Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “constrained 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 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Optimal design of acoustic metamaterial cloaks under uncertainty

In this work, we consider the problem of optimal design of an acoustic cloak under uncertainty and develop scalable approximation and optimization methods to solve this problem. The design variable is taken as an infinite-dimensional spatially-varying field that represents the material property, while an additive infinite-dimensional random field represents the variability of the material property or the manufacturing error. Discretization of this optimal design problem results in high-dimensional design variables and uncertain parameters. To solve this problem, we develop a computational approach based on a Taylor approximation and an approximate Newton method for optimization, which is based on a Hessian derived at the mean of the random field. We show our approach is scalable with respect to the dimension of both the design variables and uncertain parameters, in the sense that the necessary number of acoustic wave propagations is essentially independent of these dimensions, for numerical experiments with up to one million design variables and half a million uncertain parameters. Additionally, we demonstrate that, using our computational approach, an optimal design of the acoustic cloak that is robust to material uncertainty is achieved in a tractable manner. The optimal design under uncertainty problem is posed and solved for the classical circular obstacle surrounded by a ring-shaped cloaking region, subjected to both a single-direction single-frequency incident wave and multiple-direction multiple-frequency incident waves. Finally, we apply the method to a deterministic large-scale optimal cloaking problem with complex geometry, to demonstrate that the approximate Newton method’s Hessian computation is viable for large, complex problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Nonlinear Optimal Control of Electron Dynamics Within Hartree-Fock Theory

Consider the problem of determining the optimal applied electric field to drive a molecule from an initial state to a desired target state. For even moderately sized molecules, solving this problem directly using the exact equations of motion—the time-dependent Schrödinger equation (TDSE)—is numerically intractable. Here, we present a solution of this problem within time-dependent Hartree-Fock (TDHF) theory, a mean field approximation of the TDSE. Optimality is defined in terms of minimizing the total control effort while maximizing the overlap between desired and achieved target states. We frame this problem as an optimization problem constrained by the nonlinear TDHF equations; we solve it using trust region optimization with gradients computed via a custom-built adjoint state method. For three molecular systems, we show that with very small neural network parametrizations of the control, our method yields solutions that achieve desired targets within acceptable constraints and tolerances.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Wing design code using three-dimensional Euler equations and optimization

This paper describes a new wing design code which is based on the Euler equations and a constrained numerical optimization technique. The geometry modification is based on a set of fundamental modes define on the unit interval. A design example involving a high speed civil transport wing is presented to demonstrate the usefulness of the design code. It is shown that the use of an Euler solver in the direct numerical optimization procedures is affordable on the current generation of supercomputers.

Chang, I-Chung↗
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↗
DOE OSTI2022

Dynamic machine learning-based optimization algorithm to improve boiler efficiency

With decreasing computational costs, improvement in algorithms, and the aggregation of large industrial and commercial datasets, machine learning is becoming a ubiquitous tool for process and business innovations. Machine learning is still lacking applications in the field of dynamic optimization for real-time control. This work presents a novel framework for performing constrained dynamic optimization using a recurrent neural network model combined with a metaheuristic optimizer. The framework is designed to augment an existing control system and is purely data-driven, like most industrial Model Predictive Control applications. Several recurrent neural network models are compared as well as several metaheuristic optimizers. Hyperparameters and optimizer parameters are tuned with parameter sweeps, and the resulting values are reported. Further, the best parameters for each optimizer and model combination are demonstrated in closed-loop control of a dynamic simulation, and several recommendations are made for generalizing this framework to other systems. Up to 0.953% improvement is realized over the non-optimized case for a simulated coal-fired boiler. While this is not a large improvement in percentage, the total economic impact is $991,000 per year, and this study builds a foundation for future machine learning with dynamic optimization.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Structural stability and artificial buckling modes in topology optimization

Abstract This paper demonstrates how a strain energy transition approach can be used to remove artificial buckling modes that often occur in stability constrained topology optimization problems. To simulate the structural response, a nonlinear large deformation hyperelastic simulation is performed, wherein the fundamental load path is traversed using Newton’s method and the critical buckling load levels are estimated by an eigenvalue analysis. The goal of the optimization is to minimize displacement, subject to constraints on the lowest critical buckling loads and maximum volume. The topology optimization problem is regularized via the Helmholtz PDE-filter and the method of moving asymptotes is used to update the design. The stability and sensitivity analyses are outlined in detail. The effectiveness of the energy transition scheme is demonstrated in numerical examples.

Dalklint, Anna (ORCID:0000000346195205)↗
NASA NTRS1985

On optimal strategies in event-constrained differential games

Combat games are formulated as zero-sum differential games with unilateral event constraints. An interior penalty function approach is employed to approximate optimal strategies for the players. The method is very attractive computationally and possesses suitable approximation and convergence properties.

