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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Metroplex Optimization Model Expansion and Analysis: The Airline Fleet, Route, and Schedule Optimization Model (AFRS-OM)

This report describes the Airline Fleet, Route, and Schedule Optimization Model (AFRS-OM) that is designed to provide insights into airline decision-making with regards to markets served, schedule of flights on these markets, the type of aircraft assigned to each scheduled flight, load factors, airfares, and airline profits. The main inputs to the model are hedged fuel prices, airport capacity limits, and candidate markets. Embedded in the model are aircraft performance and associated cost factors, and willingness-to-pay (i.e. demand vs. airfare curves). Case studies demonstrate the application of the model for analysis of the effects of increased capacity and changes in operating costs (e.g. fuel prices). Although there are differences between airports (due to differences in the magnitude of travel demand and sensitivity to airfare), the system is more sensitive to changes in fuel prices than capacity. Further, the benefits of modernization in the form of increased capacity could be undermined by increases in hedged fuel prices

Sherry, Lance↗
NASA NTRS1992

A new algorithm for L2 optimal model reduction

In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. Convergence of the proposed algorithm to stationary values of the quadratic cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.

Spanos, J. T.↗
NASA NTRS1990

Optimal model reduction and frequency-weighted extension

In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. The existence of globally optimal stable solutions to the optimization problem is established, and convergence of the algorithm to stationary values of the cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.

Spanos, J. T.↗
NASA NTRS1979

Spares-optimized model

Computerized spares optimization for Space Shuttle Project comprises analytical process for developing spares quantification and budget forecasts. Model, which assesses risk associated with recommended spares quantities, is enconomical way to determine best mix of large number of spare types.

Cain, A. W.↗
NASA NTRS1984

Manual of phosphoric acid fuel cell power plant optimization model and computer program

An optimized cost and performance model for a phosphoric acid fuel cell power plant system was derived and developed into a modular FORTRAN computer code. Cost, energy, mass, and electrochemical analyses were combined to develop a mathematical model for optimizing the steam to methane ratio in the reformer, hydrogen utilization in the PAFC plates per stack. The nonlinear programming code, COMPUTE, was used to solve this model, in which the method of mixed penalty function combined with Hooke and Jeeves pattern search was chosen to evaluate this specific optimization problem.

Lu, C. Y.↗
NASA NTRS2020

GISS Model E2.2: A Climate Model Optimized for the Middle Atmosphere. Part 1: Model Structure, Climatology, Variability and Climate Sensitivity

We introduce a new climate model (GISS E2.2) that has been specially optimized for the Middle Atmosphere, and whose output is being contributed to the CMIP6 archive. The top of the model is at a geopotential altitude of 89 km, and parameterizations of moist convection and various forms of gravity wave drag based on tropospheric processes are chosen specifically for this optimization. We first evaluate the model in its configuration as a coupled atmosphere-chemistry model with respect to its simulation of the mean state of the Middle Atmosphere, from the mesosphere down through the Upper Troposphere/Lower Stratosphere. Then we assess its use as a coupled atmosphere-ocean climate model by exploring its mean ocean climatology. To evaluate its variability, we report on its simulation of the primary modes in the troposphere, stratosphere and ocean. Two climate change simulations are presented, the responses to instantaneous increases of 2xCO2 and 4xCO2, run with two different ocean models. Sensitivity studies are performed to illustrate the effect of parameterizations on the model results. We compare these results to the lower vertical resolution/top GISS Model E2.1, whose output has also been submitted to CMIP6. The different choices made for these models are explored. It is shown that important improvements in the circulation above and below the tropopause can be obtained when attention is paid to representation of Middle Atmosphere processes in climate model development.

