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In this research, the optimization problem of the steel-concrete composite I-girder bridges is investigated. The optimization process is performed using the pattern search algorithm, and a parallel processing-based approach is introduced to improve the performance of this algorithm. In addition, using the open application programming interface (OAPI), the SM toolbox is developed. In this toolbox, the OAPI commands are implemented as MATLAB functions. The design variables represent the number and dimension of the longitudinal beam and the thickness of the concrete slab. The constraints of this problem are presented in three steps. The first step includes the constraints on the web-plate and flange-plate proportion limits and those on the operating conditions. The second step consists of considering strength constraints, while the concrete slab is not yet hardened. In the third step, strength and deflection constraints are considered when the concrete slab is hardened. The AASHTO LRFD code (2007) for steel beam design and AASHTO LRFD (2014) for concrete slab design are used. The numerical examples of a sloping bridge with a skew angle are presented. Results show that active constraints are those on the operating conditions and component strength and that in terms of CPU time, a 19.6% improvement is achieved using parallel processing.

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This paper presents a novel framework for structural reliability assessment of buildings incorporating Concrete-Filled Steel Tubular columns, utilizing a deep surrogate model formulated in the complex number domain. High-fidelity numerical models are developed using SAP2000 software, with analysis outputs pre-processed in MATLAB. A hybrid deep learning architecture is implemented within the PyTorch framework, featuring complex-valued parameters and activation functions that enable superior representation of phase-dependent and oscillatory behaviors inherent in nonlinear limit state functions. Each complex parameter simultaneously encodes both real and imaginary influences, enhancing representational efficiency while requiring fewer parameters than conventional real-valued networks. Bidirectional communication between MATLAB and PyTorch is established through system-level execution protocols, enabling seamless integration with the SM Toolbox for parametric structural modeling. The surrogate model is trained on strategically sampled datasets, with architecture complexity and dataset size adaptively determined based on parameter counts. Reliability indices are computed using the Weighted Average Simulation Method applied separately to real and imaginary components, with final reliability estimated through weighted averaging. The proposed method is validated through three mathematical benchmark functions and three engineering case studies, including a three-span continuous beam, a roof truss, and a ten-story building with CFST columns. Results demonstrate minimum improvements of 79% in mathematical examples and up to 95% in engineering applications regarding required function evaluations, while maintaining essentially zero estimation error. For the ten-story building, computation time reduced from approximately 3.9 days using conventional simulation to 2.3 hours—a 98% improvement—demonstrating the framework's potential for efficient and accurate reliability assessment of complex structural systems.