Application of imperialist competitive algorithm and neural networks to optimise the volume fraction of three-parameter functionally graded beams

Abstract

This paper deals with optimisation of three-parameter power-law distribution of functionally graded (FG) beam. The main goal of the optimisation problem is to determine the optimum volume fraction relation for maximising the first natural frequency of FG beam. Since the search space is large, the optimisation processes become very complicated and too time consuming. Thus, a novel meta-heuristic called imperialist competitive algorithm (ICA), which is a socio-politically motivated global search strategy is applied to find the optimal solution. Applying the proposed algorithm to some of benchmark cost functions, it shows its ability in dealing with different types of optimisation problems. A proper and accurate artificial neural network (ANN) is trained by training data sets obtained from generalised differential quadrature method and then is applied as the objective function in ICA. The ANN improves the speed of optimisation process by a considerable amount by reproducing the fundamental natural frequency of the structure. The performance of ICA is evaluated in comparison with other nature-inspired technique genetic algorithm. Comparison shows the success of combination of ANN and ICA for design of material profile of beam. Finally the optimised material profile for the optimisation problem is presented.