Analysis of Traditional Bidirectional Evolutionary Structural Optimization (BESO) Method

Bidirectional Evolutionary Structural Optimization (BESO) is a material distribution and topology evolution-based optimization technique designed to enhance structural performance (such as stiffness, strength, or lightweight characteristics) through gradual adjustment of material distribution within the structure. While traditional BESO methods have been widely applied in macroscopic structural optimization, they still exhibit limitations in numerical computational efficiency and multiscale problem handling. The algorithm typically operates through iterative element removal/addition based on sensitivity analysis, where key functions calculate elemental sensitivity values using adjoint methods or finite difference approximations.

The primary shortcomings of traditional BESO methods lie in their computational convergence dependency on empirical parameters (such as evolution rate and filter radius), which may lead to unstable optimization results or local optima. In code implementation, these parameters often require manual tuning through trial-and-error approaches. Furthermore, the single-scale optimization approach struggles to accommodate complex performance requirements of composite materials or multiphase materials, such as simultaneously addressing macroscopic mechanical properties and microscopic material distribution in microstructure design. The standard BESO algorithm typically employs a fixed filter radius in sensitivity smoothing operations, limiting its adaptation to varying structural configurations.

To address these limitations, improved BESO methods enhance convergence efficiency by incorporating more stable numerical computation strategies, such as adaptive filtering algorithms and enhanced sensitivity analysis. The adaptive filtering technique dynamically adjusts the filter radius based on element density distribution, while modified sensitivity analysis methods incorporate higher-order derivatives or heuristic optimization techniques. Additionally, by integrating multiscale optimization frameworks, these improved methods enable co-optimization of macroscopic structural layout and microscopic material configuration, achieving integrated material/structure design. For example, in composite material optimization, macroscopic topology determines load transmission paths while microstructure controls local stiffness and toughness, thereby achieving higher-performance lightweight designs overall. Implementation typically involves nested optimization loops where macroscopic and microscopic scales are optimized alternately with data exchange through interpolation functions.

Future BESO methodologies could further incorporate machine learning techniques to accelerate optimization processes and explore more complex multi-objective optimization problems, such as simultaneous consideration of thermo-mechanical coupling performance or dynamic response characteristics. Potential implementations may include neural network-based surrogate models for sensitivity prediction or reinforcement learning for adaptive parameter control, significantly reducing computational costs in large-scale optimization problems.