D. Rind↗
NASA NTRS1997

A Critical Survey of Optimization Models for Tactical and Strategic Aspects of Air Traffic Flow Management

This document presents a critical review of the principal existing optimization models that have been applied to Air Traffic Flow Management (TFM). Emphasis will be placed on two problems, the Generalized Tactical Flow Management Problem (GTFMP) and the Ground Holding Problem (GHP), as well as on some of their variations. To perform this task, we have carried out an extensive literature review that has covered more than 40 references, most of them very recent. Based on the review of this emerging field our objectives were to: (i) identify the best available models; (ii) describe typical contexts for applications of the models; (iii) provide illustrative model formulations; and (iv) identify the methodologies that can be used to solve the models. We shall begin our presentation below by providing a brief context for the models that we are reviewing. In Section 3 we shall offer a taxonomy and identify four classes of models for review. In Sections 4, 5, and 6 we shall then review, respectively, models for the Single-Airport Ground Holding Problem, the Generalized Tactical FM P and the Multi-Airport Ground Holding Problem (for the definition of these problems see Section 3 below). In each section, we identify the best available models and discuss briefly their computational performance and applications, if any, to date. Section 7 summarizes our conclusions about the state of the art.

Bertsimas, Dimitris↗
NASA NTRS1986

An optimization model for the US Air-Traffic System

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

Mulvey, J. M.↗
NASA NTRS2010

An Optimization Model for Scheduling Problems with Two-Dimensional Spatial Resource Constraint

Traditional scheduling problems involve determining temporal assignments for a set of jobs in order to optimize some objective. Some scheduling problems also require the use of limited resources, which adds another dimension of complexity. In this paper we introduce a spatial resource-constrained scheduling problem that can arise in assembly, warehousing, cross-docking, inventory management, and other areas of logistics and supply chain management. This scheduling problem involves a twodimensional rectangular area as a limited resource. Each job, in addition to having temporal requirements, has a width and a height and utilizes a certain amount of space inside the area. We propose an optimization model for scheduling the jobs while respecting all temporal and spatial constraints.

Garcia, Christopher↗
NASA NTRS2010

Optimizing Air Transportation Service to Metroplex Airports: Analysis Using the Airline Schedule Optimization Model (ASOM) - Par 2

The air transportation system is a significant driver of the U.S. economy, providing safe, affordable, and rapid transportation. During the past three decades airspace and airport capacity has not grown in step with demand for air transportation; the failure to increase capacity at the same rate as the growth in demand results in unreliable service and systemic delay. This report describes the results of an analysis of airline strategic decision-making that affects geographic access, economic access, and airline finances, extending the analysis of these factors using historic data (from Part 1 of the report). The Airline Schedule Optimization Model (ASOM) was used to evaluate how exogenous factors (passenger demand, airline operating costs, and airport capacity limits) affect geographic access (markets-served, scheduled flights, aircraft size), economic access (airfares), airline finances (profit), and air transportation efficiency (aircraft size). This analysis captures the impact of the implementation of airport capacity limits, as well as the effect of increased hedged fuel prices, which serve as a proxy for increased costs per flight that might occur if auctions or congestion pricing are imposed; also incorporated are demand elasticity curves based on historical data that provide information about how passenger demand is affected by airfare changes.

Donoue, George↗
NASA NTRS1973

On optimal modeling of systems.

A procedure for modeling a linear system by an optimal finite-dimensional approximation is developed on the basis of Sard's (1967) generalized spline. Error bounds are given, and the application of the procedure is illustrated by two presented examples. The procedure may be employed, not only in the modeling of conventional lumped-parameter and distributed-parameter continuous dynamical systems, but also in mathematical operations such as those involved in pattern recognition and picture enhancement problems.

