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NASA NTRS1989

Optimal placement of excitations and sensors by simulated annealing

The optimal placement of discrete actuators and sensors is posed as a combinatorial optimization problem. Two examples for truss structures were used for illustration; the first dealt with the optimal placement of passive dampers along existing truss members, and the second dealt with the optimal placement of a combination of a set of actuators and a set of sensors. Except for the simplest problems, an exact solution by enumeration involves a very large number of function evaluations, and is therefore computationally intractable. By contrast, the simulated annealing heuristic involves far fewer evaluations and is best suited for the class of problems considered. As an optimization tool, the effectiveness of the algorithm is enhanced by introducing a number of rules that incorporate knowledge about the physical behavior of the problem. Some of the suggested rules are necessarily problem dependent.

Salama, Moktar↗

NASA NTRS2000

Perspectives on the Future of CFD

This viewgraph presentation gives an overview of the future of computational fluid dynamics (CFD), which in the past has pioneered the field of flow simulation. Over time CFD has progressed as computing power. Numerical methods have been advanced as CPU and memory capacity increases. Complex configurations are routinely computed now and direct numerical simulations (DNS) and large eddy simulations (LES) are used to study turbulence. As the computing resources changed to parallel and distributed platforms, computer science aspects such as scalability (algorithmic and implementation) and portability and transparent codings have advanced. Examples of potential future (or current) challenges include risk assessment, limitations of the heuristic model, and the development of CFD and information technology (IT) tools.

Kwak, Dochan↗

NASA NTRS2005

Kalman Filter Constraint Tuning for Turbofan Engine Health Estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints are often neglected because they do not fit easily into the structure of the Kalman filter. Recently published work has shown a new method for incorporating state variable inequality constraints in the Kalman filter, which has been shown to generally improve the filter s estimation accuracy. However, the incorporation of inequality constraints poses some risk to the estimation accuracy as the Kalman filter is theoretically optimal. This paper proposes a way to tune the filter constraints so that the state estimates follow the unconstrained (theoretically optimal) filter when the confidence in the unconstrained filter is high. When confidence in the unconstrained filter is not so high, then we use our heuristic knowledge to constrain the state estimates. The confidence measure is based on the agreement of measurement residuals with their theoretical values. The algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate engine health.

Simon, Dan↗

NASA NTRS2005

Centralized Planning for Multiple Exploratory Robots

A computer program automatically generates plans for a group of robotic vehicles (rovers) engaged in geological exploration of terrain. The program rapidly generates multiple command sequences that can be executed simultaneously by the rovers. Starting from a set of high-level goals, the program creates a sequence of commands for each rover while respecting hardware constraints and limitations on resources of each rover and of hardware (e.g., a radio communication terminal) shared by all the rovers. First, a separate model of each rover is loaded into a centralized planning subprogram. The centralized planning software uses the models of the rovers plus an iterative repair algorithm to resolve conflicts posed by demands for resources and by constraints associated with the all the rovers and the shared hardware. During repair, heuristics are used to make planning decisions that will result in solutions that will be better and will be found faster than would otherwise be possible. In particular, techniques from prior solutions of the multiple-traveling- salesmen problem are used as heuristics to generate plans in which the paths taken by the rovers to assigned scientific targets are shorter than they would otherwise be.

Estlin, Tara↗

DOE OSTI2022

Quantum annealing for jet clustering with thrust

Quantum computing holds the promise of substantially speeding up computationally expensive tasks, such as solving optimization problems over a large number of elements. In high-energy collider physics, quantum-assisted algorithms might accelerate the clustering of particles into jets. In this study, we benchmark quantum annealing strategies for jet clustering based on optimizing a quantity called “thrust” in electron-positron collision events. Here, we find that quantum annealing yields similar performance to exact classical approaches and classical heuristics, after tuning the annealing parameters. Without tuning, comparable performance can be obtained through a hybrid quantum/classical approach.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

A mathematical assessment of the isolation random forest method for anomaly detection in big data

