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NASA NTRS1993

A Genetic Algorithm Tool (splicer) for Complex Scheduling Problems and the Space Station Freedom Resupply Problem

The Space Station Freedom will require the supply of items in a regular fashion. A schedule for the delivery of these items is not easy to design due to the large span of time involved and the possibility of cancellations and changes in shuttle flights. This paper presents the basic concepts of a genetic algorithm model, and also presents the results of an effort to apply genetic algorithms to the design of propellant resupply schedules. As part of this effort, a simple simulator and an encoding by which a genetic algorithm can find near optimal schedules have been developed. Additionally, this paper proposes ways in which robust schedules, i.e., schedules that can tolerate small changes, can be found using genetic algorithms.

Wang, Lui↗

NASA NTRS2004

Single Airfoil Gust Response Problem: Category 3, Problem 1

An unsteady aerodynamic code, called GUST3D (ref. 3), has been developed to solve equation (8) for flows with periodic vortical disturbances. The code uses a frequency-domain approach with second-order central differences and a pressure radiation condition in the far field. GUST3D requires as input certain mean flow quantities which are calculated separately by a potential flow solver. The solver calculates the mean ow using a Gothert's Rule approximation (ref. 3). On the airfoil surface, it uses the solution calculated by the potential code FLO36 (ref. 4). Figures 1-2 show the mean pressure along the airfoil surface for the two airfoil geometries. In Figures 3 - 8, we present the RMS pressure on the airfoil surface. Each figure shows three GUST3D solutions (calculated on grids with different far-field boundary locations). Three solutions are shown to provide some indication of the numerical uncertainty in the results. Figures 9 - 13 present the acoustic intensity. We again show three solutions per case. Note that no results are presented for the k1 = k2 = 2.0 loaded airfoil case, as an acceptable solution could not be obtained. A few comments need to be made about the results shown. First, since the last Workshop, the GUST3D code has been substantially upgraded. This includes implementing a more accurate far-field boundary condition (ref. 5) and developing improved gridding capabilities. This is the reason for any differences that may exist between the present results and results from the last Workshop. Second, the intensity results on the circle R = 4C were obtained using a Kirchoff method (ref. 6). The Kirchoff surface was the circle R = 2C. Finally, the GUST3D code is most accurate for low reduced frequencies. A new domain decomposition approach (ref. 7) has been developed to improve accuracy. Both the single domain and domain decomposition approaches were used in generating the present results.

Scott, James R.↗

NASA NTRS2012

JWST Near-Infrared Detector Degradation: Finding the Problem, Fixing the Problem, and Moving Forward

The James Webb Space Telescope (JWST) is the successor to the Hubble Space Telescope. JWST will be an infrared optimized telescope, with an approximately 6.5 m diameter primary mirror, that is located at the Sun-Earth L2 Lagrange point. Three of JWST's four science instruments use Teledyne HgCdTe HAWAII-2RG (H2RG) near infrared detector arrays. During 2010, the JWST Project noticed that a few of its 5 micron cutoff H2RG detectors were degrading during room temperature storage, and NASA chartered a "Detector Degradation Failure Review Board" (DD-FRB) to investigate. The DD-FRB determined that the root cause was a design flaw that allowed indium to interdiffuse with the gold contacts and migrate into the HgCdTe detector layer. Fortunately, Teledyne already had an improved design that eliminated this degradation mechanism. During early 2012, the improved H2RG design was qualified for flight and JWST began making additional H2RGs. In this article we present the two public DD-FRB "Executiye Summaries" that: (1) determined the root cause of the detector degradation and (2) defined tests to determine whether the existing detectors are qualified for flight. We supplement these with a brief introduction to H2RG detector arrays, and a discussion of how the JWST Project is using cryogenic storage to retard the degradation rate of the existing flight spare H2RGs.

