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At least 19 records

Dynamic Optimization

We distinguish static and dynamic optimization of programs: whereas static optimization modifies a program before runtime and is based only on its syntactical structure, dynamic optimization is based on the statistical properties of the input source and examples of program execution. Explanation-based generalization is a commonly used dynamic optimization method, but its effectiveness as a speedup-learning method is limited, in part because it fails to separate the learning process from the program transformation process. This paper describes a dynamic optimization technique called a learn-optimize cycle that first uses a learning element to uncover predictable patterns in the program execution and then uses an optimization algorithm to map these patterns into beneficial transformations. The technique has been used successfully for dynamic optimization of pure Prolog.

Laird, Philip

Neighboring extremals of dynamic optimization problems with path equality constraints

Neighboring extremals of dynamic optimization problems with path equality constraints and with an unknown parameter vector are considered in this paper. With some simplifications, the problem is reduced to solving a linear, time-varying two-point boundary-value problem with integral path equality constraints. A modified backward sweep method is used to solve this problem. Two example problems are solved to illustrate the validity and usefulness of the solution technique.

Lee, A. Y.

Efficient dynamic optimization of logic programs

A summary is given of the dynamic optimization approach to speed up learning for logic programs. The problem is to restructure a recursive program into an equivalent program whose expected performance is optimal for an unknown but fixed population of problem instances. We define the term 'optimal' relative to the source of input instances and sketch an algorithm that can come within a logarithmic factor of optimal with high probability. Finally, we show that finding high-utility unfolding operations (such as EBG) can be reduced to clause reordering.

Laird, Phil

Dynamic optimization theory with multiple objectives

Let V(t) be a vector-valued function for t belonging to closed interval a,b open interval, a real interval. The main purpose of this paper is to establish the existence of a closed interval alpha,beta contained in closed interval a,b for which there exists a t(sub O) belonging to closed interval alpha,beta contained in closed interval a,b such that V(t(sub O)) = 0, the zero vector. Use of such information in the dynamic optimization theory with multiple objectives present is needed. Examples of such systems will be given.

Jones, John, Jr.

Dynamic Optimization of Multi-Spacecraft Relative Navigation Configurations in the Earth-Moon System

In this paper, the notion of relative navigation introduced by Hill, Lo and Born is analyzed for a large class of periodic orbits in the Earth-Moon three-body problem, due to its potential in supporting Moon exploration efforts. In particular, a navigation metric is introduced and used as a cost function to optimize over a class of periodic orbits. While the problem could be solve locally as an optimal control problem, a dynamical based approach that allows for a global/systematic view of the problem is proposed. First, the simpler problem of multiple spacecraft placement on a given periodic orbit is solved before the notion of continuation and bifurcation analysis is used to expand the range of solutions thus obtained.

Three Body Problem

Mystic: Implementation of the Static Dynamic Optimal Control Algorithm for High-Fidelity, Low-Thrust Trajectory Design

Mystic software is designed to compute, analyze, and visualize optimal high-fidelity, low-thrust trajectories, The software can be used to analyze inter-planetary, planetocentric, and combination trajectories, Mystic also provides utilities to assist in the operation and navigation of low-thrust spacecraft. Mystic will be used to design and navigate the NASA's Dawn Discovery mission to orbit the two largest asteroids, The underlying optimization algorithm used in the Mystic software is called Static/Dynamic Optimal Control (SDC). SDC is a nonlinear optimal control method designed to optimize both 'static variables' (parameters) and dynamic variables (functions of time) simultaneously. SDC is a general nonlinear optimal control algorithm based on Bellman's principal.

low thrust

Computational Fluid Dynamic Optimization of an Experimental Rotating Detonation Rocket Engine Nozzle

A parametric optimization study is performed on the nozzle of a laboratory rotating detonation rocket engine (RDRE) using a three-dimensional computational fluid dynamic simulation. The primary optimization objective is maximum nozzle thrust. The basic nozzle configuration is a shrouded, truncated plug. The fluid in the RDRE chamber leading to the nozzle is choked at its exit so that its cyclic behavior is unaffected by any changes to the nozzle design. Optimization is performed for a single operating point. Parameters varied are the overall nozzle area expansion ratio and the fraction of the expansion area that is provided by the shroud. These two parameters indirectly affect the angle of the plug nozzle cone, and the bluff body area associated with its truncation. Nozzle thrust is evaluated as the difference between the thrust of the RDRE chamber-plus-nozzle combination and that of the chamber alone. The nozzle produces approximately 20% of the total engine thrust. The baseline nozzle is found to perform well, yielding 58.1% of the thrust calculated for a notional ideal RDRE nozzle which can instantaneously change shape to allow isentropic expansion of every fluid element. Optimization improves the performance, bringing the nozzle thrust to 70.0% of the notional ideal, and total engine thrust (chamber-plus-nozzle) to 94% of the ideal.

