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Results for “Optimization problems”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Multiobjective Aerodynamic Shape Optimization Using Pareto Differential Evolution and Generalized Response Surface Metamodels

Differential Evolution (DE) is a simple, fast, and robust evolutionary algorithm that has proven effective in determining the global optimum for several difficult single-objective optimization problems. The DE algorithm has been recently extended to multiobjective optimization problem by using a Pareto-based approach. In this paper, a Pareto DE algorithm is applied to multiobjective aerodynamic shape optimization problems that are characterized by computationally expensive objective function evaluations. To improve computational expensive the algorithm is coupled with generalized response surface meta-models based on artificial neural networks. Results are presented for some test optimization problems from the literature to demonstrate the capabilities of the method.

Madavan, Nateri K.↗
NASA NTRS1974

Control of Finite-State, Finite Memory Stochastic Systems

A generalized problem of stochastic control is discussed in which multiple controllers with different data bases are present. The vehicle for the investigation is the finite state, finite memory (FSFM) stochastic control problem. Optimality conditions are obtained by deriving an equivalent deterministic optimal control problem. A FSFM minimum principle is obtained via the equivalent deterministic problem. The minimum principle suggests the development of a numerical optimization algorithm, the min-H algorithm. The relationship between the sufficiency of the minimum principle and the informational properties of the problem are investigated. A problem of hypothesis testing with 1-bit memory is investigated to illustrate the application of control theoretic techniques to information processing problems.

Sandell, Nils R.↗
NASA NTRS1972

Asymptotic solution to the problem of optimal low-thrust energy increase.

Consideration of the problem of optimal ascent from an initial circular planetary orbit to some specified final energy level by a spacecraft equipped with a low-thrust engine. Optimal is defined as minimum time. An accurate small parameter perturbation solution is presented, and the optimal trajectory is analyzed and compared with a tangential thrust trajectory.

Jacobson, R. A.↗
DOE OSTI2024

Scale-bridging Optimization Framework for Desalination Integrated Produced Water Networks

Produced water (PW) management poses a major challenge to U.S. oil and gas development. Due to freshwater scarcity and PW injection curtailments, desalination may become a necessity in some parts of the country. Integrating rigorous desalination process models within a produced water network for co-optimization of desalination design and network operation can be challenging to scale-up due to computational complexity. In this work we use the trust region filter framework to decompose the integrated optimization problem into an optimization master problem consisting of the network model and simplified surrogates for the desalination units and an optimization sub problem for the rigorous desalination unit model. The approach is demonstrated on a multiperiod produced water network from the PARETO library with thermal desalination units.

Naik, Sakshi↗
NASA NTRS2017

Uncertainty Aware Structural Topology Optimization Via a Stochastic Reduced Order Model Approach

This work presents a stochastic reduced order modeling strategy for the quantification and propagation of uncertainties in topology optimization. Uncertainty aware optimization problems can be computationally complex due to the substantial number of model evaluations that are necessary to accurately quantify and propagate uncertainties. This computational complexity is greatly magnified if a high-fidelity, physics-based numerical model is used for the topology optimization calculations. Stochastic reduced order model (SROM) methods are applied here to effectively 1) alleviate the prohibitive computational cost associated with an uncertainty aware topology optimization problem; and 2) quantify and propagate the inherent uncertainties due to design imperfections. A generic SROM framework that transforms the uncertainty aware, stochastic topology optimization problem into a deterministic optimization problem that relies only on independent calls to a deterministic numerical model is presented. This approach facilitates the use of existing optimization and modeling tools to accurately solve the uncertainty aware topology optimization problems in a fraction of the computational demand required by Monte Carlo methods. Finally, an example in structural topology optimization is presented to demonstrate the effectiveness of the proposed uncertainty aware structural topology optimization approach.

Aguilo, Miguel A.↗
NASA NTRS1993

Necessary and sufficient conditions under which an H2 optimal control problem has a unique solution

A set of necessary and sufficient conditions under which a general H2-optimal control problem has a unique solution is derived. It is shown that the solution for an H2-optimal control problem, if it exists, is unique if and only if (1) the transfer function from the control input to the controlled output is left invertible, and (2) the transfer function from the disturbance to the measurement output is right invertible.

