This paper presents an advanced approach to optimize the topology of structures by combining the Bidirectional Evolutionary Structural Optimization (BESO) method with the Mesh-Free Galerkin (EFG) method. The main goal of this hybrid approach is to significantly reduce the computational time while maintaining high accuracy in the optimization process. Traditional mesh-based methods, especially in problems involving complex geometries, often require precise mesh generation and repeated mesh reconstruction during the optimization process, which can significantly increase the computational cost and complexity. By incorporating a mesh-free method such as EFG, the proposed approach eliminates the need for mesh generation and, when combined with the evolutionary efficiency of the BESO algorithm, results in a faster and simpler optimization process.

Numerical results presented in this study show that this combined method is up to 2.5 times faster than conventional approaches based on the finite element method (FEM), while still ensuring reliable mechanical performance and structural integrity. Furthermore, due to the flexibility of the EFG method in handling complex geometries and variable boundary conditions, the proposed technique is particularly effective for real-world engineering applications. This method is particularly suitable for industries such as aerospace, automotive, and mechanical engineering where the demand for lightweight, strong, and complex structural designs is high. Overall, the integration of BESO and EFG provides a robust and efficient solution to the limitations of traditional topology optimization techniques.