A Firefly Metaheuristic Algorithm for Structural Size and Shape Optimization with Dynamic Constraints

Herbert M. Gomes


In this paper, a structural mass optimization on shape and size is performed taking into account dynamic constraints. Mass reduction especially conflicts with frequency constraints when they are lower bounded since vibration modes may easily switch due to shape modifications. Here it is investigated the use of a Firefly Methaheuristic Algorithm (FMA) as an optimization engine. One important feature of the algorithm is based on the fact that it is not gradient based, but just based on simple objective functions evaluations. This is of major importance when dealing of highly non-linear dynamic optimization problems with several constraints avoiding bad numerical behavior due to gradient evaluations. The algorithm is briefly revised, highlighting its most important features. Some new implementations are performed on the algorithm based on literature reports in order to improve the algorithm performance. It is presented several examples regarding the optimization on shape and sizing with frequency constraints of complex trusses that are widely reported in the literature as benchmark examples solved with several non-heuristic algorithms. The results show that the algorithm performed similar to other methaheuristic methods and better in other cases when compared with traditional gradient-based methods.

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