## 1 Introduction
Most open-source topology optimization algorithms developed on MATLAB platforms, while convenient for theoretical validation, are constrained to 2D models with simplified mechanical assumptions, proving inadequate for addressing complex 3D engineering problems [21; 22]. [PERSON] et al. [5] implemented the Bi-directional Evolutionary Structural Optimization (BESO) method for topology optimization of engine brackets, developing a MATLAB-based algorithm using von Mises stress as the governing parameter, achieving weight reduction while validating structural performance through simulations. [PERSON] et al. [23] developed a MATLAB code for concurrent multi-scale topology optimization using BESO, supporting honeycomb/composite materials and single/multi-volume constraints, thereby enabling macro-micro collaborative design and expanding engineering applications. [PERSON] et al. [24] developed a truss optimization program via geometric projection for a parametric design. [PERSON] et al. [25] proposed the TOuNN framework mapping density fields to activation functions to eliminate mesh dependency, though constrained to single-objective optimization. [PERSON] et al. [26] developed the HiTop 2.0 interactive platform, integrating multi-scale features and manufacturing constraints but lacking nonlinear analysis capabilities. Despite improved accessibility of open-source tools [27; 28], limitations remain in commercial software integration and computational scalability. Commercial finite element software (e.g., ABAQUS, ANSYS), despite incorporating 3D topology optimization modules, suffers from closed architectures with black-box algorithms and limited parameter adjustments, hindering compatibility with user-defined optimization strategies. To bridge the theory-practice gap, researchers have explored integrating commercial FE software with algorithmic platforms: [PERSON] et al. [21] implemented 3D BESO via ABAQUS scripting with INP file interactions. [PERSON] et al. [29] achieved large-displacement optimization through MATLAB-ANSYS integration. [PERSON] et al. [30] created the A2M tool for ABAQUS-MATLAB coupling, albeit limited to unidirectional data transfer. [PERSON] et al. [31] proposed Simulated Annealing BESO (SA-BESO) combining stochastic updates and dual-coding mechanisms to escape local optima, yielding lower compliance at reduced costs. [PERSON] et al. [32] introduced a BESO-reinforcement learning hybrid algorithm generating diverse solutions via \(\varepsilon\)-greedy strategies, balancing quality and diversity in 2D/3D compliance minimization. [PERSON] et al. [33] developed a MATLAB-ABAQUS interface for BESO implementation with user-friendly parameter configuration. [PERSON] et al. [34] coded DER-BESO using ANSYS APDL, accelerating convergence for 3D/periodic structures. [PERSON] et al. [35] validated crash optimization feasibility via MATLAB-ABAQUS\({}^{\circledR}\) iterative interfaces, while [PERSON] et al. [15] formulated a universal nonlinear optimization scheme using MIST with LS-Dyna. Current challenges focus on nonlinear problem decoupling and large-scale parallel acceleration, necessitating standardized interfaces for collaborative computing. In engineering practice, BESO's advantages are increasingly evident. [PERSON] et al. [36] addressed ESO limitations via critical boundary constraints, laying BESO's theoretical foundation. [PERSON] [37] developed a multi-material BESO framework using p-norm global stress modeling to reduce stress singularity, demonstrating 21% lower maximum stress versus stiffness-driven designs. [PERSON] et al. [38] proposed a tri-field BESO method, integrating density, filter radius variables, and isotropic/anisotropic filters to generate plate-like, extruded, and other morphologies, enhancing geometric control and design diversity. [PERSON] et al. [39] optimized jack-up platform legs using BESO, achieving superior load-bearing capacity, dynamic response, and weight reduction compared to traditional K/reverse-K/X-type structures, with experimental validation. [PERSON] et al.