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A parallel variable metric optimization algorithm

An algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.

Straeter, T. A.

Description and performance analysis of a generalized optimal algorithm for aerobraking guidance

A practical real-time guidance algorithm has been developed for aerobraking vehicles which nearly minimizes the maximum heating rate, the maximum structural loads, and the post-aeropass delta V requirement for orbit insertion. The algorithm is general and reusable in the sense that a minimum of assumptions are made, thus greatly reducing the number of parameters that must be determined prior to a given mission. A particularly interesting feature is that in-plane guidance performance is tuned by adjusting one mission-dependent, the bank margin; similarly, the out-of-plane guidance performance is tuned by adjusting a plane controller time constant. Other features of the algorithm are simplicity, efficiency and ease of use. The trimmed vehicle with bank angle modulation as the method of trajectory control. Performance of this guidance algorithm is examined by its use in an aerobraking testbed program. The performance inquiry extends to a wide range of entry speeds covering a number of potential mission applications. Favorable results have been obtained with a minimum of development effort, and directions for improvement of performance are indicated.

Evans, Steven W.

Aerodynamic Optimization of Rocket Control Surface Geometry Using Cartesian Methods and CAD Geometry

Aerodynamic design is an iterative process involving geometry manipulation and complex computational analysis subject to physical constraints and aerodynamic objectives. A design cycle consists of first establishing the performance of a baseline design, which is usually created with low-fidelity engineering tools, and then progressively optimizing the design to maximize its performance. Optimization techniques have evolved from relying exclusively on designer intuition and insight in traditional trial and error methods, to sophisticated local and global search methods. Recent attempts at automating the search through a large design space with formal optimization methods include both database driven and direct evaluation schemes. Databases are being used in conjunction with surrogate and neural network models as a basis on which to run optimization algorithms. Optimization algorithms are also being driven by the direct evaluation of objectives and constraints using high-fidelity simulations. Surrogate methods use data points obtained from simulations, and possibly gradients evaluated at the data points, to create mathematical approximations of a database. Neural network models work in a similar fashion, using a number of high-fidelity database calculations as training iterations to create a database model. Optimal designs are obtained by coupling an optimization algorithm to the database model. Evaluation of the current best design then gives either a new local optima and/or increases the fidelity of the approximation model for the next iteration. Surrogate methods have also been developed that iterate on the selection of data points to decrease the uncertainty of the approximation model prior to searching for an optimal design. The database approximation models for each of these cases, however, become computationally expensive with increase in dimensionality. Thus the method of using optimization algorithms to search a database model becomes problematic as the number of design variables is increased.

Nelson, Andrea

An optimal structural design algorithm using optimality criteria

An algorithm for optimal design is given which incorporates several of the desirable features of both mathematical programming and optimality criteria, while avoiding some of the undesirable features. The algorithm proceeds by approaching the optimal solution through the solutions of an associated set of constrained optimal design problems. The solutions of the constrained problems are recognized at each stage through the application of optimality criteria based on energy concepts. Two examples are described in which the optimal member size and layout of a truss is predicted, given the joint locations and loads.

Taylor, J. E.

Genetic Algorithm for Optimization of Neural Networks for Bayesian Inference of Model Uncertainty

The objective of this work was to develop a genetic optimization algorithm that can design a neural network capable of producing uncertainty estimates along with predictions. This algorithm is necessary because the inclusion of uncertainty modeling in a neural network greatly complicates the network’s design space, making the development of a converging model extremely difficult and time consuming. The genetic algorithm presented in this work uses a number of value ranges for various configurable neural network parameters to create a randomly generated population of network architectures. The initially generated population is then evolved over the course of several generations, with the best performing models breeding to produce novel network configurations. Mutations are randomly applied to the network designs to facilitate the development of adaptations beneficial to the task being performed. An experiment was conducted to validate the proposed algorithm, in which the genetic optimizer was tasked with producing a neural network capable of predicting the sound pressure level (SPL) resulting from jet-surface interaction (JSI) noise. The data used for this task was generated at the NASA Glenn Research Center in the Aero-Acoustic Propulsion Laboratory. Starting with an initial population size of 35 randomly generated networks, and evolved over the course of 10 generations, the genetic algorithm produced a design able to predict SPL as a result of JSI noise within 0.272 dB, on average.

