Reliability-based design optimization of double layer barrel vault using pattern search algorithm and optimized neural network as an surrogate model

In this research, a method based on the optimal neural network and pattern search optimization algorithm is presented to solve reliability-based design optimization problems. The main idea is to find a surrogate model that does not suffer from the phenomenon of overfitting and therefore has a good generalization accuracy. In the first stage, using the program written using the SM toolbox, a data set of inputs and outputs of the problem is created by running Sap2000. Then an optimization problem is solved to obtain the best performance of the neural network. The design variables in the neural network training stage, are the number of layers, the number of neurons in each layer and the type of transfer. The objective function is the performance ratio, which is defined as the ratio of the number of parameters in the neural network to the number of members of the data set used in the training process. Subsequently. The pattern search algorithm is used to optimize the examples using the developed optimal ANN as a surrogate model. To demonstrate the effectiveness of the presented method, two numerical examples are considered. In the first example, a ten-bar plane truss and in the second example, a two-layered 832-membered barrel vault have been investigated. In the first example, the proposed method has worked about 32 times faster in the vase of continuous variables and 25 times faster in the case of discrete variables. (Compared to solving the problem with the original SAP 2000 model and the Latin hypercube sampling method). In both examples, the surrogate model obtained from the proposed method has provided the desired performance in both the validation and the test data.