Rauscher, Bernard J.↗

NASA NTRS1995

Solutions of the benchmark problems by the dispersion-relation-preserving scheme

The 7-point stencil Dispersion-Relation-Preserving scheme of Tam and Webb is used to solve all the six categories of the CAA benchmark problems. The purpose is to show that the scheme is capable of solving linear, as well as nonlinear aeroacoustics problems accurately. Nonlinearities, inevitably, lead to the generation of spurious short wave length numerical waves. Often, these spurious waves would overwhelm the entire numerical solution. In this work, the spurious waves are removed by the addition of artificial selective damping terms to the discretized equations. Category 3 problems are for testing radiation and outflow boundary conditions. In solving these problems, the radiation and outflow boundary conditions of Tam and Webb are used. These conditions are derived from the asymptotic solutions of the linearized Euler equations. Category 4 problems involved solid walls. Here, the wall boundary conditions for high-order schemes of Tam and Dong are employed. These conditions require the use of one ghost value per boundary point per physical boundary condition. In the second problem of this category, the governing equations, when written in cylindrical coordinates, are singular along the axis of the radial coordinate. The proper boundary conditions at the axis are derived by applying the limiting process of r approaches 0 to the governing equations. The Category 5 problem deals with the numerical noise issue. In the present approach, the time-independent mean flow solution is computed first. Once the residual drops to the machine noise level, the incident sound wave is turned on gradually. The solution is marched in time until a time-periodic state is reached. No exact solution is known for the Category 6 problem. Because of this, the problem is formulated in two totally different ways, first as a scattering problem then as a direct simulation problem. There is good agreement between the two numerical solutions. This offers confidence in the computed results. Both formulations are solved as initial value problems. As such, no Kutta condition is required at the trailing edge of the airfoil.

Tam, Christopher K. W.↗

NASA NTRS2011

Component-Level Electronic-Assembly Repair (CLEAR) Analysis of the Problem Reporting and Corrective Action (PRACA) Database of the International Space Station On-Orbit Electrical Systems

The NASA Constellation Program is investigating and developing technologies to support human exploration of the Moon and Mars. The Component-Level Electronic-Assembly Repair (CLEAR) task is part of the Supportability Project managed by the Exploration Technology Development Program. CLEAR is aimed at enabling a flight crew to diagnose and repair electronic circuits in space yet minimize logistics spares, equipment, and crew time and training. For insight into actual space repair needs, in early 2008 the project examined the operational experience of the International Space Station (ISS) program. CLEAR examined the ISS on-orbit Problem Reporting and Corrective Action database for electrical and electronic system problems. The ISS has higher than predicted reliability yet, as expected, it has persistent problems. A goal was to identify which on-orbit electrical problems could be resolved by a component-level replacement. A further goal was to identify problems that could benefit from the additional diagnostic and test capability that a component-level repair capability could provide. The study indicated that many problems stem from a small set of root causes that also represent distinct component problems. The study also determined that there are certain recurring problems where the current telemetry instrumentation and built-in tests are unable to completely resolve the problem. As a result, the root cause is listed as unknown. Overall, roughly 42 percent of on-orbit electrical problems on ISS could be addressed with a component-level repair. Furthermore, 63 percent of on-orbit electrical problems on ISS could benefit from additional external diagnostic and test capability. These results indicate that in situ component-level repair in combination with diagnostic and test capability can be expected to increase system availability and reduce logistics. The CLEAR approach can increase the flight crew s ability to act decisively to resolve problems while reducing dependency on Earth-supplied logistics for future Constellation Program missions.

Oeftering, Richard C.↗

NASA NTRS1986

Intuitive reasoning about abstract and familiar physics problems

Previous research has demonstrated that many people have misconceptions about basic properties of motion. Two experiments examined whether people are more likely to produce dynamically correct predictions about basic motion problems involving situations with which they are familiar, and whether solving such problems enhances performance on a subsequent abstract problem. In experiment 1, college students were asked to predict the trajectories of objects exiting a curved tube. Subjects were more accurate on the familiar version of the problem, and there was no evidence of transfer to the abstract problem. In experiment 2, two familiar problems were provided in an attempt to enhance subjects' tendency to extract the general structure of the problems. Once again, they gave more correct responses to the familiar problems but failed to generalize to the abstract problem. Formal physics training was associated with correct predictions for the abstract problem but was unrelated to performance on the familiar problems.

Kaiser, Mary Kister↗

NASA NTRS2003

Sub-problem Optimization With Regression and Neural Network Approximators

Design optimization of large systems can be attempted through a sub-problem strategy. In this strategy, the original problem is divided into a number of smaller problems that are clustered together to obtain a sequence of sub-problems. Solution to the large problem is attempted iteratively through repeated solutions to the modest sub-problems. This strategy is applicable to structures and to multidisciplinary systems. For structures, clustering the substructures generates the sequence of sub-problems. For a multidisciplinary system, individual disciplines, accounting for coupling, can be considered as sub-problems. A sub-problem, if required, can be further broken down to accommodate sub-disciplines. The sub-problem strategy is being implemented into the NASA design optimization test bed, referred to as "CometBoards." Neural network and regression approximators are employed for reanalysis and sensitivity analysis calculations at the sub-problem level. The strategy has been implemented in sequential as well as parallel computational environments. This strategy, which attempts to alleviate algorithmic and reanalysis deficiencies, has the potential to become a powerful design tool. However, several issues have to be addressed before its full potential can be harnessed. This paper illustrates the strategy and addresses some issues.

