Keywords: truss structures, size optimization, shape optimization, real-coded genetic algorithm, adaptive penalty function, adaptive tournament selection, Gaussian mutation operator, integrated force method.

In this paper, we propose an adaptive real-coded genetic algorithm (ARCGA), for size and shape optimization of planar truss structures under stress, displacement and buckling constraints. In order to overcome the difficulties of using a binary representation, such as time consuming coding and decoding processes and long binary strings of design variables, real parameter strings are used to represent the individuals of the population.

In the current study, a mutation based approach is considered in the reproduction stage, and a Gaussian mutation operator [1] is used in an adaptive way to create two mutation operators of the proposed ARCGA. The standard deviation which is needed for each reproduction operator is adaptively adjusted by the population itself; and a global search in the initial iterations is considered, which gradually leads to a local tuning in the last iterations of the optimization process. For handling the constraints, an adaptive penalty function is proposed in order to reduce the disadvantages of using static penalty constants; for the selection stage, the tournament selection operator is used with an adaptive tournament size in order to adjust the balance between exploration and exploitation; and for structural analysis of the truss structures, the integrated force method (IFM) [2] is employed.

In order to investigate the performance of the proposed method, three examples of planar truss structures, including size and shape optimization examples, are optimized using the ARCGA. The topology of each example is assumed to be fixed. The optimized examples are typical standard optimization problems which are frequently used in the literature. To evaluate the reliability of the algorithm in each example, the ARCGA is executed 50 times and the best, worst, mean, and standard deviation of the results are all reported. The optimum designs found by the ARCGA are compared with the recently reported results in the literature. The results indicate the efficiency, reliability and robustness of the proposed ARCGA.

1

S. Tsutsui, D.E. Goldberg, "Search space boundary extension method in real-coded genetic algorithms", Information Sciences, 133(3-4), 229-247, 2001. doi:10.1016/S0020-0255(01)00087-1

2

S.N. Patnike, L. Berke, R.H. Gallagher, "Integrated force method versus displacement method for finite element analysis", Computers and Structures, 38(4), 377-407, 1991. doi:10.1016/0045-7949(91)90037-M

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