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At least 19 records

Multiobjective Optimization Using a Pareto Differential Evolution Approach

Differential Evolution is a simple, fast, and robust evolutionary algorithm that has proven effective in determining the global optimum for several difficult single-objective optimization problems. In this paper, the Differential Evolution algorithm is extended to multiobjective optimization problems by using a Pareto-based approach. The algorithm performs well when applied to several test optimization problems from the literature.

Madavan, Nateri K.

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine and compared to earlier methods. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.

On Improving Efficiency of Differential Evolution for Aerodynamic Shape Optimization Applications

Differential Evolution (DE) is a simple and robust evolutionary strategy that has been provEn effective in determining the global optimum for several difficult optimization problems. Although DE offers several advantages over traditional optimization approaches, its use in applications such as aerodynamic shape optimization where the objective function evaluations are computationally expensive is limited by the large number of function evaluations often required. In this paper various approaches for improving the efficiency of DE are reviewed and discussed. Several approaches that have proven effective for other evolutionary algorithms are modified and implemented in a DE-based aerodynamic shape optimization method that uses a Navier-Stokes solver for the objective function evaluations. Parallelization techniques on distributed computers are used to reduce turnaround times. Results are presented for standard test optimization problems and for the inverse design of a turbine airfoil. The efficiency improvements achieved by the different approaches are evaluated and compared.

Madavan, Nateri K.

Multiobjective Aerodynamic Shape Optimization Using Pareto Differential Evolution and Generalized Response Surface Metamodels

Differential Evolution (DE) is a simple, fast, and robust evolutionary algorithm that has proven effective in determining the global optimum for several difficult single-objective optimization problems. The DE algorithm has been recently extended to multiobjective optimization problem by using a Pareto-based approach. In this paper, a Pareto DE algorithm is applied to multiobjective aerodynamic shape optimization problems that are characterized by computationally expensive objective function evaluations. To improve computational expensive the algorithm is coupled with generalized response surface meta-models based on artificial neural networks. Results are presented for some test optimization problems from the literature to demonstrate the capabilities of the method.

Madavan, Nateri K.

On Improving Efficiency of Differential Evolution for Aerodynamic Shape Optimization Applications

Differential Evolution (DE) is a simple and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems. Although DE offers several advantages over traditional optimization approaches, its use in applications such as aerodynamic shape optimization where the objective function evaluations are computationally expensive is limited by the large number of function evaluations often required. In this paper various approaches for improving the efficiency of DE are reviewed and discussed. These approaches are implemented in a DE-based aerodynamic shape optimization method that uses a Navier-Stokes solver for the objective function evaluations. Parallelization techniques on distributed computers are used to reduce turnaround times. Results are presented for the inverse design of a turbine airfoil. The efficiency improvements achieved by the different approaches are evaluated and compared.

Madavan, Nateri K.

Aerodynamic Shape Optimization Using Hybridized Differential Evolution

An aerodynamic shape optimization method that uses an evolutionary algorithm known at Differential Evolution (DE) in conjunction with various hybridization strategies is described. DE is a simple and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems. Various hybridization strategies for DE are explored, including the use of neural networks as well as traditional local search methods. A Navier-Stokes solver is used to evaluate the various intermediate designs and provide inputs to the hybrid DE optimizer. The method is implemented on distributed parallel computers so that new designs can be obtained within reasonable turnaround times. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. (The final paper will include at least one other aerodynamic design application). The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated.

Madavan, Nateri K.

Single- and Multiple-Objective Optimization with Differential Evolution and Neural Networks

