, collaborative optimization approaches, and concurrent subspace optimization approaches. Execution results are presented, and the robustness and efficiency of these approaches an evaluated for these sample problems.

Balling, R. J.↗
DOE OSTI2024

Distributionally Robust Variational Quantum Algorithms With Shifted Noise

Given their potential to demonstrate near-term quantum advantage, variational quantum algorithms (VQAs) have been extensively studied. Although numerous techniques have been developed for VQA parameter optimization, it remains a significant challenge. A practical issue is the high sensitivity of quantum noise to environmental changes, and its propensity to shift in real time. This presents a critical problem as an optimized VQA ansatz may not perform effectively under a different noise environment. For the first time, we explore how to optimize VQA parameters to be robust against unknown shifted noise. We model the noise level as a random variable with an unknown probability density function (PDF), and we assume that the PDF may shift within an uncertainty set. This assumption guides us to formulate a distributionally robust optimization problem, with the goal of finding parameters that maintain effectiveness under shifted noise. We utilize a distributionally robust Bayesian optimization solver for our proposed formulation. This provides numerical evidence in both the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE) with hardware-efficient ansatz, indicating that we can identify parameters that perform more robustly under shifted noise. We regard this work as the first step towards improving the reliability of VQAs influenced by real-time noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Multistage economic MPC for systems with a cyclic steady state: A gas network case study

Multistage model predictive control (MPC) provides a robust control strategy for dynamic systems with uncertainties and a setpoint tracking objective. Moreover, extending MPC to minimize an economic cost instead of tracking a pre-calculated optimal setpoint improves controller performance. This paper presents a novel multistage economic nonlinear model predictive control (E-NMPC) framework for dynamic systems operating under uncertainty, with specific application to natural gas transmission networks. A key innovation lies in the integration of cyclic steady-state (CSS) constraints within the multistage MPC formulation, enabling the controller to manage periodic operating conditions commonly observed in energy systems. A Lyapunov-based descent condition is enforced to ensure robust stability of the controller. The multistage economic MPC framework is validated on two gas pipeline case studies, where it successfully minimizes net energy consumption, respects operational constraints under uncertain demand profiles, and guides the network to optimal cyclic operation. The Lyapunov function remains bounded in both case studies, validating the robust stability of multistage E-NMPC.

03 NATURAL GAS↗
DOE OSTI2026

Relaxations of the steady optimal gas flow problem for a non-Ideal gas

Natural gas ranks second in U.S. primary energy consumption. Because most production sites are remote, gas must be transported through pipeline networks equipped with compressors, valves, and other components. For both economic efficiency and system reliability, it is desirable to operate these networks optimally. The governing physics across pipeline components entails nonlinear, non-convex equality and inequality constraints, and the most general steady-flow operations problem is a Mixed-Integer Nonlinear Program (MINLP).This work focuses on one such steady-flow problem-the Optimal Gas Flow (OGF) for a natural gas pipeline network-which minimizes production cost subject to the steady-flow physics. For day-to-day operations, the ability to quickly compute a globally optimal solution and a strong lower bound for varying demand profiles is crucial. A promising strategy is to build tight relaxations of the OGF’s nonlinear constraints. However, many nonlinearities arising from non-ideal equations of state either lack relaxations or have relaxations that do not scale to realistic network sizes. We address this gap by combining recent advances in polyhedral relaxations for univariate functions to construct tight, computationally efficient relaxations of the OGF with a non-ideal equation of state. These relaxations solve within seconds on a standard laptop. In conclusion, we demonstrate their quality through extensive numerical experiments on very large-scale test networks from the literature and find that the proposed approach proves optimality in 92% of tested instances.

03 NATURAL GAS↗
NASA NTRS1993

DUKSUP - A high thrust trajectory optimization code

Designing missions on expendable launch vehicles (ELV's) includes determining launch vehicle performance capabilities and trajectory characteristics over the range of mission requirements for suitable launch periods. This analysis depends on mathematically modeling both the launch vehicle and the mission requirements. Generally the result is a mathematical model that is described by an objective function to be optimized subject to an assortment of algebraic and dynamic constraints. About 30 years ago, engineers at Lewis Research Center (LeRC) undertook the task of creating a software code to solve 3D versions of such problems and based it on the Calculus of Variations/Optimal Control Theory. One of these codes, DUKSUP, has been in use at LeRC for nearly 25 years, during which time it has played an important role in a large number of studies and actual missions. Currently it is being used by about 12 analysts in the Center's Advanced Space Analysis Office (ASAO) to do mission design, feasibility studies, corroboration of contractor data and planning studies for the Space Exploration Initiative (SEI). Today, it is one of the few ELV mission analysis production codes based on variational methods. With future ELV missions in mind, ASAO is presently creating a new code to upgrade DUKSUP's capabilities.

