Multimodal size, shape, and topology optimisation of truss structures using the Firefly algorithm

This paper presents an efficient single-stage Firefly-based algorithm (FA) to simultaneously optimise the size, shape and topology of truss structures. The optimisation problem uses the minimisation of structural weight as its objective function and imposes displacement, stress and kinematic stability constraints. Unstable and singular topologies are disregarded as possible solutions by checking the positive definiteness of the stiffness matrix. Because cross-sectional areas are usually defined by discrete values in practice due to manufacturing limitations, the optimisation algorithm must assess a mixed-variable optimisation problem that includes both discrete and continuous variables at the same time. The effectiveness of the FA at solving this type of optimisation problem is demonstrated with benchmark problems, the results for which are better than those reported in the literature and obtained with lower computational costs, emphasising the capabilities of the proposed methodology. In addition, the procedure is capable of providing multiple optima and near-optimal solutions in each run, providing a set of possible designs at the end of the optimisation process.

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