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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An Incremental Gradient Method for Optimization Problems With Variational Inequality Constraints

We consider minimizing a sum of agent-specific nondifferentiable merely convex functions over the solution set of a variational inequality (VI) problem in that each agent is associated with a local monotone mapping. This problem finds an application in computation of the best equilibrium in nonlinear complementarity problems arising in transportation networks. We develop an iteratively regularized incremental gradient method where at each iteration, agents communicate over a directed cycle graph to update their solution iterates using their local information about the objective and the mapping. The proposed method is single-timescale in the sense that it does not involve any excessive hard-to-project computation per iteration. We derive nonasymptotic agent-wise convergence rates for the suboptimality of the global objective function and infeasibility of the VI constraints measured by a suitably defined dual gap function. Finally, the proposed method appears to be the first fully iterative scheme equipped with iteration complexity that can address distributed optimization problems with VI constraints over cycle graphs.

convergence↗
NASA NTRS1996

Smoothers for Optimization Problems

We present a multigrid one-shot algorithm, and a smoothing analysis, for the numerical solution of optimal control problems which are governed by an elliptic PDE. The analysis provides a simple tool to determine a smoothing minimization process which is essential for multigrid application. Numerical results include optimal control of boundary data using different discretization schemes and an optimal shape design problem in 2D with Dirichlet boundary conditions.

Arian, Eyal↗
NASA NTRS2012

A Robust Initialization Scheme for a Lateral Trajectory Optimization Problem with Time of Arrival Windows

We present a robust initialization scheme that estimates parameter values for the numerical solution of a two-point boundary value problem. The two-point boundary value problem formulation stems from the optimization of a cost functional subject to the dynamics of a simplified lateral aircraft model and other constraints. Leveraging regular perturbation methods, initial parameter estimates are analytically determined and used to initialize a gradient descent optimization routine which is shown to rapidly converge over a range of initial aircraft positions and heading angles. Additionally, the velocity of the aircraft is optimized to ensure the trajectory of the aircraft terminates within a desired region in both time and space.

lateral trajectory optimization↗
NASA NTRS1983

Altitude/path-angle transitions in fuel-optimal problems for transport aircraft

Altitude/path angle transitions to fuel-optimal, energy climb and descent paths are examined for subsonic transport aircraft. These transitions are termed boundary layers in singular perturbation theory, the framework used herein to simplify solutions to the state-Euler system. The energy climb and descent paths provide equilibrium or stationary points for the boundary layer system, and thus for moderate transitions, presumed valid for the class of aircraft considered, the boundary layer system may be linearized. This simplification allows derivation of an explicit solution to the two-point boundary-value, boundary layer problem and, as a consequence, yields a nearly optimal control law, in feedback form, for the transitions. Numerical simulation results using the feedback control law are presented for a Boeing 737 airframe (NASA-ATOPS Vehicle) employing twin JT8D-7-7A engines.

Gracey, C.↗
NASA NTRS2014

An Optimizing Space Data-Communications Scheduling Method and Algorithm with Interference Mitigation, Generalized for a Broad Class of Optimization Problems

NASA's space data-communications infrastructure-the Space Network and the Ground Network-provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft. The Space Network operates several orbiting geostationary platforms (the Tracking and Data Relay Satellite System (TDRSS)), each with its own servicedelivery antennas onboard. The Ground Network operates service-delivery antennas at ground stations located around the world. Together, these networks enable data transfer between user spacecraft and their mission control centers on Earth. Scheduling data-communications events for spacecraft that use the NASA communications infrastructure-the relay satellites and the ground stations-can be accomplished today with software having an operational heritage dating from the 1980s or earlier. An implementation of the scheduling methods and algorithms disclosed and formally specified herein will produce globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary algorithms, a class of probabilistic strategies for searching large solution spaces, is the essential technology invoked and exploited in this disclosure. Also disclosed are secondary methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithms themselves. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure within the expected range of future users and space- or ground-based service-delivery assets. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally. The generalized methods and algorithms are applicable to a very broad class of combinatorial-optimization problems that encompasses, among many others, the problem of generating optimal space-data communications schedules.

ground stations↗
DOE OSTI2021

Teeport: Break the Wall Between the Optimization Algorithms and Problems

Optimization algorithms/techniques such as genetic algorithm, particle swarm optimization, and Gaussian process have been widely used in the accelerator field to tackle complex design/online optimization problems. However, connecting the algorithm with the optimization problem can be difficult, as the algorithms and the problems may be implemented in different languages, or they may require specific resources. We introduce an optimization platform named Teeport that is developed to address the above issues. This real-time communication-based platform is designed to minimize the effort of integrating the algorithms and problems. Once integrated, the users are granted a rich feature set, such as monitoring, controlling, and benchmarking. Some real-life applications of the platform are also discussed.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1977

An explicit solution to the exoatmospheric powered flight guidance and trajectory optimization problem for rocket propelled vehicles

A derivation of an explicit solution to the two point boundary-value problem of exoatmospheric guidance and trajectory optimization is presented. Fixed initial conditions and continuous burn, multistage thrusting are assumed. Any number of end conditions from one to six (throttling is required in the case of six) can be satisfied in an explicit and practically optimal manner. The explicit equations converge for off nominal conditions such as engine failure, abort, target switch, etc. The self starting, predictor/corrector solution involves no Newton-Rhapson iterations, numerical integration, or first guess values, and converges rapidly if physically possible. A form of this algorithm has been chosen for onboard guidance, as well as real time and preflight ground targeting and trajectory shaping for the NASA Space Shuttle Program.

