A Hybrid Genetic-Direct Search Algorithm for the Shape Optimization of Solid C-Frame Cross-Sections

2000 ◽  
Author(s):  
Ashraf O. Nassef ◽  
Hesham A. Hegazi ◽  
Sayed M. Metwalli
Keyword(s):  
Genetic Algorithms ◽  
Shape Optimization ◽  
Cross Section ◽  
Random Search ◽  
Direct Search ◽  
Search Method ◽  
Optimization Techniques ◽  
Hybrid Optimization ◽  
The Cross ◽  
Real Coded Genetic Algorithms

Abstract The hybridization of different optimization methods have been used to find the optimum solution of design problems. While random search techniques, such as genetic algorithms and simulated annealing, have a high probability of achieving global optimality, they usually arrive at a near optimal solution due to their random nature. On the other hand direct search methods are efficient optimization techniques but linger in local minima if the objective function is multi-modal. This paper presents the optimization of C-frame cross-section using a hybrid optimization algorithm. Real coded genetic algorithms are used as a random search method, while Nelder-Mead is used as a direct search method, where the result of the genetic algorithm search is used as the starting point of direct search. Traditionally, the cross-section of C-frame belonged to a set of primitive shapes, which included I, T, trapezoidal, circular and rectangular sections. The cross-sectional shape is represented by a non-uniform rational B-Splines (NURBS) in order to give it a kind of shape flexibility. The results showed that the use of Nelder-Mead with Real coded Genetic Algorithms has been very significant in improving the optimum shape of a solid C-frame cross-section subjected to a combined tension and bending stresses. The hybrid optimization method could be extended to more complex shape optimization problems.

Shape Optimization of NURBS Modeled 3D C-Frames Using Hybrid Genetic Algorithm

2002 ◽  
Author(s):  
Hesham A. Hegazi ◽  
Ashraf O. Nassef ◽  
Sayed M. Metwalli
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Shape Optimization ◽  
Cross Sections ◽  
Beam Theory ◽  
Direct Search ◽  
Search Method ◽  
Optimum Shape ◽  
Curved Beam ◽  
Real Coded Genetic Algorithms

The present paper introduces a new methodology for designing machine element shapes. The element is represented using non-uniform rational B-Spline (NURBS) in order to give it a form of shape flexibility. A special form of genetic algorithms known as real-coded genetic algorithms is used to conduct the search for the design objectives. Shape optimization of 3D C-frames are used as an application of the proposed methodology. The design parameters of these frames include the dimensions of their cross-sections, which should be chosen to withstand the applied loads and minimize the element’s overall weight. In a further development, the hybridization of different optimization methods has been used to find the optimum shape of the element. Real coded genetic algorithm is used as a random search method, while Nelder-Mead is used as a direct search method, where the result of the genetic algorithm search is used as the starting point of direct search. The results showed that the use of Nelder-Mead with Real coded Genetic Algorithms has been very significant in improving the optimum shape of a solid 3D C-frames subjected to a combined tension and bending stresses. The hybrid optimization method could be extended to more complex shape optimization problems. For the purpose of analysis, curved beam theory is applied on local cross-sections on the NURBS surface. A finite elements analysis was conducted on SDRC-IDEAS for verifying the results obtained using the curved beam theory.

Topology Optimization of a Compliant Gripper Using Hybrid Simulated Annealing and Direct Search

2003 ◽  
Author(s):  
Mohamed M. Shalaby ◽  
Hesham A. Hegazi ◽  
Ashraf O. Nassef ◽  
Sayed M. Metwalli
Keyword(s):  
Simulated Annealing ◽  
Topology Optimization ◽  
Simplex Method ◽  
Compliant Mechanism ◽  
Random Search ◽  
Optimization Technique ◽  
Direct Search ◽  
Search Method ◽  
Hybrid Optimization ◽  
Topology Optimization Problem

The present work introduces a new methodology for solving the topology optimization problem of a compliant gripper. A hybrid optimization technique is developed using simulated annealing as a random search method, while the simplex method (Nelder-Mead) is used as a direct search method. A new modified technique of motion from one search point to another based on the discrete nature of adding and/or removing a structural member is proposed. The traditional continuous simulated annealing technique is used to find the members’ heights. A discrete uni-variant search method is adopted following the simulated annealing and before the simplex method. This corresponds to about 14% of the number used in the old method and in the previous work in the literature, and about 86% of the optimization time is saved. The optimum design of a compliant mechanism is conducted for maximum flexibility and stiffness using the developed hybrid optimization technique.

