Search NASA⌕ Search

SEARCH · Search NASA

Results for “Discrete Optimization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Optimizations on Designing High-Resolution Finite-Difference Schemes

We describe a general optimization procedure for both maximizing the resolution characteristics of existing finite differencing schemes as well as designing finite difference schemes that will meet the error tolerance requirements of numerical solutions. The procedure is based on an optimization process. This is a generalization of the compact scheme introduced by Lele in which the resolution is improved for single, one-dimensional spatial derivative, whereas in the present approach the complete scheme, after spatial and temporal discretizations, is optimized on a range of parameters of the scheme and the governing equations. The approach is to linearize and Fourier analyze the discretized equations to check the resolving power of the scheme for various wave number ranges in the solution and optimize the resolution to satisfy the requirements of the problem. This represents a constrained nonlinear optimization problem which can be solved to obtain the nodal weights of discretization. An objective function is defined in the parametric space of wave numbers, Courant number, Mach number and other quantities of interest. Typical criterion for defining the objective function include the maximization of the resolution of high wave numbers for acoustic and electromagnetic wave propagations and turbulence calculations. The procedure is being tested on off-design conditions of non-uniform mesh, non-periodic boundary conditions, and non-constant wave speeds for scalar and system of equations. This includes the solution of wave equations and Euler equations using a conventional scheme with and without optimization and the design of an optimum scheme for the specified error tolerance.

Liu, Yen↗
NASA NTRS1990

Statistical analysis of static shape control in space structures

The article addresses the problem of efficient analysis of the statistics of initial and corrected shape distortions in space structures. Two approaches for improving efficiency are considered. One is an adjoint technique for calculating distortion shapes: the second is a modal expansion of distortion shapes in terms of pseudo-vibration modes. The two techniques are applied to the problem of optimizing actuator locations on a 55 m radiometer antenna. The adjoint analysis technique is used with a discrete-variable optimization method. The modal approximation technique is coupled with a standard conjugate-gradient continuous optimization method. The agreement between the two sets of results is good, validating both the approximate analysis and optimality of the results.

Burdisso, Ricardo A.↗
NASA NTRS1989

Sequential design of discrete linear quadratic regulators via optimal root-locus techniques

A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.

Shieh, Leang S.↗
DOE OSTI2021

Optimal Control of the Energy-Saving Hybrid Hydraulic-Electric Architecture (HHEA) for Off-Highway Mobile Machines

Most off-highway constructions and agriculture equipment use hydraulics, which has unmatched power density, for power transmission and throttling as a means for control. A novel hybrid hydraulic-electric architecture (HHEA) has recently been proposed to improve efficiency for high-power machines that would have been cost-prohibitive to electrify directly. HHEA uses a set of common pressure rails (CPRs) to transmit the majority of power hydraulically and small electric motor drives to modulate that power and to achieve precise control. This article proposes a computationally efficient Lagrange multiplier method (LMM) for computing the optimal sequence of pressure rail selections to minimize energy use. This is needed to evaluate HHEA's energy-saving potential and for iterative architecture design and sizing. An interesting complication is that the cost function is not fully defined until the candidate control sequence is fully specified. This issue is dealt with by decomposing the original problem into a set of sub-problems with additional constraints that can be solved efficiently. Computational effort can be further reduced if actuators are optimized individually instead of together. However, additional steps are required to prevent the constraint functions from becoming discontinuous with respect to the Lagrange multipliers, which is necessary for meeting the constraints. Lastly, a case study of a construction machine demonstrates the efficacy of the method and shows that the HHEA reduces energy consumption by 68%-73% compared to the baseline load-sensing architecture.

Lagrange multiplier↗
NASA NTRS1991

Minimum-weight design of laminated composite plates for postbuckling performance

Minimum-weight design of simply-supported, symmetrically laminated, thin, rectangular, specially orthotropic laminated plates for buckling and postbuckling strength is investigated. The postbuckling analysis is based on an Marguerre-type energy method. The failure load of laminates is calculated by the maximum strain failure criterion based on the in-plane strains. Design variables are individual layer thicknesses with specified fiber orientations. Optimization with discrete valued design is achieved by introducing additional penalty terms to the regular pseudoobjective function of sequential unconstrained minimization technique. The proposed optimization technique is applied to the design of rectangular laminates with various aspect ratios loaded by axial compressive loads.

Shin, Dong KU↗
NASA NTRS2001

Free-form Airfoil Shape Optimization Under Uncertainty Using Maximum Expected Value and Second-order Second-moment Strategies

Free-form shape optimization of airfoils poses unexpected difficulties. Practical experience has indicated that a deterministic optimization for discrete operating conditions can result in dramatically inferior performance when the actual operating conditions are different from the - somewhat arbitrary - design values used for the optimization. Extensions to multi-point optimization have proven unable to adequately remedy this problem of "localized optimization" near the sampled operating conditions. This paper presents an intrinsically statistical approach and demonstrates how the shortcomings of multi-point optimization with respect to "localized optimization" can be overcome. The practical examples also reveal how the relative likelihood of each of the operating conditions is automatically taken into consideration during the optimization process. This is a key advantage over the use of multipoint methods.

