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PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Design of Frames using Genetic Algorithms, Force Method and Graph Theory
A. Kaveh and M. Abdie
Department of Civil Engineering, Iran University of Science and Technology, Tehran, Iran
A. Kaveh, M. Abdie, "Design of Frames using Genetic Algorithms, Force Method and Graph Theory", in B.H.V. Topping, (Editor), "Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 130, 2003. doi:10.4203/ccp.77.130
Keywords: genetic algorithm, structural optimization, frames, force method, analysis, cycle basis.
In optimal design, the members should be proportionally designed to reduce the usage of material and cost of the structure. Optimization can be categorized as sizing optimization, shape optimization, topology optimization and layout optimization. Methods for optimization are classified as mathematical programming methods and heuristic search approaches. The latter may employ neural networks, simulated annealing or genetic algorithms.
In this paper sizing optimization of frames employing Genetic algorithm (GA) is studied. In the process of optimal design, analysis should be performed several times. Here, the force method is employed for the analysis. The advantage of using this method lies in the fact that the matrices corresponding to the particular and complementary solutions ( and matrices) are formed independently of the mechanical properties of members. These matrices are constructed using concepts from graph theory. is formed using a shortest route tree having minimum number of non-zero entries. is formed on a suboptimal cycle basis leading to highly sparse flexibility matrix [1,2]. These matrices are employed several times in the process of a sequential analyses, where the number of equations solved is the same as the degree of static indeterminacy in place of the total degrees of freedom, thus increasing the speed of optimization.
Early papers on structural optimization using GA are due to Goldberg and Samtani , Jenkins , Adeli and Cheng , Rajeev and Krishnamoorthy , Erbatur et al , Kameshki and Saka  and Kaveh and Kalatjari [9,10]. Many others have published papers improving the results and increasing the speed of GA in the last decade. Here, some of the features of the method of Reference  is extended for optimal design of frames.
In this paper, three different fitness functions are used and it is shown that the fitness function of type I has a better convergence rate. The use of different crossovers is also examined.
Though the examples are chosen from planar frames, however, the present method can equally be applied to space frames. In this method, the matrices B0, and can be modified to make the method applicable to any other space structures.
In the example presented, increasing the population size reduces the number of iteration cycles required for convergence, and vice versa.
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