基于变分辨率网格的模拟退火算法在形状优化问题上的应用研究

Study on the Application of Simulated Annealing Algorithm Based on Variable Resolution Mesh in Shape Optimization

形状优化是一类复杂的优化问题,在工业上经常作为结构优化的一个分支出现.它以几何形状作为优化对象,需要求得某种性能条件最优的几何形状,一般来说对建模和计算量的要求都比较高.模拟退火是一种用途非常广泛的优化算法,可以处理各种复杂的优化问题.但标准的模拟退火算法在处理形状优化问题时,由于搜索空间的范围太大,经常陷入局部最优解,所以需要耗费巨大的计算量,实用性有限.本文讨论了在变分辨率的离散网格中的模拟退火算法,将低分辨率网格下的最优结果过渡到高分辨率网格下作为一个良好的初始解,这样可以有效地规避局部最优点,缩小搜索范围,极大地提高模拟退火算法的效率.并以蚱蜢问题为算例,对算法的效果进行了验证.

Shape optimization is a complex type of optimization problems.It takes the geometric shape as the object of optimization,which needs to obtain the optimal geometric shape under certain performance conditions.It often appears as a branch of structural optimization in engineering.In general,the requirements for modeling and calculation of this problem are relatively high.Simulated annealing is a widely used optimization algorithm,which can deal with various complex optimization problems.However,when the standard simulated annealing algorithm is used to solve the shape optimization problem,because of the large plausible solution space,it often converges to a local optimal solution,so it requires a huge amount of calculation impractically and has limited practical significance.In this paper,we discuss a simulated annealing algorithm on a discrete grid with multiple resolutions.The optimal solution in a low-resolution grid is transitioned to a high-resolution grid as a good initial solution.It can avoid locally optimal solutions effectively and improve the computational efficiency of the simulated annealing algorithm.The efficiency of the algorithm is verified by taking the grasshopper problem as an example.