De Figueiredo, R. J. P.↗
NASA NTRS2014

A Formal Approach to Empirical Dynamic Model Optimization and Validation

A framework was developed for the optimization and validation of empirical dynamic models subject to an arbitrary set of validation criteria. The validation requirements imposed upon the model, which may involve several sets of input-output data and arbitrary specifications in time and frequency domains, are used to determine if model predictions are within admissible error limits. The parameters of the empirical model are estimated by finding the parameter realization for which the smallest of the margins of requirement compliance is as large as possible. The uncertainty in the value of this estimate is characterized by studying the set of model parameters yielding predictions that comply with all the requirements. Strategies are presented for bounding this set, studying its dependence on admissible prediction error set by the analyst, and evaluating the sensitivity of the model predictions to parameter variations. This information is instrumental in characterizing uncertainty models used for evaluating the dynamic model at operating conditions differing from those used for its identification and validation. A practical example based on the short period dynamics of the F-16 is used for illustration.

Crespo, Luis G↗
NASA NTRS2003

A method of hidden Markov model optimization for use with geophysical data sets

Geophysics research has been faced with a growing need for automated techniques with which to process large quantities of data. A successful tool must meet a number of requirements: it should be consistent, require minimal parameter tuning, and produce scientifically meaningful results in reasonable time. We introduce a hidden Markov model (HMM)-based method for analysis of geophysical data sets that attempts to address these issues.

Markov model optimization geophysical data sets↗
NASA NTRS2009

Regression Model Optimization for the Analysis of Experimental Data

A candidate math model search algorithm was developed at Ames Research Center that determines a recommended math model for the multivariate regression analysis of experimental data. The search algorithm is applicable to classical regression analysis problems as well as wind tunnel strain gage balance calibration analysis applications. The algorithm compares the predictive capability of different regression models using the standard deviation of the PRESS residuals of the responses as a search metric. This search metric is minimized during the search. Singular value decomposition is used during the search to reject math models that lead to a singular solution of the regression analysis problem. Two threshold dependent constraints are also applied. The first constraint rejects math models with insignificant terms. The second constraint rejects math models with near-linear dependencies between terms. The math term hierarchy rule may also be applied as an optional constraint during or after the candidate math model search. The final term selection of the recommended math model depends on the regressor and response values of the data set, the user s function class combination choice, the user s constraint selections, and the result of the search metric minimization. A frequently used regression analysis example from the literature is used to illustrate the application of the search algorithm to experimental data.

Ulbrich, N.↗
NASA NTRS2009

The Integrated Medical Model - Optimizing In-flight Space Medical Systems to Reduce Crew Health Risk and Mission Impacts

The Integrated Medical Model (IMM) is a decision support tool used by medical system planners and designers as they prepare for exploration planning activities of the Constellation program (CxP). IMM provides an evidence-based approach to help optimize the allocation of in-flight medical resources for a specified level of risk within spacecraft operational constraints. Eighty medical conditions and associated resources are represented in IMM. Nine conditions are due to Space Adaptation Syndrome. The IMM helps answer fundamental medical mission planning questions such as What medical conditions can be expected? What type and quantity of medical resources are most likely to be used?", and "What is the probability of crew death or evacuation due to medical events?" For a specified mission and crew profile, the IMM effectively characterizes the sequence of events that could potentially occur should a medical condition happen. The mathematical relationships among mission and crew attributes, medical conditions and incidence data, in-flight medical resources, potential clinical and crew health end states are established to generate end state probabilities. A Monte Carlo computational method is used to determine the probable outcomes and requires up to 25,000 mission trials to reach convergence. For each mission trial, the pharmaceuticals and supplies required to diagnose and treat prevalent medical conditions are tracked and decremented. The uncertainty of patient response to treatment is bounded via a best-case, worst-case, untreated case algorithm. A Crew Health Index (CHI) metric, developed to account for functional impairment due to a medical condition, provides a quantified measure of risk and enables risk comparisons across mission scenarios. The use of historical in-flight medical data, terrestrial surrogate data as appropriate, and space medicine subject matter expertise has enabled the development of a probabilistic, stochastic decision support tool capable of optimizing in-flight medical systems based on crew and mission parameters. This presentation will illustrate how to apply quantitative risk assessment methods to optimize the mass and volume of space-based medical systems for a space flight mission given the level of crew health and mission risk.

Kerstman, Eric↗