detonation

Computational Fluid Dynamic Optimization of an Experimental Rotating Detonation Rocket Engine Nozzle

A parametric optimization study is performed on the nozzle of a laboratory rotating detonation rocket engine (RDRE) using a three-dimensional computational fluid dynamic simulation. The primary optimization objective is maximum nozzle thrust. The basic nozzle configuration is a shrouded, truncated plug. The fluid in the RDRE chamber leading to the nozzle is choked at its exit so that its cyclic behavior is unaffected by any changes to the nozzle design. Optimization is performed for a single operating point. Parameters varied are the overall nozzle area expansion ratio and the fraction of the expansion area that is provided by the shroud. These two parameters indirectly affect the angle of the plug nozzle cone, and the bluff body area associated with its truncation. Nozzle thrust is evaluated as the difference between the thrust of the RDRE chamber-plus-nozzle combination and that of the chamber alone. The nozzle produces approximately 20% of the total engine thrust. The baseline nozzle is found to perform well, yielding 58.1% of the thrust calculated for a notional ideal RDRE nozzle which can instantaneously change shape to allow isentropic expansion of every fluid element. Optimization improves the performance, bringing the nozzle thrust to 70.0% of the notional ideal, and total engine thrust (chamber-plus-nozzle) to 94% of the ideal.

detonation

Optimal dynamic control of resources in a distributed system

The authors quantitatively formulate the problem of controlling resources in a distributed system so as to optimize a reward function and derive optimal control strategies using Markov decision theory. The control variables treated are quite general; they could be control decisions related to system configuration, repair, diagnostics, files, or data. Two algorithms for resource control in distributed systems are derived for time-invariant and periodic environments, respectively. A detailed example to demonstrate the power and usefulness of the approach is provided.

Shin, Kang G.

Optimal dynamic remapping of data parallel computations

A large class of data parallel computations is characterized by a sequence of phases, with phase changes occurring unpredictably. Dynamic remapping of the workload to processors may be required to maintain good performance. The problem considered, for which the utility of remapping and the future behavior of the workload are uncertain, arises when phases exhibit stable execution requirements during a given phase, but requirements change radically between phases. For these situations, a workload assignment generated for one phase may hinder performance during the next phase. This problem is treated formally for a probabilistic model of computation with at most two phases. The authors address the fundamental problem of balancing the expected remapping performance gain against the delay cost, and they derive the optimal remapping decision policy. The promise of the approach is shown by application to multiprocessor implementations of an adaptive gridding fluid dynamics program and to a battlefield simulation program.

Nicol, David M.

Optimal dynamic remapping of parallel computations

A large class of computations are characterized by a sequence of phases, with phase changes occurring unpredictably. The decision problem was considered regarding the remapping of workload to processors in a parallel computation when the utility of remapping and the future behavior of the workload is uncertain, and phases exhibit stable execution requirements during a given phase, but requirements may change radically between phases. For these problems a workload assignment generated for one phase may hinder performance during the next phase. This problem is treated formally for a probabilistic model of computation with at most two phases. The fundamental problem of balancing the expected remapping performance gain against the delay cost was addressed. Stochastic dynamic programming is used to show that the remapping decision policy minimizing the expected running time of the computation has an extremely simple structure. Because the gain may not be predictable, the performance of a heuristic policy that does not require estimnation of the gain is examined. The heuristic method's feasibility is demonstrated by its use on an adaptive fluid dynamics code on a multiprocessor. The results suggest that except in extreme cases, the remapping decision problem is essentially that of dynamically determining whether gain can be achieved by remapping after a phase change. The results also suggest that this heuristic is applicable to computations with more than two phases.

Nicol, David M.