Jaggers, R. F.↗
NASA NTRS1985

Algorithm Solves Constrained and Unconstrained Optimization Problems

Is quasi-Newton iteration utilizing Broyden/Fletcher/Goldfarb/Shanno update on inverse Hessian matrix. Capable of solving constrained optimization unconstrained optimization and constraints only problems with one to five independent variables from one to five constraint functions and one dependent function optimized.

Denson, M. A.↗
NASA NTRS2010

An Optimizing Space Data-Communications Scheduling Method and Algorithm with Interference Mitigation, Generalized for a Broad Class of Optimization Problems

NASA's space data-communications infrastructure, the Space Network and the Ground Network, provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft via orbiting relay satellites and ground stations. An implementation of the methods and algorithms disclosed herein will be a system that produces globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary search, a class of probabilistic strategies for searching large solution spaces, constitutes the essential technology in this disclosure. Also disclosed are methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithm itself. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally, with applicability to a very broad class of combinatorial optimization problems.

Rash, James L.↗
NASA NTRS2005

At-Least Version of the Generalized Minimum Spanning Tree Problem: Optimization Through Ant Colony System and Genetic Algorithms

The At-Least version of the Generalized Minimum Spanning Tree Problem (L-GMST) is a problem in which the optimal solution connects all defined clusters of nodes in a given network at a minimum cost. The L-GMST is NPHard; therefore, metaheuristic algorithms have been used to find reasonable solutions to the problem as opposed to computationally feasible exact algorithms, which many believe do not exist for such a problem. One such metaheuristic uses a swarm-intelligent Ant Colony System (ACS) algorithm, in which agents converge on a solution through the weighing of local heuristics, such as the shortest available path and the number of agents that recently used a given path. However, in a network using a solution derived from the ACS algorithm, some nodes may move around to different clusters and cause small changes in the network makeup. Rerunning the algorithm from the start would be somewhat inefficient due to the significance of the changes, so a genetic algorithm based on the top few solutions found in the ACS algorithm is proposed to quickly and efficiently adapt the network to these small changes.

Janich, Karl W.↗
DOE OSTI2022

Sampling electronic structure quadratic unconstrained binary optimization problems (QUBOs) with Ocean and Mukai solvers

The most advanced D-Wave Advantage quantum annealer has 5000+ qubits, however, every qubit is connected to a small number of neighbors. As such, implementation of a fully-connected graph results in an order of magnitude reduction in qubit count. To compensate for the reduced number of qubits, one has to rely on special heuristic software such as qbsolv, the purpose of which is to decompose a large quadratic unconstrained binary optimization (QUBO) problem into smaller pieces that fit onto a quantum annealer. In this work, we compare the performance of the open-source qbsolv which is a part of the D-Wave Ocean tools and a new Mukai QUBO solver from Quantum Computing Inc. (QCI). The comparison is done for solving the electronic structure problem and is implemented in a classical mode (Tabu search techniques). The Quantum Annealer Eigensolver is used to map the electronic structure eigenvalue-eigenvector equation to a QUBO problem, solvable on a D-Wave annealer. We find that the Mukai QUBO solver outperforms the Ocean qbsolv with one to two orders of magnitude more accurate energies for all calculations done in the present work, both the ground and excited state calculations. This work stimulates the further development of software to assist in the utilization of modern quantum annealers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Graph-Based Modeling and Decomposition of Hierarchical Optimization Problems

We present a graph-theoretic modeling approach for hierarchical optimization that leverages the OptiGraph abstraction implemented in the Julia package Plasmo.jl. We show that the abstraction is flexible and can effectively capture complex hierarchical connectivity that arises from decision-making over multiple spatial and temporal scales (e.g., integration of planning, scheduling, and operations in manufacturing and infrastructures). We also show that the graph abstraction facilitates the conceptualization and implementation of decomposition and approximation schemes. Specifically, we propose a graph-based Benders decomposition (gBD) framework that enables the exploitation of hierarchical (nested) structures and that uses graph aggregation/partitioning procedures to discover such structures. In addition, we provide a Julia implementation of gBD, which we call PlasmoBenders.jl. We illustrate the capabilities using examples arising in the context of energy and power systems.

97 MATHEMATICS AND COMPUTING↗
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.↗