We present the mathematical analysis of the Isolation Random Forest Method (IRF Method) for anomaly detection, proposed by Liu F.T., Ting K.M. and Zhou Z. H. in their seminal work as a heuristic method for anomaly detection in Big Data. We prove that the IRF space can be endowed with a probability induced by the Isolation Tree algorithm (iTree). In this setting, the convergence of the IRF method is proved, using the Law of Large Numbers. Here, a couple of counterexamples are presented to show that the method is inconclusive and no certificate of quality can be given, when using it as a means to detect anomalies. Hence, an alternative version of the method is proposed whose mathematical foundation is fully justified. Furthermore, a criterion for choosing the number of sampled trees needed to guarantee confidence intervals of the numerical results is presented. Finally, numerical experiments are presented to compare the performance of the classic method with the proposed one.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2022

TESS Eclipsing Binary Stars. I. Short-cadence Observations of 4584 Eclipsing Binaries in Sectors 1–26

In this paper we present a catalog of 4584 eclipsing binaries observed during the first two years (26 sectors) of the TESS survey. We discuss selection criteria for eclipsing binary candidates, detection of hitherto unknown eclipsing systems, determination of the ephemerides, the validation and triage process, and the derivation of heuristic estimates for the ephemerides. Instead of keeping to the widely used discrete classes, we propose a binary star morphology classification based on a dimensionality reduction algorithm. Finally, we present statistical properties of the sample, we qualitatively estimate completeness, and we discuss the results. The work presented here is organized and performed within the TESS Eclipsing Binary Working Group, an open group of professional and citizen scientists; we conclude by describing ongoing work and future goals for the group. The catalog is available from http://tessEBs.villanova.edu and from MAST.

Andrej Prša↗

DOE OSTI2023

Description of reaction and vibrational energetics of CO 2 –NH 3 interaction using quantum computing algorithms

CO 2 capture is critical to solving global warming. Amine-based solvents are extensively used to chemically absorb CO 2 . Thus, it is crucial to study the chemical absorption of CO 2 by amine-based solvents to better understand and optimize CO 2 capture processes. Here, we use quantum computing algorithms to quantify molecular vibrational energies and reaction pathways between CO 2 and a simplified amine-based solvent model—NH 3 . Molecular vibrational properties are important to understanding kinetics of reactions. However, the molecule size correlates with the strength of anharmonicity effect on vibrational properties, which can be challenging to address using classical computing. Quantum computing can help enhance molecular vibrational calculations by including anharmonicity. We implement a variational quantum eigensolver (VQE) algorithm in a quantum simulator to calculate ground state vibrational energies of reactants and products of the CO 2 and NH 3 reaction. The VQE calculations yield ground vibrational energies of CO 2 and NH 3 with similar accuracy to classical computing. In the presence of hardware noise, Compact Heuristic for Chemistry (CHC) ansatz with shallower circuit depth performs better than Unitary Vibrational Coupled Cluster. The “Zero Noise Extrapolation” error-mitigation approach in combination with CHC ansatz improves the vibrational calculation accuracy. Excited vibrational states are accessed with quantum equation of motion method for CO 2 and NH 3 . Using quantum Hartree–Fock (HF) embedding algorithm to calculate electronic energies, the corresponding reaction profile compares favorably with Coupled Cluster Singles and Doubles while being more accurate than HF. Our research showcases quantum computing applications in the study of CO 2 capture reactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1988

A multistage linear array assignment problem

The implementation of certain algorithms on parallel processing computing architectures can involve partitioning contiguous elements into a fixed number of groups, each of which is to be handled by a single processor. It is desired to find an assignment of elements to processors that minimizes the sum of the maximum workloads experienced at each stage. This problem can be viewed as a multi-objective network optimization problem. Polynomially-bounded algorithms are developed for the case of two stages, whereas the associated decision problem (for an arbitrary number of stages) is shown to be NP-complete. Heuristic procedures are therefore proposed and analyzed for the general problem. Computational experience with one of the exact problems, incorporating certain pruning rules, is presented with one of the exact problems. Empirical results also demonstrate that one of the heuristic procedures is especially effective in practice.