Genetic and evolutionary algorithms have been applied to solve numerous problems in engineering design where they have been used primarily as optimization procedures. These methods have an advantage over conventional gradient-based search procedures became they are capable of finding global optima of multi-modal functions and searching design spaces with disjoint feasible regions. They are also robust in the presence of noisy data. Another desirable feature of these methods is that they can efficiently use distributed and parallel computing resources since multiple function evaluations (flow simulations in aerodynamics design) can be performed simultaneously and independently on ultiple processors. For these reasons genetic and evolutionary algorithms are being used more frequently in design optimization. Examples include airfoil and wing design and compressor and turbine airfoil design. They are also finding increasing use in multiple-objective and multidisciplinary optimization. This lecture will focus on an evolutionary method that is a relatively new member to the general class of evolutionary methods called differential evolution (DE). This method is easy to use and program and it requires relatively few user-specified constants. These constants are easily determined for a wide class of problems. Fine-tuning the constants will off course yield the solution to the optimization problem at hand more rapidly. DE can be efficiently implemented on parallel computers and can be used for continuous, discrete and mixed discrete/continuous optimization problems. It does not require the objective function to be continuous and is noise tolerant. DE and applications to single and multiple-objective optimization will be included in the presentation and lecture notes. A method for aerodynamic design optimization that is based on neural networks will also be included as a part of this lecture. The method offers advantages over traditional optimization methods. It is more flexible than other methods in dealing with design in the context of both steady and unsteady flows, partial and complete data sets, combined experimental and numerical data, inclusion of various constraints and rules of thumb, and other issues that characterize the aerodynamic design process. Neural networks provide a natural framework within which a succession of numerical solutions of increasing fidelity, incorporating more realistic flow physics, can be represented and utilized for optimization. Neural networks also offer an excellent framework for multiple-objective and multi-disciplinary design optimization. Simulation tools from various disciplines can be integrated within this framework and rapid trade-off studies involving one or many disciplines can be performed. The prospect of combining neural network based optimization methods and evolutionary algorithms to obtain a hybrid method with the best properties of both methods will be included in this presentation. Achieving solution diversity and accurate convergence to the exact Pareto front in multiple objective optimization usually requires a significant computational effort with evolutionary algorithms. In this lecture we will also explore the possibility of using neural networks to obtain estimates of the Pareto optimal front using non-dominated solutions generated by DE as training data. Neural network estimators have the potential advantage of reducing the number of function evaluations required to obtain solution accuracy and diversity, thus reducing cost to design.

Rai, Man Mohan

The Ground Flash Fraction Retrieval Algorithm Employing Differential Evolution: Simulations and Applications

The ability to estimate the fraction of ground flashes in a set of flashes observed by a satellite lightning imager, such as the future GOES-R Geostationary Lightning Mapper (GLM), would likely improve operational and scientific applications (e.g., severe weather warnings, lightning nitrogen oxides studies, and global electric circuit analyses). A Bayesian inversion method, called the Ground Flash Fraction Retrieval Algorithm (GoFFRA), was recently developed for estimating the ground flash fraction. The method uses a constrained mixed exponential distribution model to describe a particular lightning optical measurement called the Maximum Group Area (MGA). To obtain the optimum model parameters (one of which is the desired ground flash fraction), a scalar function must be minimized. This minimization is difficult because of two problems: (1) Label Switching (LS), and (2) Parameter Identity Theft (PIT). The LS problem is well known in the literature on mixed exponential distributions, and the PIT problem was discovered in this study. Each problem occurs when one allows the numerical minimizer to freely roam through the parameter search space; this allows certain solution parameters to interchange roles which leads to fundamental ambiguities, and solution error. A major accomplishment of this study is that we have employed a state-of-the-art genetic-based global optimization algorithm called Differential Evolution (DE) that constrains the parameter search in such a way as to remove both the LS and PIT problems. To test the performance of the GoFFRA when DE is employed, we applied it to analyze simulated MGA datasets that we generated from known mixed exponential distributions. Moreover, we evaluated the GoFFRA/DE method by applying it to analyze actual MGAs derived from low-Earth orbiting lightning imaging sensor data; the actual MGA data were classified as either ground or cloud flash MGAs using National Lightning Detection Network[TM] (NLDN) data. Solution error plots are provided for both the simulations and actual data analyses.

Koshak, William

Lunar initial Nd-143/Nd-144 - Differential evolution of the lunar crust and mantle

The Sm-Nd evolution of Apollo 15 green glass is discussed. The ICE age (intercept with chondritic evolution) of 3.8 + or - 0.4 eons overlaps the range of reported (Ar-39)-(Ar-40) ages and implies a distinct source region for green glass, characterized by very low and unfractionated REE abundances. Evidence is presented that LINd (lunar initial Nd) is compatible with a 'chondritic'-type Nd isotopic evolution as observed in the Juvinas meteorite. This normalization is used to study the Sm-Nd system of various lunar rock types. The results obtained from a limited number of rocks clearly indicate differential Sm-Nd evolution for the lunar crust and mantle. High-Ti basalts returned by the Apollo 11 and 17 missions were derived from distinct source regions. The Nd-143 evolution in KREEP requires a source region which is clearly distinct from any mantle reservoir.