Accuracy and Fitting-Time Minimization in the Reverse Engineering of Prismatic Features

1999 ◽  
Author(s):  
Ashraf O. Nassef ◽  
Ayman M. Ashraf ◽  
Sayed M. Metwalli
Keyword(s):  
Genetic Algorithms ◽  
Reverse Engineering ◽  
Three Dimensional ◽  
Direct Search ◽  
Search Method ◽  
Direct Search Method ◽  
Simplex Search ◽  
Time Minimization ◽  
Engineering Models ◽  
Real Coded Genetic Algorithms

Abstract In many years of industry, it is desirable to create geometric models of existing objects for which no such models are available. Reverse engineering transforms real parts into engineering models and concepts. This paper presents an approach for fitting three-dimensional prismatic features using real-coded genetic algorithms. The approach is compared with the Nelder Meade Simplex search method as a variant of the traditional direct search method. The results show the superiority of the real-coded genetic algorithms over the traditional direct search method with respect to accuracy. The paper also concerns with the minimization of the fitting time through minimizing the number of objective function evaluations. This is done by optimizing the genetic algorithms parameters such as the number of times for which the various cross-overs and mutations should be applied.

Design of C-Frames Using Real-Coded Genetic Optimization Algorithms and NURBS

1999 ◽  
Author(s):  
Ashraf O. Nassef ◽  
Hesham A. Hegazi ◽  
Sayed M. Metwalli
Keyword(s):  
Genetic Algorithms ◽  
Cross Section ◽  
Cross Sections ◽  
Design Parameters ◽  
Binary Representation ◽  
Cross Sectional ◽  
Search Spaces ◽  
The Cross ◽  
Sectional Shape ◽  
Real Coded Genetic Algorithms

Abstract C-frames constitute a large portion of machine tools that are currently used in industry. Examples of these frames include drilling machines, presses, punching and stamping machines, clamps, hooks, etc. The design parameters of these frames include the dimensions of their cross-sections, which should be chosen to withstand the applied loads and minimize the element’s overall weight. Traditionally, the cross-section of C-frame belonged to a set of primitive shapes, which included I, T, trapezoidal and rectangular sections. This paper introduces a new methodology for designing the frame’s cross-section. The cross-sectional shape is represented using non-uniform rational B-Spline (NURBS) in order to give it a form of shape flexibility. A special form of genetic algorithms known as real-coded genetic algorithms is used to conduct the search for the design objectives. Real-coded genetic algorithms are known to outperform the simple binary representation genetic algorithms when dealing with continuous search spaces. The results showed that the optimal shape was a semi I/T-section with the material bulk related to the applied load.

Shape Optimization of a Camoid Follower Surface

2008 ◽  
Author(s):  
Karim A. Aguib ◽  
Keith A. Hekman ◽  
Ashraf O. Nassef
Keyword(s):  
Genetic Algorithms ◽  
Shape Optimization ◽  
Three Dimensional ◽  
Characteristic Surface ◽  
Design Constraints ◽  
B Splines ◽  
Surface Interpolation ◽  
Specific Objective ◽  
Interpolation Technique ◽  
Real Coded Genetic Algorithms

Camoids are three dimensional cams that can produce more complex follower output than plain disc cams. A camoid follower motion is described by a surface rather than a curve. The camoid profile can be directly synthesized once the follower surface is fully described. To define a camoid follower motion surface it is required that the surface pass by all predefined constraints. Constraints can be follower position, velocity and acceleration. These design constraints are scattered all along the camoid follower surface. Hence a fitting technique is needed to satisfy these constraints which include position and its derivatives (velocity and acceleration). Furthermore if the fitting function can be of a parametric nature, then it would be possible to optimize the follower surface to obtain better performance according to a specific objective. Previous research has established a method to fit camoid follower surface positions, but did not tackle the satisfaction of derivative constraints. This paper presents a method for defining a camoid follower characteristic surface B-Splines on two steps first synthesizing the sectional cam curves then using a surface interpolation technique to generate the follower characteristic surface. The fitting technique is parametric in nature which allows for its optimization. Real coded Genetic algorithms are used to optimize the parameters of the surface to meet a specified objective function. A demonstration problem to illustrate the suggested methodology is presented.