Nicol, David M.↗

NASA NTRS2009

Computing Bounds on Resource Levels for Flexible Plans

A new algorithm efficiently computes the tightest exact bound on the levels of resources induced by a flexible activity plan (see figure). Tightness of bounds is extremely important for computations involved in planning because tight bounds can save potentially exponential amounts of search (through early backtracking and detection of solutions), relative to looser bounds. The bound computed by the new algorithm, denoted the resource-level envelope, constitutes the measure of maximum and minimum consumption of resources at any time for all fixed-time schedules in the flexible plan. At each time, the envelope guarantees that there are two fixed-time instantiations one that produces the minimum level and one that produces the maximum level. Therefore, the resource-level envelope is the tightest possible resource-level bound for a flexible plan because any tighter bound would exclude the contribution of at least one fixed-time schedule. If the resource- level envelope can be computed efficiently, one could substitute looser bounds that are currently used in the inner cores of constraint-posting scheduling algorithms, with the potential for great improvements in performance. What is needed to reduce the cost of computation is an algorithm, the measure of complexity of which is no greater than a low-degree polynomial in N (where N is the number of activities). The new algorithm satisfies this need. In this algorithm, the computation of resource-level envelopes is based on a novel combination of (1) the theory of shortest paths in the temporal-constraint network for the flexible plan and (2) the theory of maximum flows for a flow network derived from the temporal and resource constraints. The measure of asymptotic complexity of the algorithm is O(N O(maxflow(N)), where O(x) denotes an amount of computing time or a number of arithmetic operations proportional to a number of the order of x and O(maxflow(N)) is the measure of complexity (and thus of cost) of a maximumflow algorithm applied to an auxiliary flow network of 2N nodes. The algorithm is believed to be efficient in practice; experimental analysis shows the practical cost of maxflow to be as low as O(N1.5). The algorithm could be enhanced following at least two approaches. In the first approach, incremental subalgorithms for the computation of the envelope could be developed. By use of temporal scanning of the events in the temporal network, it may be possible to significantly reduce the size of the networks on which it is necessary to run the maximum-flow subalgorithm, thereby significantly reducing the time required for envelope calculation. In the second approach, the practical effectiveness of resource envelopes in the inner loops of search algorithms could be tested for multi-capacity resource scheduling. This testing would include inner-loop backtracking and termination tests and variable and value-ordering heuristics that exploit the properties of resource envelopes more directly.

Muscvettola, Nicola↗

DOE OSTI2022

graphenv: a Python library for reinforcement learning on graph search spaces

Many important and challenging problems in combinatorial optimization (CO) can be expressed as graph search problems, in which graph vertices represent full or partial solutions and edges represent decisions that connect them. Graph structure not only introduces strong relational inductive biases for learning (Battaglia et al., 2018) - in this context, by providing a way to explicitly model the value of transitioning (along edges) between one search state (vertex) and the next - but lends itself to problems both with and without clearly defined algebraic structure. For example, classic CO problems on graphs such as the Traveling Salesman Problem (TSP) can be expressed as either pure graph search or integer programs. Other problems, however, such as molecular optimization, do no have concise algebraic formulations and yet are readily implemented as a graph search (V. et al., 2022; Zhou et al., 2019). Such "model-free" problems constitute a large fraction of modern reinforcement learning (RL) research owing to the fact that it is often much easier to write a forward simulation that expresses all of the state transitions and rewards, than to write down the precise mathematical expression of the full optimization problem. In the case of molecular optimization, for example, one can use domain knowledge alongside existing software libraries to model the effect of adding a single bond or atom to an existing but incomplete molecule, and let the RL algorithm build a model of how good a given decision is by "experiencing" the simulated environment many times through. In contrast, a model-based mathematical formulation that fully expresses all the chemical and physical constraints is intractable. In recent years, RL has emerged as an effective paradigm for optimizing searches over graphs and led to state-of-the-art heuristics for games like Go and chess, as well as for classical CO problems such as the TSP. This combination of graph search and RL, while powerful, requires non-trivial software to execute, especially when combining advanced state representations such as Graph Neural Networks (GNN) with scalable RL algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Fixed-angle conjectures for the quantum approximate optimization algorithm on regular MaxCut graphs

The quantum approximate optimization algorithm (QAOA) is a near-term combinatorial optimization algorithm suitable for noisy quantum devices. However, little is known about performance guarantees for p > 2. A recent work computing MaxCut performance guarantees for 3-regular graphs conjectures that any d-regular graph evaluated at particular fixed angles has an approximation ratio greater than some worst-case guarantee. In this work, we provide numerical evidence for this fixed angle conjecture for p < 12. We compute and provide these angles via numerical optimization and tensor networks. These fixed angles serve for an optimization-free version of QAOA and have universally good performance on any 3-regular graph. Heuristic evidence is presented for the fixed angle conjecture on graph ensembles, which suggests that these fixed angles are "close" to global optimum. Under the fixed angle conjecture, QAOA has a larger performance guarantee than the Goemans Williamson algorithm on 3-regular graphs for p >= 11.