Heymann, M.↗
NASA NTRS1994

Optimization of Wing-Body Configurations by the Euler Equations

This paper describes a new wing-body design procedure which is based on the Euler equations and a constrained numerical optimization technique. The geometry modification is based on a set of fundamental modes defined on the unit interval. A design example involving a generic wing-body model is presented to demonstrate the usefulness of the design program. It is shown that the use of an Euler solver coupled with a direct numerical optimization procedure is affordable on the current generation of supercomputers.

Chang, I.-Chung↗
DOE OSTI2025

Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations

In this article, we focus on the communication costs of three symmetric matrix computations: (i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) (ii) adding the result of the multiplication of a matrix with the transpose of another matrix and the transpose of that result, known as a symmetric rank-2k update (SYR2K) (iii) performing matrix multiplication with a symmetric input matrix (SYMM). All three computations appear in the Level 3 Basic Linear Algebra Subroutines (BLAS) and have wide use in applications involving symmetric matrices. We establish communication lower bounds for these kernels using sequential and distributed-memory parallel computational models, and we show that our bounds are tight by presenting communication-optimal algorithms for each setting. Our lower bound proofs rely on applying a geometric inequality for symmetric computations and analytically solving constrained nonlinear optimization problems. As a result, the symmetric matrix and its corresponding computations are accessed and performed according to a triangular block partitioning scheme in the optimal algorithms.

Al Daas, Hussam [Rutherford Appleton Laboratory, D↗
DOE OSTI2023

Stochastic optimization of a uranium oxide reaction mechanism using plasma flow reactor measurements

Abstract In this work, a coupled Monte Carlo Genetic Algorithm (MCGA) approach is used to optimize a gas phase uranium oxide reaction mechanism based on plasma flow reactor (PFR) measurements. The PFR produces a steady Ar plasma containing U, O, H, and N species with high temperature regions (3000–5000 K) relevant to observing UO formation via optical emission spectroscopy. A global kinetic treatment is used to model the chemical evolution in the PFR and to produce synthetic emission signals for direct comparison with experiments. The parameter space of a uranium oxide reaction mechanism is then explored via Monte Carlo sampling using objective functions to quantify the model-experiment agreement. The Monte Carlo results are subsequently refined using a genetic algorithm to obtain an experimentally corroborated set of reaction pathways and rate coefficients. Out of 12 reaction channels targeted for optimization, four channels are found to be well constrained across all optimization runs while another three channels are constrained in select cases. The optimized channels highlight the importance of the OH radical in oxidizing uranium in the PFR. This study comprises a first step toward producing a comprehensive experimentally validated reaction mechanism for gas phase uranium molecular species formation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Parallel Memory-Independent Communication Bounds for SYRK

In this paper, we focus on the parallel communication cost of multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK). SYRK requires half the computation of general matrix multiplication because of the symmetry of the output matrix. Recent work (Beaumont et al., SPAA '22) has demonstrated that the sequential I/O complexity of SYRK is also a constant factor smaller than that of general matrix multiplication. Inspired by this progress, we establish memory-independent parallel communication lower bounds for SYRK with smaller constants than general matrix multiplication, and we show that these constants are tight by presenting communication-optimal algorithms. The crux of the lower bound proof relies on extending a key geometric inequality to symmetric computations and analytically solving a constrained nonlinear optimization problem. Here, the optimal algorithms use a triangular blocking scheme for parallel distribution of the symmetric output matrix and corresponding computation.

Communication costs↗
NASA NTRS1980

A new method for optimizing multiple flyby trajectories

A new procedure has been developed which minimizes total impulsive Delta V for multiple flyby trajectories with constraints on flyby parameters and maneuver times. The method involves solving a bounds-constrained parameter optimization problem with a Newton algorithm utilizing analytic first and second derivatives. Each trajectory segment connecting consecutive maneuver points is found by first targeting from the preceding maneuver point to the parameters of the upcoming flyby and then propagating the resulting trajectory to the next maneuver point. Multi-conic techniques are used for trajectory propagation and for computation of the state transition matrix. This procedure has successfully optimized Galileo satellite tours containing up to 11 flybys.

Damario, L. A.↗
DOE OSTI2025

Constrained or unconstrained? Neural-network-based equation discovery from data

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or the accurate resolution of their solutions may be intractable. Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations (PDEs), on a spectrum of interpretability. The success of these strategies is often contingent upon the correct identification of representative equations from noisy observations of state variables and, as importantly and intertwined with that, the mathematical strategies utilized to enforce those equations. Specifically, the latter has been commonly addressed via unconstrained optimization strategies. Representing the PDE as a neural network, we propose to discover the PDE (or the associated operator) by solving a constrained optimization problem and using an intermediate state representation similar to a physics-informed neural network (PINN). The objective function of this constrained optimization problem promotes matching the data, while the constraints require that the discovered PDE is satisfied at a number of spatial collocation points. We present a penalty method and a widely used trust-region barrier method to solve this constrained optimization problem, and we compare these methods on numerical examples. Our results on several example problems demonstrate that the latter constrained method outperforms the penalty method, particularly for higher noise levels or fewer collocation points. This work motivates further exploration into using sophisticated constrained optimization methods in scientific machine learning, as opposed to their commonly used, penalty-method or unconstrained counterparts. For both of these methods, we solve these discovered neural network PDEs with classical methods, such as finite difference methods, as opposed to PINNs-type methods relying on automatic differentiation. Here, we briefly highlight how simultaneously fitting the data while discovering the PDE improves the robustness to noise and other small, yet crucial, implementation details.

