A firefly metaheuristic structural size and shape optimisation with natural frequency constraints

A structural mass optimisation on shape and size is performed in this paper taking into account natural frequency constraints. Mass reduction conflicts with frequency constraints when they are lower bounded since vibration mode shapes may easily switch due to shape modifications. Here, it is investigated the use of the firefly metaheuristic algorithm (FMA) as an optimisation engine. One important feature of the algorithm is the non-gradient based evaluations, but on single objective function evaluations. This is of paramount importance when dealing with non-linear optimisation problems with several constraints avoiding bad numerical behaviour due to gradient evaluations. The algorithm is revised, highlighting its most important features. It is suggested some new implementations of the basic algorithm based on literature reports in order to improve its performance. The paper presents several examples regarding the optimisation on shape and sizing with natural frequency constraints of complex trusses that are widely reported in the literature as benchmark examples solved with several non-heuristic and heuristic algorithms. The results show that the algorithm outperforms deterministic algorithms but behaves similar to other metaheuristic methods.