Guptill, James D.↗

NASA NTRS1984

Applying optimization software libraries to engineering problems

Nonlinear programming, preliminary design problems, performance simulation problems trajectory optimization, flight computer optimization, and linear least squares problems are among the topics covered. The nonlinear programming applications encountered in a large aerospace company are a real challenge to those who provide mathematical software libraries and consultation services. Typical applications include preliminary design studies, data fitting and filtering, jet engine simulations, control system analysis, and trajectory optimization and optimal control. Problem sizes range from single-variable unconstrained minimization to constrained problems with highly nonlinear functions and hundreds of variables. Most of the applications can be posed as nonlinearly constrained minimization problems. Highly complex optimization problems with many variables were formulated in the early days of computing. At the time, many problems had to be reformulated or bypassed entirely, and solution methods often relied on problem-specific strategies. Problems with more than ten variables usually went unsolved.

Healy, M. J.↗

NASA NTRS1923

Aeronautic instruments. Section I : general classification of instruments and problems including bibliography

This report is intended as a technical introduction to the series of reports on aeronautic instruments. It presents a discussion of those subjects which are common to all instruments. First, a general classification is given, embracing all types of instruments used in aeronautics. Finally, a classification is given of the various problems confronted by the instrument expert and investigator. In this way the following groups of problems are brought up for consideration: problems of mechanical design, human factor, manufacturing problems, supply and selection of instruments, problems concerning the technique of testing, problems of installation, problems concerning the use of instruments, problems of maintenance, and physical research problems. This enumeration of problems which are common to instruments in general serves to indicate the different points of view which should be kept in mind in approaching the study of any particular instrument.

Hersey, Mayo D↗

NASA NTRS1997

Least-Squares Spectral Element Solutions to the CAA Workshop Benchmark Problems

This paper presents computed results for some of the CAA benchmark problems via the acoustic solver developed at Rocketdyne CFD Technology Center under the corporate agreement between Boeing North American, Inc. and NASA for the Aerospace Industry Technology Program. The calculations are considered as benchmark testing of the functionality, accuracy, and performance of the solver. Results of these computations demonstrate that the solver is capable of solving the propagation of aeroacoustic signals. Testing of sound generation and on more realistic problems is now pursued for the industrial applications of this solver. Numerical calculations were performed for the second problem of Category 1 of the current workshop problems for an acoustic pulse scattered from a rigid circular cylinder, and for two of the first CAA workshop problems, i. e., the first problem of Category 1 for the propagation of a linear wave and the first problem of Category 4 for an acoustic pulse reflected from a rigid wall in a uniform flow of Mach 0.5. The aim for including the last two problems in this workshop is to test the effectiveness of some boundary conditions set up in the solver. Numerical results of the last two benchmark problems have been compared with their corresponding exact solutions and the comparisons are excellent. This demonstrates the high fidelity of the solver in handling wave propagation problems. This feature lends the method quite attractive in developing a computational acoustic solver for calculating the aero/hydrodynamic noise in a violent flow environment.

