Reliability-based structural optimization using adaptive neural network multisphere importance sampling

An innovative adaptive neural network multisphere importance sampling (ANNM- IS) is proposed and integrated with symbiotic organism search (SOS) to form a framework for finding an engineering optimal design. Building a single sphere in IS to enhance the computational efficiency has been used for decades, ANNM-IS provides a pioneering idea, in which multi-spheres are built. "Adaptive point", found by neural network (NN), is proposed to help for generating multiple spheres. ANNM- IS is further integrated with SOS to update NN for next iteration. As optimization iterations increase, adaptive NN provides more accurate reliability estimates. A two-step SOS, considering exploration and exploitation, is designed to enhance the search performance. Four reliability problem are first solved to confirm the correctness and effectiveness of ANNM-IS, then another four structural optimization problem including a building controller design and a 25-bar truss design are solved. Results shown that the proposed method drastically reduces the amount of function evaluation and computation time without sacrificing accuracy in reliability compared to those of other sampling methods. The developed framework can solve a complex structural optimization problem of accurate reliability with affordable price. The supporting source codes are available for download at https://github.com/johnthedy/RBDO- using-MIS-NN-SOS.