Data-driven discovery↗
DOE OSTI2024

Gains in operational flexibility, safety margins, and cost efficiencies via integrated Plant Reload Optimization platform

The U.S. Department of Energy Light Water Reactor Sustainability Program Risk-Informed Systems Analysis Pathway Plant Reload Optimization Project aims to develop an integrated, comprehensive framework offering an all-in-one solution for reload evaluations with a special focus on optimizing core design. Optimizing the fuel loading pattern is one of the most important considerations in reducing the amount of new fuel used in the core. Due to thousands of possible core configuration options, finding optimal solutions is an unachievable task for a human. The Plant ReLoad Optimization platform, which supports artificial-intelligence-based reactor core designing, is now fully capable of handling realistic problems. The Plant ReLoad Optimization platform development project aims to build a reactor core design tool that includes reactor safety and fuel performance analyses and uses artificial intelligence to support the optimization of core design solutions. The NSGA-II (Non-dominated Sorting Genetic Algorithm II) optimizer was developed and tested within RAVEN (Risk Analysis and Virtual ENvironment) to handle many constraints by using an augmented objectives methodology. The demonstration was performed with constrained multiobjective optimization of a 17 × 17 pressurized-water reactor core loading patterns to minimize fuel cost and maximize fuel cycle length.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

A safe reinforcement learning algorithm for supervisory control of power plants

Traditional control theory-based methods require tailored engineering for each system and constant fine-tuning. In power plant control, one often needs to obtain a precise representation of the system dynamics and carefully design the control scheme accordingly. Model-free Reinforcement learning (RL) has emerged as a promising solution for control tasks due to its ability to learn from trial-and-error interactions with the environment. It eliminates the need for explicitly modeling the environment’s dynamics, which is potentially inaccurate. However, the direct imposition of state constraints in power plant control raises challenges for standard RL methods. To address this, we propose a chance-constrained RL algorithm based on Proximal Policy Optimization for supervisory control. Our method employs Lagrangian relaxation to convert the constrained optimization problem into an unconstrained objective, where trainable Lagrange multipliers enforce the state constraints. In conclusion, our approach achieves the smallest distance of violation and violation rate in a load-follow maneuver for an advanced Nuclear Power Plant design.

constrained optimization↗
DOE OSTI2022

Rolling Optimization of Transmission Network Recovery and Load Restoration Considering Hybrid Wind-Storage System and Cold Load Pickup

A common solution to deal with the stochasticity introduced by fast-ramping wind power integration is to equip wind farms (WFs) with energy storage systems (ESSs) to formulate hybrid WF-ESSs. In addition to leveling off wind power fluctuations during normal operations, a hybrid WF-ESS can be a flexible power source to accumulate the power system restoration. In this paper, we propose a rolling optimization model for transmission network recovery and load restoration considering the contributions of WF-ESSs. The proposed model is formulated as a mixed integer linear programming problem that simultaneously optimizes the amount and location of restorable load blocks as well as the restoration lines. The cold load pickup features of interrupted loads considering the outage duration are modeled in detail. A chance-constrained method is employed to deal with the uncertainty of wind power, and a rolling horizon-based framework is adopted to reduce the influence of forecast error. Case studies are conducted on both New England 39-bus system and part of a provincial power system in China. The results show that the load restoration process can be significantly accelerated by employing the proposed method and contributions of hybrid WF-ESSs to power system restoration are validated.

chance-constrained optimization↗
NASA NTRS2016

Global Optimization of Low-Thrust Interplanetary Trajectories Subject to Operational Constraints

Low-thrust interplanetary space missions are highly complex and there can be many locally optimal solutions. While several techniques exist to search for globally optimal solutions to low-thrust trajectory design problems, they are typically limited to unconstrained trajectories. The operational design community in turn has largely avoided using such techniques and has primarily focused on accurate constrained local optimization combined with grid searches and intuitive design processes at the expense of efficient exploration of the global design space. This work is an attempt to bridge the gap between the global optimization and operational design communities by presenting a mathematical framework for global optimization of low-thrust trajectories subject to complex constraints including the targeting of planetary landing sites, a solar range constraint to simplify the thermal design of the spacecraft, and a real-world multi-thruster electric propulsion system that must switch thrusters on and off as available power changes over the course of a mission.

Design↗