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NASA NTRS2000

Analytical and Computational Aspects of Collaborative Optimization

Bilevel problem formulations have received considerable attention as an approach to multidisciplinary optimization in engineering. We examine the analytical and computational properties of one such approach, collaborative optimization. The resulting system-level optimization problems suffer from inherent computational difficulties due to the bilevel nature of the method. Most notably, it is impossible to characterize and hence identify solutions of the system-level problems because the standard first-order conditions for solutions of constrained optimization problems do not hold. The analytical features of the system-level problem make it difficult to apply conventional nonlinear programming algorithms. Simple examples illustrate the analysis and the algorithmic consequences for optimization methods. We conclude with additional observations on the practical implications of the analytical and computational properties of collaborative optimization.

Alexandrov, Natalia M.↗

NASA NTRS2000

An Enhanced Multi-Objective Optimization Technique for Comprehensive Aerospace Design

An enhanced multiobjective formulation technique, capable of emphasizing specific objective functions during the optimization process, has been demonstrated on a complex multidisciplinary design application. The Kreisselmeier-Steinhauser (K-S) function approach, which has been used successfully in a variety of multiobjective optimization problems, has been modified using weight factors which enables the designer to emphasize specific design objectives during the optimization process. The technique has been implemented in two distinctively different problems. The first is a classical three bar truss problem and the second is a high-speed aircraft (a doubly swept wing-body configuration) application in which the multiobjective optimization procedure simultaneously minimizes the sonic boom and the drag-to-lift ratio (C(sub D)/C(sub L)) of the aircraft while maintaining the lift coefficient within prescribed limits. The results are compared with those of an equally weighted K-S multiobjective optimization. Results demonstrate the effectiveness of the enhanced multiobjective optimization procedure.

Chattopadhyay, Aditi↗

NASA NTRS2000

Global Design Optimization for Aerodynamics and Rocket Propulsion Components

Modern computational and experimental tools for aerodynamics and propulsion applications have matured to a stage where they can provide substantial insight into engineering processes involving fluid flows, and can be fruitfully utilized to help improve the design of practical devices. In particular, rapid and continuous development in aerospace engineering demands that new design concepts be regularly proposed to meet goals for increased performance, robustness and safety while concurrently decreasing cost. To date, the majority of the effort in design optimization of fluid dynamics has relied on gradient-based search algorithms. Global optimization methods can utilize the information collected from various sources and by different tools. These methods offer multi-criterion optimization, handle the existence of multiple design points and trade-offs via insight into the entire design space, can easily perform tasks in parallel, and are often effective in filtering the noise intrinsic to numerical and experimental data. However, a successful application of the global optimization method needs to address issues related to data requirements with an increase in the number of design variables, and methods for predicting the model performance. In this article, we review recent progress made in establishing suitable global optimization techniques employing neural network and polynomial-based response surface methodologies. Issues addressed include techniques for construction of the response surface, design of experiment techniques for supplying information in an economical manner, optimization procedures and multi-level techniques, and assessment of relative performance between polynomials and neural networks. Examples drawn from wing aerodynamics, turbulent diffuser flows, gas-gas injectors, and supersonic turbines are employed to help demonstrate the issues involved in an engineering design context. Both the usefulness of the existing knowledge to aid current design practices and the need for future research are identified.

Shyy, Wei↗

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↗

NASA NTRS1995

Optimal Trajectories and Control Strategies for the Helicopter in One-Engine-Inoperative Terminal-Area Operations

Engine failure represents a major safety concern to helicopter operations, especially in the critical flight phases of takeoff and landing from/to small, confined areas. As a result, the JAA and FAA both certificate a transport helicopter as either Category-A or Category-B according to the ability to continue its operations following engine failures. A Category-B helicopter must be able to land safely in the event of one or all engine failures. There is no requirement, however, for continued flight capability. In contrast, Category-A certification, which applies to multi-engine transport helicopters with independent engine systems, requires that they continue the flight with one engine inoperative (OEI). These stringent requirements, while permitting its operations from rooftops and oil rigs and flight to areas where no emergency landing sites are available, restrict the payload of a Category-A transport helicopter to a value safe for continued flight as well as for landing with one engine inoperative. The current certification process involves extensive flight tests, which are potentially dangerous, costly, and time consuming. These tests require the pilot to simulate engine failures at increasingly critical conditions, Flight manuals based on these tests tend to provide very conservative recommendations with regard to maximum takeoff weight or required runway length. There are very few theoretical studies on this subject to identify the fundamental parameters and tradeoff factors involved. Furthermore, a capability for real-time generation of OEI optimal trajectories is very desirable for providing timely cockpit display guidance to assist the pilot in reducing his workload and to increase safety in a consistent and reliable manner. A joint research program involving NASA Ames Research Center, the FAA, and the University of Minnesota is being conducted to determine OEI optimal control strategies and the associated optimal,trajectories for continued takeoff (CTO), rejected takeoff (RTO), balked landing (BL), and continued landing (CL) for a twin engine helicopter in both VTOL and STOL terminal-area operations. This proposed paper will present the problem formulation, the optimal control solution methods, and the key results of the trajectory optimization studies for both STOL and VTOL OEI operations. In addition, new results concerning the recently developed methodology, which enable a real-time generation of optimal OEI trajectories, will be presented in the paper. This new real-time capability was developed to support the second piloted simulator investigation on cockpit displays for Category-A operations being scheduled for the NASA Ames Vertical Motion Simulator in June-August of 1995. The first VMS simulation was conducted in 1994 and reported.