Huyse, Luc↗
NASA NTRS2009

Discrete Adjoint-Based Design Optimization of Unsteady Turbulent Flows on Dynamic Unstructured Grids

An adjoint-based methodology for design optimization of unsteady turbulent flows on dynamic unstructured grids is described. The implementation relies on an existing unsteady three-dimensional unstructured grid solver capable of dynamic mesh simulations and discrete adjoint capabilities previously developed for steady flows. The discrete equations for the primal and adjoint systems are presented for the backward-difference family of time-integration schemes on both static and dynamic grids. The consistency of sensitivity derivatives is established via comparisons with complex-variable computations. The current work is believed to be the first verified implementation of an adjoint-based optimization methodology for the true time-dependent formulation of the Navier-Stokes equations in a practical computational code. Large-scale shape optimizations are demonstrated for turbulent flows over a tiltrotor geometry and a simulated aeroelastic motion of a fighter jet.

Nielsen, Eric J.↗
DOE OSTI2026

A Comprehensive Comparative Study of Active Learning Schemes for Nanophotonics Design

We present a benchmarking study of active learning (AL) schemes for designing planar multilayer nanophotonic metamaterials, where the design tasks are formulated as binary optimization problems. Different surrogate models, including factorization machine (FM), Gaussian process regression (GPR), and convolutional neural network (CNN), combined with different optimization methods, including exhaustive enumeration, discrete particle swarm optimization (DPSO), quantum annealing (QA), hybrid QA, and simulated annealing are studied. The benchmark cases investigated range from small problems with short binary lengths (N = 25) to large problems with N up to 100, focusing on the design of two classes of photonic structures, including antireflective coatings for the long-wavelength infrared region and transparent radiative coolers. For small problems, CNN coupled with DPSO in AL achieves the best performance. As N increases, FM with QA outperforms GPR and CNN. For FM-based AL, hybrid QA yields the best optimization results, particularly in high-dimensional cases (N = 100). These results demonstrate that the optimization method can significantly affect in AL performance as N increases, and that QA-based optimization can provide practical routes for mitigating the optimization bottleneck in high-dimensional problems.

Jung, Serang [Kyung Hee University, Korea]↗
NASA NTRS2002

Combinatorial Multiobjective Optimization Using Genetic Algorithms

The research proposed in this document investigated multiobjective optimization approaches based upon the Genetic Algorithm (GA). Several versions of the GA have been adopted for multiobjective design, but, prior to this research, there had not been significant comparisons of the most popular strategies. The research effort first generalized the two-branch tournament genetic algorithm in to an N-branch genetic algorithm, then the N-branch GA was compared with a version of the popular Multi-Objective Genetic Algorithm (MOGA). Because the genetic algorithm is well suited to combinatorial (mixed discrete / continuous) optimization problems, the GA can be used in the conceptual phase of design to combine selection (discrete variable) and sizing (continuous variable) tasks. Using a multiobjective formulation for the design of a 50-passenger aircraft to meet the competing objectives of minimizing takeoff gross weight and minimizing trip time, the GA generated a range of tradeoff designs that illustrate which aircraft features change from a low-weight, slow trip-time aircraft design to a heavy-weight, short trip-time aircraft design. Given the objective formulation and analysis methods used, the results of this study identify where turboprop-powered aircraft and turbofan-powered aircraft become more desirable for the 50 seat passenger application. This aircraft design application also begins to suggest how a combinatorial multiobjective optimization technique could be used to assist in the design of morphing aircraft.

Crossley, William A.↗
DOE OSTI2025

Comparing three generations of D-Wave quantum annealers for minor embedded combinatorial optimization problems

Abstract Quantum annealing (QA) is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. QA in the transverse Ising model, implemented on D-Wave quantum processing units, are available as cloud computing resources. In this study we report concise benchmarks across three generations of D-Wave quantum annealers, consisting of four different devices, for the NP-hard discrete combinatorial optimization problems unweighted maximum clique and unweighted maximum cut on random graphs. The Ising, or equivalently quadratic unconstrained binary optimization, formulation of these problems do not require auxiliary variables for order reduction, and their overall structure and weights are not highly variable, which makes these problems simple test cases to understand the sampling capability of current D-Wave quantum annealers. All-to-all minor embeddings of size 52, with relatively uniform chain lengths, are used for a direct comparison across the Chimera, Pegasus, and Zephyr device topologies. A grid-search over annealing times and the minor embedding chain strengths is performed in order to determine the level of reasonable performance for each device and problem type. Experiment metrics that are reported are approximation ratios for non-broken chain samples, chain break proportions, and time-to-solution for the maximum clique problem instances. How fairly the quantum annealers sample optimal maximum cliques, for instances which contain multiple maximum cliques, is quantified using entropy of the measured ground state distributions. The newest generation of quantum annealing hardware, which has a Zephyr hardware connectivity, performed the best overall with respect to approximation ratios and chain break frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1991

Analysis of the optimal laminated target made up of discrete set of materials

A new class of problems was analyzed to estimate an optimal structure of laminated targets fabricated from the specified set of homogeneous materials. An approximate description of the perforation process is based on the model of radial hole extension. The problem is solved by using the needle-type variation technique. The desired optimization conditions and quantitative/qualitative estimations of optimal targets were obtained and are discussed using specific examples.

