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All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

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.↗
NASA NTRS2006

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↗
NASA NTRS2002

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.↗
NASA NTRS2002

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.↗
NASA NTRS2002

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.↗
NASA NTRS2007

Evolutionary Optimization of a Geometrically Refined Truss

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.

Hull, P. V.↗
NASA NTRS2005

Evolutionary optimization of a Genetically Refined Truss

Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This paper will present a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: Genetic Algorithms and Differential Evolution to successfully optimize a benchmark structural optimization problem. An non-traditional solution to the benchmark problem is presented in this paper, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.

Hull, Patrick V.↗
NASA NTRS2004

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.↗
NASA NTRS2004

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.↗
NASA NTRS2004

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.↗
NASA NTRS2011

Evolutionary Computational Methods for Identifying Emergent Behavior in Autonomous Systems

A technique based on Evolutionary Computational Methods (ECMs) was developed that allows for the automated optimization of complex computationally modeled systems, such as autonomous systems. The primary technology, which enables the ECM to find optimal solutions in complex search spaces, derives from evolutionary algorithms such as the genetic algorithm and differential evolution. These methods are based on biological processes, particularly genetics, and define an iterative process that evolves parameter sets into an optimum. Evolutionary computation is a method that operates on a population of existing computational-based engineering models (or simulators) and competes them using biologically inspired genetic operators on large parallel cluster computers. The result is the ability to automatically find design optimizations and trades, and thereby greatly amplify the role of the system engineer.

Terrile, Richard J.↗
NASA NTRS2006

Towards Robust Designs Via Multiple-Objective Optimization Methods

Fabricating and operating complex systems involves dealing with uncertainty in the relevant variables. In the case of aircraft, flow conditions are subject to change during operation. Efficiency and engine noise may be different from the expected values because of manufacturing tolerances and normal wear and tear. Engine components may have a shorter life than expected because of manufacturing tolerances. In spite of the important effect of operating- and manufacturing-uncertainty on the performance and expected life of the component or system, traditional aerodynamic shape optimization has focused on obtaining the best design given a set of deterministic flow conditions. Clearly it is important to both maintain near-optimal performance levels at off-design operating conditions, and, ensure that performance does not degrade appreciably when the component shape differs from the optimal shape due to manufacturing tolerances and normal wear and tear. These requirements naturally lead to the idea of robust optimal design wherein the concept of robustness to various perturbations is built into the design optimization procedure. The basic ideas involved in robust optimal design will be included in this lecture. The imposition of the additional requirement of robustness results in a multiple-objective optimization problem requiring appropriate solution procedures. Typically the costs associated with multiple-objective optimization are substantial. Therefore efficient multiple-objective optimization procedures are crucial to the rapid deployment of the principles of robust design in industry. Hence the companion set of lecture notes (Single- and Multiple-Objective Optimization with Differential Evolution and Neural Networks ) deals with methodology for solving multiple-objective Optimization problems efficiently, reliably and with little user intervention. Applications of the methodologies presented in the companion lecture to robust design will be included here. The evolutionary method (DE) is first used to solve a relatively difficult problem in extended surface heat transfer wherein optimal fin geometries are obtained for different safe operating base temperatures. The objective of maximizing the safe operating base temperature range is in direct conflict with the objective of maximizing fin heat transfer. This problem is a good example of achieving robustness in the context of changing operating conditions. The evolutionary method is then used to design a turbine airfoil; the two objectives being reduced sensitivity of the pressure distribution to small changes in the airfoil shape and the maximization of the trailing edge wedge angle with the consequent increase in airfoil thickness and strength. This is a relevant example of achieving robustness to manufacturing tolerances and wear and tear in the presence of other objectives.

Man Mohan, Rai↗
NASA NTRS2013

Experiments with a Parallel Multi-Objective Evolutionary Algorithm for Scheduling

Evolutionary multi-objective algorithms have great potential for scheduling in those situations where tradeoffs among competing objectives represent a key requirement. One challenge, however, is runtime performance, as a consequence of evolving not just a single schedule, but an entire population, while attempting to sample the Pareto frontier as accurately and uniformly as possible. The growing availability of multi-core processors in end user workstations, and even laptops, has raised the question of the extent to which such hardware can be used to speed up evolutionary algorithms. In this paper we report on early experiments in parallelizing a Generalized Differential Evolution (GDE) algorithm for scheduling long-range activities on NASA's Deep Space Network. Initial results show that significant speedups can be achieved, but that performance does not necessarily improve as more cores are utilized. We describe our preliminary results and some initial suggestions from parallelizing the GDE algorithm. Directions for future work are outlined.

scheduling↗