Chen, Robert T. N.↗

NASA NTRS2002

Options for Robust Airfoil Optimization under Uncertainty

A robust optimization method is developed to overcome point-optimization at the sampled design points. This method combines the best features from several preliminary methods proposed by the authors and their colleagues. The robust airfoil shape optimization is a direct method for drag reduction over a given range of operating conditions and has three advantages: (1) it prevents severe degradation in the off-design performance by using a smart descent direction in each optimization iteration, (2) it uses a large number of spline control points as design variables yet the resulting airfoil shape does not need to be smoothed, and (3) it allows the user to make a tradeoff between the level of optimization and the amount of computing time consumed. For illustration purposes, the robust optimization method is used to solve a lift-constrained drag minimization problem for a two-dimensional (2-D) airfoil in Euler flow with 20 geometric design variables.

Padula, Sharon L.↗

NASA NTRS2003

Tractable Pareto Optimization of Temporal Preferences

This paper focuses on temporal constraint problems where the objective is to optimize a set of local preferences for when events occur. In previous work, a subclass of these problems has been formalized as a generalization of Temporal CSPs, and a tractable strategy for optimization has been proposed, where global optimality is defined as maximizing the minimum of the component preference values. This criterion for optimality, which we call 'Weakest Link Optimization' (WLO), is known to have limited practical usefulness because solutions are compared only on the basis of their worst value; thus, there is no requirement to improve the other values. To address this limitation, we introduce a new algorithm that re-applies WLO iteratively in a way that leads to improvement of all the values. We show the value of this strategy by proving that, with suitable preference functions, the resulting solutions are Pareto Optimal.

Morris, Robert↗

NASA NTRS2003

Aerospace Applications of Optimization under Uncertainty

The Multidisciplinary Optimization (MDO) Branch at NASA Langley Research Center develops new methods and investigates opportunities for applying optimization to aerospace vehicle design. This paper describes MDO Branch experiences with three applications of optimization under uncertainty: (1) improved impact dynamics for airframes, (2) transonic airfoil optimization for low drag, and (3) coupled aerodynamic/structures optimization of a 3-D wing. For each case, a brief overview of the problem and references to previous publications are provided. The three cases are aerospace examples of the challenges and opportunities presented by optimization under uncertainty. The present paper will illustrate a variety of needs for this technology, summarize promising methods, and uncover fruitful areas for new research.

Padula, Sharon↗

NASA NTRS2004

Adaptive Multi-Agent Systems for Constrained Optimization

Product Distribution (PD) theory is a new framework for analyzing and controlling distributed systems. Here we demonstrate its use for distributed stochastic optimization. First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint state of the agents. When the game in question is a team game with constraints, that equilibrium optimizes the expected value of the team game utility, subject to those constraints. The updating of the Lagrange parameters in the Lagrangian can be viewed as a form of automated annealing, that focuses the MAS more and more on the optimal pure strategy. This provides a simple way to map the solution of any constrained optimization problem onto the equilibrium of a Multi-Agent System (MAS). We present computer experiments involving both the Queen s problem and K-SAT validating the predictions of PD theory and its use for off-the-shelf distributed adaptive optimization.

