ARPA-e Grid Optimization Competition: Benchmark Algorithm Overview
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Energy Sciences↗
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Leveraging Machine Learning Algorithms for Efficient Optimization
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Engineering - Aeronautics, Mathematics and Computi↗
Control optimization, stabilization and computer algorithms for space applications
Research of control optimization, stochastic stability, and air traffic control problems
Source record↗
Control optimization, stabilization and computer algorithms for aircraft applications
The analysis and design of complex multivariable reliable control systems are considered. High performance and fault tolerant aircraft systems are the objectives. A preliminary feasibility study of the design of a lateral control system for a VTOL aircraft that is to land on a DD963 class destroyer under high sea state conditions is provided. Progress in the following areas is summarized: (1) VTOL control system design studies; (2) robust multivariable control system synthesis; (3) adaptive control systems; (4) failure detection algorithms; and (5) fault tolerant optimal control theory.
Athans, M.↗
Optimal Limited Contingency Planning
For a given problem, the optimal Markov policy over a finite horizon is a conditional plan containing a potentially large number of branches. However, there are applications where it is desirable to strictly limit the number of decision points and branches in a plan. This raises the question of how one goes about finding optimal plans containing only a limited number of branches. In this paper, we present an any-time algorithm for optimal k-contingency planning. It is the first optimal algorithm for limited contingency planning that is not an explicit enumeration of possible contingent plans. By modelling the problem as a partially observable Markov decision process, it implements the Bellman optimality principle and prunes the solution space. We present experimental results of applying this algorithm to some simple test cases.
Meuleau, Nicolas↗
Low-Thrust Trajectory Optimization with Simplified SQP Algorithm
The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper de-scribes a fast, robust method to design a trajectory in the CRTBP (circular restricted three body problem), beginning with no or very little knowledge of the system. The approach is inspired by the SQP (sequential quadratic programming) algorithm, in which a general nonlinear programming problem is solved via a sequence of quadratic problems. A few key simplifications make the algorithm presented fast and robust to initial guess: a quadratic cost function, neglecting the line search step when the solution is known to be far away, judicious use of end-point constraints, and mesh refinement on multiple shooting with fixed-step integration.In comparison to the traditional approach of plugging the problem into a “black-box” NLP solver, the methods shown converge even when given no knowledge of the solution at all. It was found that the only piece of information that the user needs to provide is a rough guess for the time of flight, as the transfer time guess will dictate which set of local solutions the algorithm could converge on. This robustness to initial guess is a compelling feature, as three-body orbit transfers are challenging to design with intuition alone. Of course, if a high-quality initial guess is available, the methods shown are still valid.We have shown that endpoints can be efficiently constrained to lie on 3-body repeating orbits, and that time of flight can be optimized as well. When optimizing the endpoints, we must make a trade between converging quickly on sub-optimal endpoints or converging more slowly on end-points that are arbitrarily close to optimal. It is easy for the mission design engineer to adjust this trade based on the problem at hand.The biggest limitation to the algorithm at this point is that multi-revolution transfers (greater than 2 revolutions) do not work nearly as well. This restriction comes in because the relationship between node 1 and node N becomes increasingly nonlinear as the angular distance grows. Trans-fers with more than about 1.5 complete revolutions generally require the line search to improve convergence. Future work includes: Comparison of this algorithm with other established tools; improvements to how multiple-revolution transfers are handled; parallelization of the Jacobian computation; in-creased efficiency for the line search; and optimization of many more trajectories between a variety of 3-body orbits.
Parrish, Nathan L.↗
The "Best Worst" Field Optimization and Focusing
A simple algorithm for optimizing and focusing lens designs is presented. The goal of the algorithm is to simultaneously create the best and most uniform image quality over the field of view. Rather than relatively weighting multiple field points, only the image quality from the worst field point is considered. When optimizing a lens design, iterations are made to make this worst field point better until such a time as a different field point becomes worse. The same technique is used to determine focus position. The algorithm works with all the various image quality metrics. It works with both symmetrical and asymmetrical systems. It works with theoretical models and real hardware.