Lin, Wen H.↗

NASA NTRS1997

Dynamic Flow Management Problems in Air Transportation

In 1995, over six hundred thousand licensed pilots flew nearly thirty-five million flights into over eighteen thousand U.S. airports, logging more than 519 billion passenger miles. Since demand for air travel has increased by more than 50% in the last decade while capacity has stagnated, congestion is a problem of undeniable practical significance. In this thesis, we will develop optimization techniques that reduce the impact of congestion on the national airspace. We start by determining the optimal release times for flights into the airspace and the optimal speed adjustment while airborne taking into account the capacitated airspace. This is called the Air Traffic Flow Management Problem (TFMP). We address the complexity, showing that it is NP-hard. We build an integer programming formulation that is quite strong as some of the proposed inequalities are facet defining for the convex hull of solutions. For practical problems, the solutions of the LP relaxation of the TFMP are very often integral. In essence, we reduce the problem to efficiently solving large scale linear programming problems. Thus, the computation times are reasonably small for large scale, practical problems involving thousands of flights. Next, we address the problem of determining how to reroute aircraft in the airspace system when faced with dynamically changing weather conditions. This is called the Air Traffic Flow Management Rerouting Problem (TFMRP) We present an integrated mathematical programming approach for the TFMRP, which utilizes several methodologies, in order to minimize delay costs. In order to address the high dimensionality, we present an aggregate model, in which we formulate the TFMRP as a multicommodity, integer, dynamic network flow problem with certain side constraints. Using Lagrangian relaxation, we generate aggregate flows that are decomposed into a collection of flight paths using a randomized rounding heuristic. This collection of paths is used in a packing integer programming formulation, the solution of which generates feasible and near-optimal routes for individual flights. The algorithm, termed the Lagrangian Generation Algorithm, is used to solve practical problems in the southwestern portion of United States in which the solutions are within 1% of the corresponding lower bounds.

Patterson, Sarah Stock↗

NASA NTRS2006

NASA Taxonomies for Searching Problem Reports and FMEAs

Many types of hazard and risk analyses are used during the life cycle of complex systems, including Failure Modes and Effects Analysis (FMEA), Hazard Analysis, Fault Tree and Event Tree Analysis, Probabilistic Risk Assessment, Reliability Analysis and analysis of Problem Reporting and Corrective Action (PRACA) databases. The success of these methods depends on the availability of input data and the analysts knowledge. Standard nomenclature can increase the reusability of hazard, risk and problem data. When nomenclature in the source texts is not standard, taxonomies with mapping words (sets of rough synonyms) can be combined with semantic search to identify items and tag them with metadata based on a rich standard nomenclature. Semantic search uses word meanings in the context of parsed phrases to find matches. The NASA taxonomies provide the word meanings. Spacecraft taxonomies and ontologies (generalization hierarchies with attributes and relationships, based on terms meanings) are being developed for types of subsystems, functions, entities, hazards and failures. The ontologies are broad and general, covering hardware, software and human systems. Semantic search of Space Station texts was used to validate and extend the taxonomies. The taxonomies have also been used to extract system connectivity (interaction) models and functions from requirements text. Now the Reconciler semantic search tool and the taxonomies are being applied to improve search in the Space Shuttle PRACA database, to discover recurring patterns of failure. Usual methods of string search and keyword search fall short because the entries are terse and have numerous shortcuts (irregular abbreviations, nonstandard acronyms, cryptic codes) and modifier words cannot be used in sentence context to refine the search. The limited and fixed FMEA categories associated with the entries do not make the fine distinctions needed in the search. The approach assigns PRACA report titles to problem classes in the taxonomy. Each ontology class includes mapping words - near-synonyms naming different manifestations of that problem class. The mapping words for Problems, Entities and Functions are converted to a canonical form plus any of a small set of modifier words (e.g. non-uniformity NOT + UNIFORM.) The report titles are parsed as sentences if possible, or treated as a flat sequence of word tokens if parsing fails. When canonical forms in the title match mapping words, the PRACA entry is associated with the corresponding Problem, Entity or Function in the ontology. The user can search for types of failures associated with types of equipment, clustering by type of problem (e.g., all bearings found with problems of being uneven: rough, irregular, gritty ). The results could also be used for tagging PRACA report entries with rich metadata. This approach could also be applied to searching and tagging failure modes, failure effects and mitigations in FMEAs. In the pilot work, parsing 52K+ truncated titles (the test cases that were available), has resulted in identification of both a type of equipment and type of problem in about 75% of the cases. The results are displayed in a manner analogous to Google search results. The effort has also led to the enrichment of the taxonomy, adding some new categories and many new mapping words. Further work would make enhancements that have been identified for improving the clustering and further reducing the false alarm rate. (In searching for recurring problems, good clustering is more important than reducing false alarms). Searching complete PRACA reports should lead to immediate improvement.

