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Abstract
Volume fraction optimisation of functionally graded beams is studied for maximising the fundamental natural frequency by applying a new meta-heuristic nature-inspired algorithm called firefly algorithm (FA) which is based on the flashing behaviour of fireflies. Nature-inspired algorithms are among the most powerful algorithms for optimisation of engineering problems. The primary optimisation variables are the three parameters in the power-law distribution. Since the search space is large, the optimisation processes becomes so complicated and too much time consuming. Thus, a suitable Adaptive Neuro-Fuzzy Inference System (ANFIS) that is based on Takagi–Sugeno fuzzy inference system is combined with FA to reproduce the behaviour of the structure in free vibration. The ANFIS improves the speed of optimisation process by a considerable amount. The results are compared with those obtained by imperialist competitive algorithm, genetic algorithm and Artificial Neural Networks proposed in our previous work. Results show that the combination of FA and ANFIS is capable of yielding better optimal solution in comparison with other available techniques. It is believed that new results are of interest to the scientific and engineering community in the area of engineering design.