Balkanyi, Leslie R.↗
DOE OSTI2026

Superstructure Optimization for Brine Valorization from Brackish Water Desalination

This poster presents preliminary results from a superstructure optimization framework developed to identify cost-optimal brine valorization configurations for brackish water desalination plants across diverse U.S. regional feed chemistries. The study uses brackish groundwater compositions from Arizona, California, Florida, New Mexico, and Texas. Using Pyomo Generalized Disjunctive Programming (GDP) within the WaterTAP modeling environment, the optimization framework simultaneously evaluates thousands of candidate treatment configurations, spanning nanofiltration, reverse osmosis, and chemical precipitation, to minimize the levelized cost of water (LCOW) while meeting water recovery targets and product recovery constraints. Results across eight representative feed clusters demonstrate water recovery rates of 57–87% and net LCOW values ranging from -$0.032/m³ (net revenue-positive) to $0.80/m. Notably, no single process configuration was optimal across all feed types, underscoring the necessity of feed-specific optimization. Products targeted include calcium carbonate (CaCO₃) at $0.01/kg and sodium chloride (NaCl) at $0.10/kg, both at 95% purity, with product revenues offsetting treatment costs in several scenarios. The work advances NAWI's process systems engineering capabilities for multi-configuration screening.

58 GEOSCIENCES↗
DOE OSTI2024

Optimizing Desalination Operations for Energy Flexibility

Despite the value of energy optimization in desalination processes, modeling dynamic operations for monthly billing periods has remained a computational challenge. This work proposes a framework for energy flexibility optimization, which includes new modeling features for independent operation of parallel skids, start-up delays associated with chemical stabilization, the consideration of industrial energy tariff structures, and inclusion of hourly electrical carbon intensities. This is done using a modular and computationally efficient formulation that guarantees a globally optimal solution with standard optimization solvers. In this study, the approach is demonstrated in two distinct case studies: a seawater desalination plant in Santa Barbara, CA, and an indirect potable reuse facility in San Jose, CA. Trends predicted from the model are validated against operational facility measurements from a demand response shutdown event. Preliminary results show that optimizing energy flexibility can result in 18.51% monthly cost savings over energy efficiency-optimized operation. The value extracted from a facility-wide shutdown during peak electricity price hours is hampered by start-up delays in post-treatment chemical stabilization. In cases in which a facility does not have much excess capacity, using a flow equalization tank or operating over a wide recovery range may be cost-effective.

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

Graph decomposition techniques for solving combinatorial optimization problems with variational quantum algorithms

The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to hardware constraints. In this work, we develop an algorithm that decomposes the QAOA input problem graph into a smaller problem and solves MaxCut using QAOA on the reduced graph. The algorithm requires a subroutine that can be classical or quantum—in this work, we implement the algorithm twice on each graph. One implementation uses the classical solver Gurobi in the subroutine and the other uses QAOA. We solve these reduced problems with QAOA. On average, the reduced problems require only approximately 1/10 of the number of vertices than the original MaxCut instances. Furthermore, the average approximation ratio of the original MaxCut problems is 0.75, while the approximation ratios of the decomposed graphs are on average of 0.96 for both Gurobi and QAOA. With this decomposition, we are able to measure optimal solutions for ten 100-vertex graphs by running single-layer QAOA circuits on the Quantinuum trapped-ion quantum computer H1-1, sampling each circuit only 500 times. This approach is best suited for sparse, particularly k-regular graphs, as k-regular graphs on n vertices can be decomposed into a graph with at most $\frac{nk}{k+1}$ vertices in polynomial time. Further reductions can be obtained with a potential trade-off in computational time. In conclusion, while this paper applies the decomposition method to the MaxCut problem, it can be applied to more general classes of combinatorial optimization problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Bayes_Opt-SWMM: A Gaussian process-based Bayesian optimization tool for real-time flood modeling with SWMM

Real-time flood model plays a pivotal role in averting urban flood damage, particularly when there is minimal lead time for preparatory measures. However, urban flood modeling in real-time often contends with inherent uncertainties arising from input data uncertainty and parameter ambiguities. Here this study introduces a real-time calibration (RTC) tool called Bayes_Opt-SWMM, specifically tailored for real-time urban flood modeling and uncertainty optimization. This tool leverages the Gaussian process-based Bayesian optimization algorithm and interfaces seamlessly with the Stormwater Management Model (SWMM). It integrates real-time model forcing data and flood monitoring collected through sensors and gauges which are strategically placed within critical locations of urban drainage systems. Our approach hinges on the Surrogate Model based Uncertainty Optimization (SMUO) concept, providing an avenue for enhancing real-time flood modeling. Bayes_Opt-SWMM runs the optimization process using a surrogate model called Gaussian Process emulator with two inference methods: (1) the Gaussian Process (GP) model and (2) Markov Chain Monte Carlo (MCMC) algorithm in GP model (GP_MCMC). Furthermore, three acquisition functions, namely Expected Improvement (EI), Maximum Probability of Improvement (MPI), and Lower Confidence Bound (LCB), facilitate optimal parameter fitting within the surrogate models. The efficiency of GP-based surrogate models in learning SWMM model parameters, leads to an improved uncertainty quantification and accelerated real-time flood modeling in urban areas. Overall, Bayes_Opt-SWMM emerges as a cost-effective and valuable tool for real-time flood modeling and monitoring, with significant potential for managing intelligent storm water systems in urban environments.

54 ENVIRONMENTAL SCIENCES↗