离散变量优化相对差分法

A Discrete Optimization Method Based on Relative Difference

根据离散变量问题的特点,在相对差分概念的基础上研究了一种改进的离散变量优化方法。该方法通过相对差分来确定搜索方向。在可行域内,沿目标函数下降最快而约束增加最少的坐标方向搜索;在可行域外,使设计点沿目标函数增加最少,约束降低最多的坐标方向回到可行域。该方法的特点是迭代点均是离散点,无需邻域查点和圆整。并且通过聚合函数法处理约束,而不是只考虑最严约束,同时缩减问题求解规模。通过经典考题验证该方法的收敛性。

Based on the features of discrete variable optimization, an improved discrete variable optimization method is put forward based on the concept of relative difference. The iterative directions are determined by relative difference. In feasible regions, the iteration is along the direction while the objective functions decrease the fastest and the constraints increase the least. In infeasible regions, along the direction while the constraints decrease the most and the objective functions increase the least. So it makes the iteration go back to the feasible regions. Compared to the existing algorithms, it shows some advantages, such as： All the iterative design points are all discrete points, so don＇t need the neighborhood enumeration and roundness. All constraints are aggregated into one constraint to reduce the problem scale, rather than considering only the strict constraints. The convergency of this mothed is verified through a classical problem.