Lugmair, G. W.

Starspot evolution, differential rotation, and magnetic cycles in the chromospherically active binaries lambda andromedae, sigma Geminorum, II Pegasi, and V711 Tauri

We have analyzed 15-19 yr of photoelectric photometry, obtained manually and with automated telescopes, of the chromospherically active binaries lambda And, sigma Gem, II Peg, and V711 Tau. These observations let us identify individual dark starspots on the stellar surfaces from periodic dimming of the starlight, follow the evolution of these spots, and search for long-term cyclic changes in the properties of these starspots that might reveal magnetic cycles analogous to the Sun's 11 yr sunspot cycle. We developed a computer code to fit a simple two-spot model to our observed light curves that allows us to extract the most easily determinable and most reliable spot parameters from the light curves, i.e., spot longitudes and radii. We then used these measured properties to identify individual spots and to chart their life histories by constructing migration and amplitude curves. We identified and followed 11 spots in lambda And, 16 in sigma Gem, 12 in II Peg, and 15 in V711 Tau. Lifetimes of individual spots ranged from a few months to longer than 6 yr. Differential rotation coefficients, estimated from the observed range of spot rotation periods for each star and defined by equation (2), were 0.04 for lambda And, 0.038 for sigma Gem, 0.005 for II Peg, and 0.006 for V711 Tau, versus 0.19 for the Sun. We searched for cyclic changes in mean brightness, B-V color index, and spot rotation period as evidence for long-term cycles. Of these, long-term variability in mean brightness appears to offer the best evidence for such cycles in these four stars. Cycles of 11.1 yr for lambda And, 8.5 yr for sigma Gem, 11 yr for II Peg, and 16 yr V711 Tau are implied by these mean brightness changes. Cyclic changes in spot rotation period were found in lambda And and possibly II Peg. Errors in B-V were too large for any long-term changes to be detectable.

Henry, Gregory W.

Differential evolution of radio quiet and radio loud quasars

We have observed 40 optically selected high-redshift quasars with the Very Large Array (VLA) at 1515 MHz (20 cm). Three quasars are detected above our 3 sigma limit of 0.2 mJy. We review all available evidence on radio detections of optically selected quasars in terms of their ratio R of radio to optical luminosity. We find that the quasars ranked in the top 5-20 percent in R show strong evolution in their R distribution. We present two interpretations of this phenomenon. The first one poses that the R values decrease by a factor of around 100 from redshift 0.3 to 1.3. In the second interpretation, we consider that there are two populations of quasars, which we call radio silent and radio active, separated by R approximately 0.1. The radio-silent fraction of quasars increases from approximately 16% at redshift 0.3, to approximately 75% at redshift 1.3.

Schmidt, Maarten

Differential Evolution Optimization for Targeting Spacecraft Maneuver Plans

Previous analysis identified specific orbital parameters as being safer for conjunction avoidance for the TDRS fleet. With TDRS-9 being considered an at-risk spacecraft, a potential conjunction concern was raised should TDRS-9 fail while at a longitude of 12W. This document summarizes the analysis performed to identify if these specific orbital parameters could be targeted using the remaining drift-termination maneuvers for the relocation of TDRS-9 from 41W longitude to 12W longitude.

Manuever

Grainsize evolution and differential comminution in an experimental regolith

The comminution of planetary surfaces by exposure to continuous meteorite bombardment was simulated by impacting the same fragmental gabbro target 200 times. The role of comminution and in situ gardening of planetary regoliths was addressed. Mean grain size continuously decreased with increasing shot number. Initially it decreased linearly with accumulated energy, but at some stage comminution efficiency started to decrease gradually. Point counting techniques, aided by the electron microprobe for mineral identification, were performed on a number of comminution products. Bulk chemical analyses of specific grain size fractions were also carried out. The finest sizes ( 10 microns) display generally the strongest enrichment/depletion factors. Similar, if not exactly identical, trends are reported from lunar soils. It is, therefore, not necessarily correct to explain the chemical characteristics of various grain sizes via different admixtures of materials from distant source terrains. Differential comminution of local source rocks may be the dominating factor.

Horz, F.

