Improved branched multi-point approximation method and its application in spacecraft topology optimization

The branched multi-point approximation (BMA) method holds immense potential in tackling topology optimization challenges involving discrete variables. This research focuses on enhancing the adaptability, approximation efficiency and engineering application of the method. Four key advancements are presented below. Firstly, an adjusted BMA function is introduced, which comprehensively incorporates the topologies of known and current points, utilizing topological difference between them as the foundation for function segmentation. This function further mitigates singularities as continuous variables approach zero, and is verified for its approximation capability through randomized numerical simulations. Secondly, the concept of adjacent individuals is proposed to ensure that the topological disparities between the current point and current optimal solution remain within manageable limits. This approach prevents approximation failures while maintaining the diversity of the population generated by genetic algorithm. Thirdly, for optimizing continuous variable in complex problems, an improved separable-variable approximation is formulated to ensure strong duality validity. Finally, an adaptive technique for move limit of the retained continuous variables is established. Benchmark examples demonstrate the effectiveness of the improved method in iterations and optimal results. Optimization systems capable of performing topology optimization for spacecraft such as stiffened satellite and carrier rocket have been rare in prior research.