Genetic algorithm

Genetic Algorithm for Optimization: Preprocessor and Algorithm

Genetic algorithm (GA) inspired by Darwin's theory of evolution and employed to solve optimization problems - unconstrained or constrained - uses an evolutionary process. A GA has several parameters such the population size, search space, crossover and mutation probabilities, and fitness criterion. These parameters are not universally known/determined a priori for all problems. Depending on the problem at hand, these parameters need to be decided such that the resulting GA performs the best. We present here a preprocessor that achieves just that, i.e., it determines, for a specified problem, the foregoing parameters so that the consequent GA is a best for the problem. We stress also the need for such a preprocessor both for quality (error) and for cost (complexity) to produce the solution. The preprocessor includes, as its first step, making use of all the information such as that of nature/character of the function/system, search space, physical/laboratory experimentation (if already done/available), and the physical environment. It also includes the information that can be generated through any means - deterministic/nondeterministic/graphics. Instead of attempting a solution of the problem straightway through a GA without having/using the information/knowledge of the character of the system, we would do consciously a much better job of producing a solution by using the information generated/created in the very first step of the preprocessor. We, therefore, unstintingly advocate the use of a preprocessor to solve a real-world optimization problem including NP-complete ones before using the statistically most appropriate GA. We also include such a GA for unconstrained function optimization problems.

Sen, S. K.

Performance seeking control (PSC) for the F-15 highly integrated digital electronic control (HIDEC) aircraft

The performance seeking control algorithm optimizes total propulsion system performance. This adaptive, model-based optimization algorithm has been successfully flight demonstrated on two engines with differing levels of degradation. Models of the engine, nozzle, and inlet produce reliable, accurate estimates of engine performance. But, because of an observability problem, component levels of degradation cannot be accurately determined. Depending on engine-specific operating characteristics PSC achieves various levels performance improvement. For example, engines with more deterioration typically operate at higher turbine temperatures than less deteriorated engines. Thus when the PSC maximum thrust mode is applied, for example, there will be less temperature margin available to be traded for increasing thrust.

Orme, John S.

Hardware-Efficient Quantum Optimization Layered Algorithms and Experiments

Quantum optimization algorithms, such as QAOA, that implement parametrized stochastic optimization solvers attempt to identify low-energy solutions of Ising systems by exploiting available quantum effects in noisy-intermediate scale machines. Engineering a well-performing parametrized quantum optimization circuit is indeed an exercise in balancing the trade-off between expressivity and implementation complexity. We show that, for MaxCut QAOA circuits defined on native hardware topology (Rigetti’s Aspen Quantum Processors), error-mitigation techniques recover simulated features of the noiseless theory. Moreover, we explore a design space for QAOA-like ansatze that perform well in theory as well as in hardware for fully-connected problems. We also discuss how efficient coherence and entanglement detection methods that could be coupled with quantum optimization experiments require only linear overhead in benchmarking time.

quantum computing

Parallel projected variable metric algorithms for unconstrained optimization

The parallel variable metric optimization algorithms of Straeter (1973) and van Laarhoven (1985) are reviewed, and the possible drawbacks of the algorithms are noted. By including Davidon (1975) projections in the variable metric updating, researchers can generalize Straeter's algorithm to a family of parallel projected variable metric algorithms which do not suffer the above drawbacks and which retain quadratic termination. Finally researchers consider the numerical performance of one member of the family on several standard example problems and illustrate how the choice of the displacement vectors affects the performance of the algorithm.

Freeman, T. L.

A Simulated Annealing Algorithm for the Optimization of Multistage Depressed Collector Efficiency

The microwave traveling wave tube amplifier (TWTA) is widely used as a high-power transmitting source for space and airborne communications. One critical factor in designing a TWTA is the overall efficiency. However, overall efficiency is highly dependent upon collector efficiency; so collector design is critical to the performance of a TWTA. Therefore, NASA Glenn Research Center has developed an optimization algorithm based on Simulated Annealing to quickly design highly efficient multi-stage depressed collectors (MDC).

Vaden, Karl R.