Chemical differentiation, thermal evolution, and catastrophic overturn on Venus: Predictions and geologic observations

Observations from Magellan show that: (1) the surface of Venus is generally geologically young, (2) there is no evidence for widespread recent crustal spreading or subduction, (3) the crater population permits the hypothesis that the surface is in production, and (4) relatively few impact craters appear to be embayed by volcanic deposits suggesting that the volcanic flux has drastically decreased as a function of time. These observations have led to consideration of hypotheses suggesting that the geological history of Venus may have changed dramatically as a function of time due to general thermal evolution, and/or thermal and chemical evolution of a depleted mantle layer, perhaps punctuated by catastrophic overturn of upper layers or episodic plate tectonics. We have previously examined the geological implications of some of these models, and here we review the predictions associated with two periods of Venus history. Stationary thick lithosphere and depleted mantle layer, and development of regional to global development of regional to global instabilities, and compare these predictions to the geological characteristics of Venus revealed by Magellan.

Head, James W.

Re-Os Isotopic Constraints on the Chemical Evolution and Differentiation of the Martian Mantle

The (187)Re-187Os isotopic systematics of SNC meteorites, thought to be from Mars, provide valuable information regarding the chemical processes that affected the Martian mantle, particularly with regard to the relative abundances of highly siderophile elements (HSE). Previously published data (Birck and Allegre 1994, Brandon et al. 2000), and new data obtained since these studies, indicate that the HSE and Os isotopic composition of the Martian mantle was primarily set in its earliest differentiation history. If so, then these meteorites provide key constraints on the processes that lead to variation in HSE observed in not only Mars, but also Earth, the Moon and other rocky bodies in the Solar System. Processes that likely have an effect on the HSE budgets of terrestrial mantles include core formation, magma ocean crystallization, development of juvenile crust, and the addition of a late veneer. Each of these processes will result in different HSE variation and the isotopic composition of mantle materials and mantle derived lavas. Two observations on the SNC data to present provide a framework for which to test the importance of each of these processes. First, the concentrations of Re and Os in SNC meteorites indicate that they are derived from a mantle that has similar concentrations to the Earth's mantle. Such an observation is consistent with a model where a chondritic late veneer replenished the Earth and Martian mantles subsequent to core formation on each planet. Alternative models to explain this observation do exist, but will require additional data to test the limitations of each. Second, Re-Os isotopic results from Brandon et al. (2000) and new data presented here, show that initial yos correlates with variations in the short-lived systems of (182)Hf- (182)W and (142)Sm-142Nd in the SNC meteorites (epsilon(sub W) and epsilon(sub 142Nd)). These systematics require an isolation of mantle reservoirs during the earliest differentiation history of Mars, and subsequent inefficient mixing between these reservoirs. These data show that models for the origin of isotopic variation for SNC meteorites require at least two long-lived mantle reservoirs, and possibly three. The range in the projected present day gamma(sub Os) of these reservoirs is from -5.4+/-2.6, to +4+/-1. The isotopic systematics of these reservoirs may be linked to development of cumulate crystal piles in a Martian magma ocean and variable amounts of late stage intercumulus melt. In this model, fractional crystallization of olivine and possibly other phases with slightly subchondritic Re/Os, from a solidifying magma ocean, resulted in a lower Re/Os ratio early cumulates, and a resultant low gamma(sub Os). Later cumulates or evolved melts crystallized with higher Re/Os ratios to produce the mantle reservoir(s) with consequent higher gamma(sub Os). Crystallization of the Martian magma ocean followed earliest core formation, as indicated by the correlation of epsilon(sub W) with epsilon(sub 142Nd) and initial gamma(sub Os).

Brandon, Alan D.

Multiclass Reduced-Set Support Vector Machines

There are well-established methods for reducing the number of support vectors in a trained binary support vector machine, often with minimal impact on accuracy. We show how reduced-set methods can be applied to multiclass SVMs made up of several binary SVMs, with significantly better results than reducing each binary SVM independently. Our approach is based on Burges' approach that constructs each reduced-set vector as the pre-image of a vector in kernel space, but we extend this by recomputing the SVM weights and bias optimally using the original SVM objective function. This leads to greater accuracy for a binary reduced-set SVM, and also allows vectors to be 'shared' between multiple binary SVMs for greater multiclass accuracy with fewer reduced-set vectors. We also propose computing pre-images using differential evolution, which we have found to be more robust than gradient descent alone. We show experimental results on a variety of problems and find that this new approach is consistently better than previous multiclass reduced-set methods, sometimes with a dramatic difference.

reduced set methods