Aptukov, Valery N.↗
DOE OSTI2023

Automated Adversary-in-the-Loop Cyber-Physical Defense Planning

Security of cyber-physical systems (CPS) continues to pose new challenges due to the tight integration and operational complexity of the cyber and physical components. To address these challenges, this article presents a domain-aware, optimization-based approach to determine an effective defense strategy for CPS in an automated fashion—by emulating a strategic adversary in the loop that exploits system vulnerabilities, interconnection of the CPS, and the dynamics of the physical components. Our approach builds on an adversarial decision-making model based on a Markov Decision Process (MDP) that determines the optimal cyber (discrete) and physical (continuous) attack actions over a CPS attack graph. The defense planning problem is modeled as a non-zero-sum game between the adversary and defender. We use a model-free reinforcement learning method to solve the adversary’s problem as a function of the defense strategy. We then employ Bayesian optimization (BO) to find an approximate best-response for the defender to harden the network against the resulting adversary policy. This process is iterated multiple times to improve the strategy for both players. We demonstrate the effectiveness of our approach on a ransomware-inspired graph with a smart building system as the physical process. Numerical studies show that our method converges to a Nash equilibrium for various defender-specific costs of network hardening.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

PolyMat: an efficient Matlab code for multi-material topology optimization

We introduce a Matlab implementation of topology optimization for compliance minimization on unstructured polygonal finite element meshes that efficiently accommodates many materials and many volume constraints. Leveraging the modular structure of the educational code, PolyTop, we extend it to the multi-material version, PolyMat, with only a few modifications. First, a design variable for each candidate material is defined in each finite element. Next, we couple a Discrete Material Optimization interpolation with the existing penalization and introduce a new parameter such that we can employ continuation and smoothly transition from a convex problem without any penalization to a non-convex problem in which material mixing and intermediate densities are penalized. Mixing that remains due to the density filter operation is eliminated via continuation on the filter radius. To accommodate flexibility in the volume constraint definition, the constraint function is modified to compute multiple volume constraints and the design variable update is modified in accordance with the Zhang-Paulino-Ramos Jr. (ZPR) update scheme, which updates the design variables associated with each constraint independently. The formulation allows for volume constraints controlling any subset of the design variables, i.e., they can be defined globally or locally for any subset of the candidate materials. Borrowing ideas for mesh generation on complex domains from PolyMesher, we conclude which design variables are associated with each local constraint of arbitrary geometry. A number of examples are presented to demonstrate the many material capability, the flexibility of the volume constraint definition, the ease with which we can accommodate passive regions, and how we may use local constraints to break symmetries or achieve graded geometries.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Computational optimal transport for molecular spectra: The fully discrete case

In this study, the use of computational optimal transport is investigated as a tool for comparing two molecular spectra. Unlike other techniques for comparing molecular spectra in a pattern-recognition framework, transport distances simultaneously encode information about line positions and intensities. In addition, it is shown that transport distances are a useful alternative to Euclidean distances as Euclidean distances are based on line-by-line comparisons, while transport distances reflect broader features of molecular spectra and adequately compare spectra with different resolutions. This paper includes a tutorial on the use of optimal transport and investigates several well-chosen examples to illustrate the utility of computational optimal transport for comparing molecular spectra.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

The potential of quantum annealing for rapid solution structure identification

Abstract The recent emergence of novel computational devices, such as quantum computers, coherent Ising machines, and digital annealers presents new opportunities for hardware-accelerated hybrid optimization algorithms. Unfortunately, demonstrations of unquestionable performance gains leveraging novel hardware platforms have faced significant obstacles. One key challenge is understanding the algorithmic properties that distinguish such devices from established optimization approaches. Through the careful design of contrived optimization tasks, this work provides new insights into the computation properties of quantum annealing and suggests that this model has the potential to quickly identify the structure of high-quality solutions. A meticulous comparison to a variety of algorithms spanning both complete and local search suggests that quantum annealing’s performance on the proposed optimization tasks is distinct. This result provides new insights into the time scales and types of optimization problems where quantum annealing has the potential to provide notable performance gains over established optimization algorithms and suggests the development of hybrid algorithms that combine the best features of quantum annealing and state-of-the-art classical approaches.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2005

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.

Nielsen, Eric J.↗
NASA NTRS2006

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

An algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method is based on an adjoint approach and eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered practical large-scale design optimization using discrete adjoint methods. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product scaling with the number of design variables and the resolution of the parameterized surface grid. The accuracy of the implementation is established and dramatic computational savings obtained using the new approach are demonstrated using several test cases. Sample design optimizations are also shown.

Nielsen, Eric J.↗