Wurtz, Jonathan↗

NASA NTRS1975

A timeline algorithm for astronomy missions

An algorithm is presented for generating viewing timelines for orbital astronomy missions of the pointing (nonsurvey/scan) type. The algorithm establishes a target sequence from a list of candidate targets in a way which maximizes total viewing time. Two special cases are treated. One concerns dim targets which, due to lighting constraints, are scheduled only during the antipolar portion of each orbit. They normally require long observation times extending over several revolutions. A minimum slew heuristic is employed to select the sequence of dim targets. The other case deals with bright, or short duration, targets, which have less restrictive lighting constraints and are scheduled during the portion of each orbit when dim targets cannot be viewed. Since this process moves much more rapidly than the dim path, an enumeration algorithm is used to select the sequence that maximizes total viewing time.

Moore, J. E.↗

DOE OSTI2020

Scenario Grouping and Decomposition Algorithms for Chance-Constrained Programs

A lower bound for a finite-scenario-based chance-constrained program is the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. The quality of the bound depends on how the scenarios are grouped. In this paper, we formulate a mixed-integer bilevel program that optimally groups scenarios to tighten the quantile bounds. For general chance-constrained programs, we propose a branch-and-cut algorithm to optimize the bilevel program, and for chance-constrained linear programs, a mixed-integer linear-programming reformulation is derived. Here, we also propose several heuristics for grouping similar or dissimilar scenarios. Our computational results demonstrate that optimal grouping bounds are much tighter than heuristic bounds, resulting in smaller root-node gaps and better performance of scenario decomposition for solving chance-constrained 0-1 programs. Also, the optimal grouping bounds can be greatly strengthened using larger group size.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Light Water Reactor LEU+ Lattice Optimization

Commercial light water reactor (LWR) operators and fuel vendors in the United States are exploring potential changes to nuclear fuel that include low-enriched uranium plus (LEU+) designs to further improve operational economics (e.g., extend cycle length). LEU+ fuel is fuel with a maximum enrichment between 5 wt% and 10 wt% 235 U; it allows for higher assembly burnup but likely requires additional reactivity control, e.g., increased burnable absorbers. This report examines possible LEU+ fuel lattice design changes using the lattice physics code, SCALE/Polaris. An optimization driver called the Metaheuristic Optimization Tool (MOT) is used to automate domain space exploration and optimization of LEU+ lattice designs. Heuristics from previous LWR lattice optimization studies were used to construct the objective function and define the domain space for optimization. This work successfully demonstrated that the optimization algorithms of MOT can generate feasible, nonproprietary LEU+ lattice designs (GE14 10 × 10 and Westinghouse 17 × 17) that meet the constraints of traditional LWR lattices while extending cycle length.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS1974

Optimum frame synchronization for biorthogonally coded data

Many recent American unmanned planetary probes have used biorthogonally coded spacecraft-to-earth telemetry links. An examination of the frame-synchronization (sync) techniques employed on these missions revealed that they were not specifically designed for coded data. This led to a consideration of the optimum frame-sync problem for biorthogonally coded data received over the additive white Gaussian noise (AWGN) channel and decoded prior to sync acquisition. A frame-sync algorithm for biorthogonally coded data based on a super-symbol distance rule is proposed, along with a corresponding selection criterion for the sync sequence. It is argued heuristically that this approach is optimum with regard to minimizing the probability of false synchronization.

Levitt, B. K.↗

NASA NTRS1992

Approximation, abstraction and decomposition in search and optimization

In this paper, I discuss four different areas of my research. One portion of my research has focused on automatic synthesis of search control heuristics for constraint satisfaction problems (CSPs). I have developed techniques for automatically synthesizing two types of heuristics for CSPs: Filtering functions are used to remove portions of a search space from consideration. Another portion of my research is focused on automatic synthesis of hierarchic algorithms for solving constraint satisfaction problems (CSPs). I have developed a technique for constructing hierarchic problem solvers based on numeric interval algebra. Another portion of my research is focused on automatic decomposition of design optimization problems. We are using the design of racing yacht hulls as a testbed domain for this research. Decomposition is especially important in the design of complex physical shapes such as yacht hulls. Another portion of my research is focused on intelligent model selection in design optimization. The model selection problem results from the difficulty of using exact models to analyze the performance of candidate designs.

Ellman, Thomas↗

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↗