Macready, William↗

NASA NTRS2003

Search-based optimization

The problem of determining the minimum cost hypothetical ancestral sequences for a given cladogram is known to be NP-complete (Wang and Jiang, 1994). Traditionally, point estimations of hypothetical ancestral sequences have been used to gain heuristic, upper bounds on cladogram cost. These include procedures with such diverse approaches as non-additive optimization of multiple sequence alignment, direct optimization (Wheeler, 1996), and fixed-state character optimization (Wheeler, 1999). A method is proposed here which, by extending fixed-state character optimization, replaces the estimation process with a search. This form of optimization examines a diversity of potential state solutions for cost-efficient hypothetical ancestral sequences and can result in greatly more parsimonious cladograms. Additionally, such an approach can be applied to other NP-complete phylogenetic optimization problems such as genomic break-point analysis. c2003 The Willi Hennig Society. Published by Elsevier Science (USA). All rights reserved.

Non-NASA Center↗

NASA NTRS2004

A Subsonic Aircraft Design Optimization With Neural Network and Regression Approximators

The Flight-Optimization-System (FLOPS) code encountered difficulty in analyzing a subsonic aircraft. The limitation made the design optimization problematic. The deficiencies have been alleviated through use of neural network and regression approximations. The insight gained from using the approximators is discussed in this paper. The FLOPS code is reviewed. Analysis models are developed and validated for each approximator. The regression method appears to hug the data points, while the neural network approximation follows a mean path. For an analysis cycle, the approximate model required milliseconds of central processing unit (CPU) time versus seconds by the FLOPS code. Performance of the approximators was satisfactory for aircraft analysis. A design optimization capability has been created by coupling the derived analyzers to the optimization test bed CometBoards. The approximators were efficient reanalysis tools in the aircraft design optimization. Instability encountered in the FLOPS analyzer was eliminated. The convergence characteristics were improved for the design optimization. The CPU time required to calculate the optimum solution, measured in hours with the FLOPS code was reduced to minutes with the neural network approximation and to seconds with the regression method. Generation of the approximators required the manipulation of a very large quantity of data. Design sensitivity with respect to the bounds of aircraft constraints is easily generated.

Patnaik, Surya N.↗

NASA NTRS2004

Optimal Synthesis of Compliant Mechanisms using Subdivision and Commercial FEA (DETC2004-57497)

The field of distributed-compliance mechanisms has seen significant work in developing suitable topology optimization tools for their design. These optimal design tools have grown out of the techniques of structural optimization. This paper will build on the previous work in topology optimization and compliant mechanism design by proposing an alternative design space parameterization through control points and adding another step to the process, that of subdivision. The control points allow a specific design to be represented as a solid model during the optimization process. The process of subdivision creates an additional number of control points that help smooth the surface (for example a C(sup 2) continuous surface depending on the method of subdivision chosen) creating a manufacturable design free of some traditional numerical instabilities. Note that these additional control points do not add to the number of design parameters. This alternative parameterization and description as a solid model effectively and completely separates the design variables from the analysis variables during the optimization procedure. The motivation behind this work is to create an automated design tool from task definition to functional prototype created on a CNC or rapid-prototype machine. This paper will describe the proposed compliant mechanism design process and will demonstrate the procedure on several examples common in the literature.

Hull, Patrick V.↗

NASA NTRS2005

Multidisciplinary Multiobjective Optimal Design for Turbomachinery Using Evolutionary Algorithm

This report summarizes Dr. Lian s efforts toward developing a robust and efficient tool for multidisciplinary and multi-objective optimal design for turbomachinery using evolutionary algorithms. This work consisted of two stages. The first stage (from July 2003 to June 2004) Dr. Lian focused on building essential capabilities required for the project. More specifically, Dr. Lian worked on two subjects: an enhanced genetic algorithm (GA) and an integrated optimization system with a GA and a surrogate model. The second stage (from July 2004 to February 2005) Dr. Lian formulated aerodynamic optimization and structural optimization into a multi-objective optimization problem and performed multidisciplinary and multi-objective optimizations on a transonic compressor blade based on the proposed model. Dr. Lian s numerical results showed that the proposed approach can effectively reduce the blade weight and increase the stage pressure ratio in an efficient manner. In addition, the new design was structurally safer than the original design. Five conference papers and three journal papers were published on this topic by Dr. Lian.

