Keywords: structural optimization, genetic algorithm, neural networks, approximation concepts.

Optimum design of structures with stress and displacement constraints is achieved by a modified genetic algorithm (GA). The GA has the capability of finding the optimal solution with discrete design variables and the method does not require the derivatives of the functions under consideration. The probabilistic nature of the standard GA makes the convergence of the method slow thus the computational cost of the large scaled structures is very high. To reduce the computational burden of the standard GA, the optimization approach is enhanced with two different aspects. The first improvement is achieved by modifying the standard GA. The method is referred to as virtual sub-population method (VSP). In this method an initial population with a small number of individuals is selected. The number of population is much smaller than the standard GA. With the reduced initial population, all the necessary operations of the standard GA are carried out and the optimal solution is achieved. As the size of the population is not adequate, the method converges to a pre-matured solution. Now the best solution is chosen and copied many times to create a new population. In the new population, about half of the points are chosen as the repeated best solution of the previous results. The remaining members of the population are selected randomly. Again the process of optimization is repeated by standard GA with a reduced population to achieve a new solution. The process of creating the reduced population with repeated individuals in each iteration is continued until the method converges. The numerical results show that the computational work by VSP is less than the standard GA. This is basically due to the fact that in each iteration, a smaller population is employed and a number of members are similar with less objective function. In summary, VSP is repeated application of the standard GA with smaller population and some similar members in each iteration.

Despite improvements in GA, optimization of large-scale structures with many degrees of freedom requires great number of structural analyses. This makes the optimization process of practical problems inefficient. To overcome this difficulty, a second enhancement is employed. The functions that are the output of the structural analysis are approximated by a number of neural network approaches. By introducing such approximation, the analysis of the structure under consideration is not necessary during the optimization process. As the standard GA or VSP deal with a population with members spread all over in the design space, suitable neural network methods should be employed to create a satisfactory function approximation. In this study, radial basis function (RBF), counter propagation (CP) and generalized regression (GR) neural networks are used. These three methods have some similarities with different nature. The numerical experiences indicate that RBF works better than CP and GR performs better than the other two methods.

In the full-length paper, the details of the modified GA and the basis of function approximation by the different approaches of neural networks will be discussed. The results of the standard GA and VSP with exact and approximate analysis will be compared for some large-scale space structures.

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