A reliability-based design approach for topology, size and shape optimization of trusses with multiple kinematic and probabilistic mechanical constraints

This article develops a reliability-based adaptive hybrid evolutionary firefly algorithm (RB-AHEFA) for the simultaneous optimization of the topology, size and shape of trusses under uncertainties of design parameters for the weight minimum. The proposed methodology is refined by integrating modified sequential optimization and reliability assessment (MSORA) into the optimization process of the AHEFA for handling multiple kinematic and probabilistic mechanical constraints. By eliminating the repeated process of finding most probable points (MPPs) in the original SORA, the computational cost of shifting probabilistic constraints into equivalent deterministic ones can be significantly reduced while still providing optimal results with high accuracy. Accordingly, the probabilistic restrictions can still be evaluated during the optimization process without requiring nested optimization-reliability loops. Four benchmark trusses are illustrated to confirm the suggested paradigm's efficiency. Obtained outcomes indicate that RB-AHEFA not only surpasses the traditional reliability-based design optimization (RBDO) algorithm in terms of computational time but also demonstrates greater solution stability across independent runs.