Thermoacoustic Shape Optimization of a Subsonic Nozzle

2013 ◽  
Author(s):  
Alexis Giauque ◽  
Maxime Huet ◽  
Franck Clero ◽  
Sébastien Ducruix ◽  
Franck Richecoeur
Keyword(s):  
Acoustic Emission ◽  
Shape Optimization ◽  
Cross Section ◽  
Emission Factor ◽  
Source Term ◽  
Combustion Noise ◽  
Noise Emission ◽  
Cross Section Area ◽  
Section Area ◽  
The Cross

Indirect combustion noise originates from the acceleration of non-uniform temperature or high vorticity regions when convected through a nozzle or a turbine. In an recent contribution (Giauque et al., JEGTP, 2012), the authors have presented an analytical thermoacoustic model providing the indirect combustion noise generated by a subcritical nozzle when forced with entropy waves. This model explicitly takes into account the effect of the local changes in the cross-section area along the configuration of interest. In this article, the authors introduce this model into an optimization procedure in order to minimize or maximize the thermoacoustic noise emitted by arbitrary shaped nozzles operating under subsonic conditions. Each component of the complete algorithm is described in details. The evolution of the cross-section changes are introduced using Beziers splines which provide the necessary freedom to actually achieve arbitrary shapes. Beziers poles coordinates constitute the parameters defining the geometry of a given individual nozzle. Starting from a population of nozzles of random shapes, it is shown that a specifically designed genetic optimization algorithm coupled with the analytical model converges at will toward a quieter or noisier population. As already described by Bloy (JFM, 1979), results therefore confirm the significant dependence of the indirect combustion noise with respect to the shape of the nozzle, even when the operating regime is kept constant. It appears that the quietest nozzle profile evolves almost linearly along its converging and diverging sections leading to a square evolution of the cross-section area. Providing insight in the underlying physical reason leading to the difference in noise emission between two extreme individuals, the integral value of the source term of the equation describing the behavior of the acoustic pressure of the nozzle is considered. It is shown that its evolution with the frequency can be related to the global acoustic emission. Strong evidence suggest that the noise emission increases as the source term in the converging and diverging parts less compensate each other. The main result of this article is the definition and proposition of an Acoustic Emission Factor which can be used as a surrogate to the complex determination of the exact acoustic levels in the nozzle for the thermoacoustic shape optimization of nozzle flows. This Acoustic Emission Factor, much faster to compute, only involves the knowledge of the evolution of the cross-section area as well as the inlet thermodynamic and velocity characteristics to be computed.

scholarly journals On Generating Optimal Signal Probabilities for Random Tests: A Genetic Approach

VLSI Design ◽  
1996 ◽  
Vol 4 (3) ◽  
pp. 207-215 ◽  
Author(s):  
M. Srinivas ◽  
L. M. Patnaik
Keyword(s):  
Genetic Algorithms ◽  
Cost Function ◽  
Gradient Descent ◽  
Random Search ◽  
Search Space ◽  
Optimization Techniques ◽  
Gradient Descent Methods ◽  
Test Vectors ◽  
The Cost ◽  
Optimal Signal

Genetic Algorithms are robust search and optimization techniques. A Genetic Algorithm based approach for determining the optimal input distributions for generating random test vectors is proposed in the paper. A cost function based on the COP testability measure for determining the efficacy of the input distributions is discussed. A brief overview of Genetic Algorithms (GAs) and the specific details of our implementation are described. Experimental results based on ISCAS-85 benchmark circuits are presented. The performance of our GAbased approach is compared with previous results. While the GA generates more efficient input distributions than the previous methods which are based on gradient descent search, the overheads of the GA in computing the input distributions are larger.To account for the relatively quick convergence of the gradient descent methods, we analyze the landscape of the COP-based cost function. We prove that the cost function is unimodal in the search space. This feature makes the cost function amenable to optimization by gradient-descent techniques as compared to random search methods such as Genetic Algorithms.

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