Vaughnn, David↗
An algorithm for the systematic disturbance of optimal rotational solutions
An algorithm for introducing a systematic rotational disturbance into an optimal (i.e., single axis) rotational trajectory is described. This disturbance introduces a motion vector orthogonal to the quaternion-defined optimal rotation axis. By altering the magnitude of this vector, the degree of non-optimality can be controlled. The metric properties of the distortion parameter are described, with analogies to two-dimensional translational motion. This algorithm was implemented in a motion-control program on a three-dimensional graphic workstation. It supports a series of human performance studies on the detectability of rotational trajectory optimality by naive observers.
Grunwald, Arthur J.↗
Random search optimization based on genetic algorithm and discriminant function
The general problem of optimization with arbitrary merit and constraint functions, which could be convex, concave, monotonic, or non-monotonic, is treated using stochastic methods. To improve the efficiency of the random search methods, a genetic algorithm for the search phase and a discriminant function for the constraint-control phase were utilized. The validity of the technique is demonstrated by comparing the results to published test problem results. Numerical experimentation indicated that for cases where a quick near optimum solution is desired, a general, user-friendly optimization code can be developed without serious penalties in both total computer time and accuracy.
Kiciman, M. O.↗
Next-Generation Optimization under Uncertainty: Structure-Oriented Algorithms
With the advent of the smart grid, renewable technologies, and carbon emission programs, a key concern is the coordination of national infrastructures such as the electricity, natural gas, and water supply network systems. Anticipating and mitigating uncertainty of weather, demands, and contingencies in a more integrated environment is necessary to maximize resource efficiency and prevent cascading failures that can ultimately lead to catastrophic shortages of supplies. This project developed scalable algorithms for stochastic optimization capable of addressing extreme-scale problems (motivated by challenges in the design and operation of national infrastructures). Specifically, the project developed a new family of algorithms to solve continuous stochastic problems to local and global optimality as well as algorithms to solve mixed-integer convex and nonconvex stochastic programs. We developed supporting local and global convergence theory for these algorithms and implemented the algorithms in open-source software packages that can leverage high-performance computing architectures.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Optimization and Prediction of Spectral Response of Metasurfaces Using Artificial Intelligence
Hot-electron generation has been a topic of intense research for decades for numerous applications ranging from photodetection and photochemistry to biosensing. Recently, the technique of hot-electron generation using non-radiative decay of surface plasmons excited by metallic nanoantennas, or meta-atoms, in a metasurface has attracted attention. These metasurfaces can be designed with thicknesses on the order of the hot-electron diffusion length. The plasmonic resonances of these ultrathin metasurfaces can be tailored by changing the shape and size of the meta-atoms. One of the fundamental mechanisms leading to generation of hot-electrons in such systems is optical absorption, therefore, optimization of absorption is a key step in enhancing the performance of any metasurface based hot-electron device. Here we utilized an artificial intelligence-based approach, the genetic algorithm, to optimize absorption spectra of plasmonic metasurfaces. Using genetic algorithm optimization strategies, we designed a polarization insensitive plasmonic metasurface with 90% absorption at 1550 nm that does not require an optically thick ground plane. We fabricated and optically characterized the metasurface and our experimental results agree with simulations. Finally, we present a convolutional neural network that can predict the absorption spectra of metasurfaces never seen by the network, thereby eliminating the need for computationally expensive simulations. Our results suggest a new direction for optimizing hot-electron based photodetectors and sensors.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Inexact Newton-CG algorithms with complexity guarantees
Abstract We consider variants of a recently developed Newton-CG algorithm for nonconvex problems (Royer, C. W. & Wright, S. J. (2018) Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization. SIAM J. Optim., 28, 1448–1477) in which inexact estimates of the gradient and the Hessian information are used for various steps. Under certain conditions on the inexactness measures, we derive iteration complexity bounds for achieving $\epsilon $-approximate second-order optimality that match best-known lower bounds. Our inexactness condition on the gradient is adaptive, allowing for crude accuracy in regions with large gradients. We describe two variants of our approach, one in which the step size along the computed search direction is chosen adaptively, and another in which the step size is pre-defined. To obtain second-order optimality, our algorithms will make use of a negative curvature direction on some steps. These directions can be obtained, with high probability, using the randomized Lanczos algorithm. In this sense, all of our results hold with high probability over the run of the algorithm. We evaluate the performance of our proposed algorithms empirically on several machine learning models. Our approach is a first attempt to introduce inexact Hessian and/or gradient information into the Newton-CG algorithm of Royer & Wright (2018, Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization. SIAM J. Optim., 28, 1448–1477).