Malin, Jane T.↗

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 OSTI2025

Optimization problems governed by systems of PDEs with uncertainties

This paper reviews current theoretical and numerical approaches to optimization problems governed by partial differential equations (PDEs) that depend on random variables or random fields. Such problems arise in many engineering, science, economics and societal decision-making tasks. This paper focuses on problems in which the governing PDEs are parametrized by the random variables/fields, and the decisions are made at the beginning and are not revised once uncertainty is revealed. Examples of such problems are presented to motivate the topic of this paper, and to illustrate the impact of different ways to model uncertainty in the formulations of the optimization problem and their impact on the solution. A linear–quadratic elliptic optimal control problem is used to provide a detailed discussion of the set-up for the risk-neutral optimization problem formulation, study the existence and characterization of its solution, and survey numerical methods for computing it. Different ways to model uncertainty in the PDE-constrained optimization problem are surveyed in an abstract setting, including risk measures, distributionally robust optimization formulations, probabilistic functions and chance constraints, and stochastic orders. Furthermore, approximation-based optimization approaches and stochastic methods for the solution of the large-scale PDE-constrained optimization problems under uncertainty are described. Some possible future research directions are outlined.

Heinkenschloss, Matthias [Rice Univ., Houston, TX ↗

DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗

NASA NTRS1984

Fundamental differences between optimization code test problems in engineering applications

The purpose here is to suggest that there is at least one fundamental difference between the problems used for testing optimization codes and the problems that engineers often need to solve; in particular, the level of precision that can be practically achieved in the numerical evaluation of the objective function, derivatives, and constraints. This difference affects the performance of optimization codes, as illustrated by two examples. Two classes of optimization problem were defined. Class One functions and constraints can be evaluated to a high precision that depends primarily on the word length of the computer. Class Two functions and/or constraints can only be evaluated to a moderate or a low level of precision for economic or modeling reasons, regardless of the computer word length. Optimization codes have not been adequately tested on Class Two problems. There are very few Class Two test problems in the literature, while there are literally hundreds of Class One test problems. The relative performance of two codes may be markedly different for Class One and Class Two problems. Less sophisticated direct search type codes may be less likely to be confused or to waste many function evaluations on Class Two problems. The analysis accuracy and minimization performance are related in a complex way that probably varies from code to code. On a problem where the analysis precision was varied over a range, the simple Hooke and Jeeves code was more efficient at low precision while the Powell code was more efficient at high precision.

Eason, E. D.↗

NASA NTRS1991

AI techniques for a space application scheduling problem

Scheduling is a very complex optimization problem which can be categorized as an NP-complete problem. NP-complete problems are quite diverse, as are the algorithms used in searching for an optimal solution. In most cases, the best solutions that can be derived for these combinatorial explosive problems are near-optimal solutions. Due to the complexity of the scheduling problem, artificial intelligence (AI) can aid in solving these types of problems. Some of the factors are examined which make space application scheduling problems difficult and presents a fairly new AI-based technique called tabu search as applied to a real scheduling application. the specific problem is concerned with scheduling application. The specific problem is concerned with scheduling solar and stellar observations for the SOLar-STellar Irradiance Comparison Experiment (SOLSTICE) instrument in a constrained environment which produces minimum impact on the other instruments and maximizes target observation times. The SOLSTICE instrument will gly on-board the Upper Atmosphere Research Satellite (UARS) in 1991, and a similar instrument will fly on the earth observing system (Eos).

Thalman, N.↗

NASA NTRS1991

Balancing antagonistic time and resource utilization constraints in over-subscribed scheduling problems

In this paper, we report work aimed at applying concepts of constraint-based problem structuring and multi-perspective scheduling to an over-subscribed scheduling problem. Previous research has demonstrated the utility of these concepts as a means for effectively balancing conflicting objectives in constraint-relaxable scheduling problems, and our goal here is to provide evidence of their similar potential in the context of HST observation scheduling. To this end, we define and experimentally assess the performance of two time-bounded heuristic scheduling strategies in balancing the tradeoff between resource setup time minimization and satisfaction of absolute time constraints. The first strategy considered is motivated by dispatch-based manufacturing scheduling research, and employs a problem decomposition that concentrates local search on minimizing resource idle time due to setup activities. The second is motivated by research in opportunistic scheduling and advocates a problem decomposition that focuses attention on the goal activities that have the tightest temporal constraints. Analysis of experimental results gives evidence of differential superiority on the part of each strategy in different problem solving circumstances. A composite strategy based on recognition of characteristics of the current problem solving state is then defined and tested to illustrate the potential benefits of constraint-based problem structuring and multi-perspective scheduling in over-subscribe scheduling problems.

Smith, Stephen F.↗