Source record↗

NASA NTRS2006

In-Space Radiator Shape Optimization using Genetic Algorithms

Future space exploration missions will require the development of more advanced in-space radiators. These radiators should be highly efficient and lightweight, deployable heat rejection systems. Typical radiators for in-space heat mitigation commonly comprise a substantial portion of the total vehicle mass. A small mass savings of even 5-10% can greatly improve vehicle performance. The objective of this paper is to present the development of detailed tools for the analysis and design of in-space radiators using evolutionary computation techniques. The optimality criterion is defined as a two-dimensional radiator with a shape demonstrating the smallest mass for the greatest overall heat transfer, thus the end result is a set of highly functional radiator designs. This cross-disciplinary work combines topology optimization and thermal analysis design by means of a genetic algorithm The proposed design tool consists of the following steps; design parameterization based on the exterior boundary of the radiator, objective function definition (mass minimization and heat loss maximization), objective function evaluation via finite element analysis (thermal radiation analysis) and optimization based on evolutionary algorithms. The radiator design problem is defined as follows: the input force is a driving temperature and the output reaction is heat loss. Appropriate modeling of the space environment is added to capture its effect on the radiator. The design parameters chosen for this radiator shape optimization problem fall into two classes, variable height along the width of the radiator and a spline curve defining the -material boundary of the radiator. The implementation of multiple design parameter schemes allows the user to have more confidence in the radiator optimization tool upon demonstration of convergence between the two design parameter schemes. This tool easily allows the user to manipulate the driving temperature regions thus permitting detailed design of in-space radiators for unique situations. Preliminary results indicate an optimized shape following that of the temperature distribution regions in the "cooler" portions of the radiator. The results closely follow the expected radiator shape.

Hull, Patrick V.↗

NASA NTRS2006

Orbit design and optimization based on global telecommunication performance metrics

The orbit selection of telecommunications orbiters is one of the critical design processes and should be guided by global telecom performance metrics and mission-specific constraints. In order to aid the orbit selection, we have coupled the Telecom Orbit Analysis and Simulation Tool (TOAST) with genetic optimization algorithms. As a demonstration, we have applied the developed tool to select an optimal orbit for general Mars telecommunications orbiters with the constraint of being a frozen orbit. While a typical optimization goal is to minimize tele-communications down time, several relevant performance metrics are examined: 1) area-weighted average gap time, 2) global maximum of local maximum gap time, 3) global maximum of local minimum gap time. Optimal solutions are found with each of the metrics. Common and different features among the optimal solutions as well as the advantage and disadvantage of each metric are presented. The optimal solutions are compared with several candidate orbits that were considered during the development of Mars Telecommunications Orbiter.

genetic algorithms↗

NASA NTRS2006

Aerospace Applications of Optimization under Uncertainty

Padula, Sharon↗

NASA NTRS2007

Translator for Optimizing Fluid-Handling Components

A software interface has been devised to facilitate optimization of the shapes of valves, elbows, fittings, and other components used to handle fluids under extreme conditions. This software interface translates data files generated by PLOT3D (a NASA grid-based plotting-and- data-display program) and by computational fluid dynamics (CFD) software into a format in which the files can be read by Sculptor, which is a shape-deformation- and-optimization program. Sculptor enables the user to interactively, smoothly, and arbitrarily deform the surfaces and volumes in two- and three-dimensional CFD models. Sculptor also includes design-optimization algorithms that can be used in conjunction with the arbitrary-shape-deformation components to perform automatic shape optimization. In the optimization process, the output of the CFD software is used as feedback while the optimizer strives to satisfy design criteria that could include, for example, improved values of pressure loss, velocity, flow quality, mass flow, etc.

Landon, Mark↗

NASA NTRS2010

Optimization Testbed Cometboards Extended into Stochastic Domain

COMparative Evaluation Testbed of Optimization and Analysis Routines for the Design of Structures (CometBoards) is a multidisciplinary design optimization software. It was originally developed for deterministic calculation. It has now been extended into the stochastic domain for structural design problems. For deterministic problems, CometBoards is introduced through its subproblem solution strategy as well as the approximation concept in optimization. In the stochastic domain, a design is formulated as a function of the risk or reliability. Optimum solution including the weight of a structure, is also obtained as a function of reliability. Weight versus reliability traced out an inverted-S-shaped graph. The center of the graph corresponded to 50 percent probability of success, or one failure in two samples. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure that corresponded to unity for reliability. Weight can be reduced to a small value for the most failure-prone design with a compromised reliability approaching zero. The stochastic design optimization (SDO) capability for an industrial problem was obtained by combining three codes: MSC/Nastran code was the deterministic analysis tool, fast probabilistic integrator, or the FPI module of the NESSUS software, was the probabilistic calculator, and CometBoards became the optimizer. The SDO capability requires a finite element structural model, a material model, a load model, and a design model. The stochastic optimization concept is illustrated considering an academic example and a real-life airframe component made of metallic and composite materials.

Patnaik, Surya N.↗