Dynamic optimization problems with bounded terminal conditions

Bounded terminal conditions of nonlinear optimization problems are converted to equality terminal conditions via Valentine's device. In so doing, additional unknown parameters are introduced into the problem. The transformed problems can still be easily solved using the sequential gradient-restoration algorithm (SGRA) via a simple augmentation of the unknown parameter vector pi. Three example problems with bounded terminal conditions are solved to verify this technique.

Lee, A. Y.

A generalized gradient algorithm for dynamic optimization

A gradient algorithm is developed that determines optimal trajectories with path equality constraints and terminal constraints. A generalized gradient is formed which improves both the performance index and the path equality constraints simultaneously. The algorithm is extended to treat terminal constraints by using Bryson's impulse response technique. The main features of this algorithm are its numerical stability and smooth convergence near the optimum.

Zhao, Yiyuan

A Dynamic Optimization Technique for Siting the NASA-Clark Atlanta Urban Rain Gauge Network (NCURN)

NASA satellites and ground instruments have indicated that cities like Atlanta, Georgia may create or alter rainfall. Scientists speculate that the urban heat island caused by man-made surfaces in cities impact the heat and wind patterns that form clouds and rainfall. However, more conclusive evidence is required to substantiate findings from satellites. NASA, along with scientists at Clark Atlanta University, are implementing a dense, urban rain gauge network in the metropolitan Atlanta area to support a satellite validation program called Studies of PRecipitation Anomalies from Widespread Urban Landuse (SPRAWL). SPRAWL will be conducted during the summer of 2003 to further identify and understand the impact of urban Atlanta on precipitation variability. The paper provides an. overview of SPRAWL, which represents one of the more comprehensive efforts in recent years to focus exclusively on urban-impacted rainfall. The paper also introduces a novel technique for deploying rain gauges for SPRAWL. The deployment of the dense Atlanta network is unique because it utilizes Geographic Information Systems (GIS) and Decision Support Systems (DSS) to optimize deployment of the rain gauges. These computer aided systems consider access to roads, drainage systems, tree cover, and other factors in guiding the deployment of the gauge network. GIS and DSS also provide decision-makers with additional resources and flexibility to make informed decisions while considering numerous factors. Also, the new Atlanta network and SPRAWL provide a unique opportunity to merge the high-resolution, urban rain gauge network with satellite-derived rainfall products to understand how cities are changing rainfall patterns, and possibly climate.

Shepherd, J. Marshall

Optimal Dynamic Sub-Threshold Technique for Extreme Low Power Consumption for VLSI

For miniaturization of electronics systems, power consumption plays a key role in the realm of constraints. Considering the very large scale integration (VLSI) design aspect, as transistor feature size is decreased to 50 nm and below, there is sizable increase in the number of transistors as more functional building blocks are embedded in the same chip. However, the consequent increase in power consumption (dynamic and leakage) will serve as a key constraint to inhibit the advantages of transistor feature size reduction. Power consumption can be reduced by minimizing the voltage supply (for dynamic power consumption) and/or increasing threshold voltage (V(sub th), for reducing leakage power). When the feature size of the transistor is reduced, supply voltage (V(sub dd)) and threshold voltage (V(sub th)) are also reduced accordingly; then, the leakage current becomes a bigger factor of the total power consumption. To maintain low power consumption, operation of electronics at sub-threshold levels can be a potentially strong contender; however, there are two obstacles to be faced: more leakage current per transistor will cause more leakage power consumption, and slow response time when the transistor is operated in weak inversion region. To enable low power consumption and yet obtain high performance, the CMOS (complementary metal oxide semiconductor) transistor as a basic element is viewed and controlled as a four-terminal device: source, drain, gate, and body, as differentiated from the traditional approach with three terminals: i.e., source and body, drain, and gate. This technique features multiple voltage sources to supply the dynamic control, and uses dynamic control to enable low-threshold voltage when the channel (N or P) is active, for speed response enhancement and high threshold voltage, and when the transistor channel (N or P) is inactive, to reduce the leakage current for low-leakage power consumption.

Duong, Tuan A.

Appendix: Results obtained to date

Optimization procedures are described for the rotor blade design process by integrating appropriate disciplines and accounting for important interactions among the disciplines. Progress is reported in the areas of aerodynamic performance optimization, dynamic optimization, optimum placement of tuning masses for vibration reduction, and structural optimization. Selected results from these activities are highlighted in this appendix.

Walsh, Joanne L.