Chen, Ben M.↗
NASA NTRS1994

Finite element approximation of an optimal control problem for the von Karman equations

This paper is concerned with optimal control problems for the von Karman equations with distributed controls. We first show that optimal solutions exist. We then show that Lagrange multipliers may be used to enforce the constraints and derive an optimality system from which optimal states and controls may be deduced. Finally we define finite element approximations of solutions for the optimality system and derive error estimates for the approximations.

Hou, L. Steven↗
NASA NTRS1991

Advanced design for orbital debris removal in support of solar system exploration

The development of an Autonomous Space Processor for Orbital Debris (ASPOD) is the ultimate goal. The craft will process, in situ, orbital debris using resources available in low Earth orbit (LEO). The serious problem of orbital debris is briefly described and the nature of the large debris population is outlined. This year, focus was on development of a versatile robotic manipulator to augment an existing robotic arm; incorporation of remote operation of robotic arms; and formulation of optimal (time and energy) trajectory planning algorithms for coordinating robotic arms. The mechanical design of the new arm is described in detail. The versatile work envelope is explained showing the flexibility of the new design. Several telemetry communication systems are described which will enable the remote operation of the robotic arms. The trajectory planning algorithms are fully developed for both the time-optimal and energy-optimal problem. The optimal problem is solved using phase plane techniques while the energy optimal problem is solved using dynamics programming.

Source record↗
DOE OSTI2025

A Scalable Interior‐Point Gauss–Newton Method for PDE‐Constrained Optimization With Bound Constraints

Here, we present a scalable approach to solve a class of partial differential equation (PDE)‐constrained optimization problems with bound constraints. This approach utilizes a robust full‐space interior‐point (IP)‐Gauss–Newton optimization method. To cope with the poorly‐conditioned IP‐Gauss–Newton saddle‐point linear systems that need to be solved approximately, once per optimization step, we propose two spectrally related preconditioners. These preconditioners leverage the limited informativeness of data in regularized PDE‐constrained optimization problems. A block Gauss–Seidel preconditioner is proposed for the GMRES‐based solution of the IP‐Gauss–Newton linear systems. It is shown, for a large‐class of PDE‐ and bound‐constrained optimization problems, that the spectrum of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix is asymptotically independent of discretization and is not impacted by the ill‐conditioning that notoriously plagues interior‐point methods. We exploit symmetry of the IP‐Gauss–Newton linear systems and propose a regularization and log‐barrier Hessian preconditioner for the preconditioned conjugate gradient (PCG)‐based solution of the equivalent IP‐Gauss–Newton–Schur complement linear systems. The eigenvalues of the block Gauss–Seidel preconditioned IP‐Gauss–Newton matrix, that are not equal to one, are identical to the eigenvalues of the regularization and log‐barrier Hessian preconditioned Schur complement matrix. The scalability of the approach is demonstrated on two example problems. The numerical solution of these optimization problems is shown to require a discretization independent number of IP‐Gauss–Newton linear solves. Furthermore, the linear systems are solved in a discretization and IP ill‐conditioning independent number of preconditioned Krylov subspace iterations. The parallel scalability of the preconditioner, achieved via algebraic multigrid component solvers when applicable, and the aforementioned algorithmic scalability permits a parallel scalable means to compute solutions of a large class of PDE‐ and bound‐constrained problems.

PDE-constrained optimization↗
NASA NTRS1992

Combining constraint satisfaction and local improvement algorithms to construct anaesthetists' rotas

A system is described which was built to compile weekly rotas for the anaesthetists in a large hospital. The rota compilation problem is an optimization problem (the number of tasks which cannot be assigned to an anaesthetist must be minimized) and was formulated as a constraint satisfaction problem (CSP). The forward checking algorithm is used to find a feasible rota, but because of the size of the problem, it cannot find an optimal (or even a good enough) solution in an acceptable time. Instead, an algorithm was devised which makes local improvements to a feasible solution. The algorithm makes use of the constraints as expressed in the CSP to ensure that feasibility is maintained, and produces very good rotas which are being used by the hospital involved in the project. It is argued that formulation as a constraint satisfaction problem may be a good approach to solving discrete optimization problems, even if the resulting CSP is too large to be solved exactly in an acceptable time. A CSP algorithm may be able to produce a feasible solution which can then be improved, giving a good, if not provably optimal, solution.

Smith, Barbara M.↗