Mathematics↗
Issues and Strategies in Solving Multidisciplinary Optimization Problems
Optimization research at NASA Glenn Research Center has addressed the design of structures, aircraft and airbreathing propulsion engines. The accumulated multidisciplinary design activity is collected under a testbed entitled COMETBOARDS. Several issues were encountered during the solution of the problems. Four issues and the strategies adapted for their resolution are discussed. This is followed by a discussion on analytical methods that is limited to structural design application. An optimization process can lead to an inefficient local solution. This deficiency was encountered during design of an engine component. The limitation was overcome through an augmentation of animation into optimization. Optimum solutions obtained were infeasible for aircraft and airbreathing propulsion engine problems. Alleviation of this deficiency required a cascading of multiple algorithms. Profile optimization of a beam produced an irregular shape. Engineering intuition restored the regular shape for the beam. The solution obtained for a cylindrical shell by a subproblem strategy converged to a design that can be difficult to manufacture. Resolution of this issue remains a challenge. The issues and resolutions are illustrated through a set of problems: Design of an engine component, Synthesis of a subsonic aircraft, Operation optimization of a supersonic engine, Design of a wave-rotor-topping device, Profile optimization of a cantilever beam, and Design of a cylindrical shell. This chapter provides a cursory account of the issues. Cited references provide detailed discussion on the topics. Design of a structure can also be generated by traditional method and the stochastic design concept. Merits and limitations of the three methods (traditional method, optimization method and stochastic concept) are illustrated. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions can be produced by all the three methods. The variation in the weight calculated by the methods was found to be modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.
Patnaik, Surya↗
Fast tensor disentangling algorithm
Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an approximate, fast, and simple algorithm to optimize disentangling unitary tensors. Our algorithm is asymptotically faster than previous iterative algorithms and often results in a residual entanglement entropy that is within 10 to 40% of the minimum. For certain input tensors, our algorithm returns an optimal solution. When disentangling order-4 tensors with equal bond dimensions, our algorithm achieves an entanglement spectrum where nearly half of the singular values are zero. We further validate our algorithm by showing that it can efficiently disentangle random 1D states of qubits.
Slagle, Kevin↗
Control optimization, stabilization and computer algorithms for aircraft applications
Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.
Source record↗
sbovqaopt: Surrogate-based optimizer for variational quantum algorithms v.0.1.0
SAND2022-13232 O The sbovqaopt package provides a surrogate-based optimizer for variational quantum algorithms as introduced in the journal publication of the same title. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
SciDAC↗
Control Optimization, Stabilization and Computer Algorithms for Space Applications First Status Report, Mar. 1 - Aug. 31 1966
Control optimization, stabilization, and computer algorithms for space applications
FEEDBACK CONTROL SYSTEM↗
Intelligent perturbation algorithms to space scheduling optimization
The limited availability and high cost of crew time and scarce resources make optimization of space operations critical. Advances in computer technology coupled with new iterative search techniques permit the near optimization of complex scheduling problems that were previously considered computationally intractable. Described here is a class of search techniques called Intelligent Perturbation Algorithms. Several scheduling systems which use these algorithms to optimize the scheduling of space crew, payload, and resource operations are also discussed.
Kurtzman, Clifford R.↗