单纯形的加速算法

An Accelerated Simplex Method

该文提出了能有效加快收敛速度的修改单纯形算法。在原单纯形算法的基础上增加了一种新的反射方向的计算方法 ;用“映射单纯形”方法代替“单纯形顶点代换”方法 ;有选择地采用“单纯形压缩”计算。计算结果表明 ,修改单纯形算法对初值的适应范围更宽 ,收敛速度更快 ,收敛次数从 50～ 1 0 0次降低到 30次左右 。

A new modified simplex method can effectively accelerate convergence velocity of iteration. A new expansion direction is added. The 'Mapping Simplex Method' is used instead of the 'Substitution of Simplex Vertexes'. The 'Simplex Compression' can be chosen in the calculation. The results show that the modified simplex method allows broader initial values with fast convergence velocity, whose iterations decrease from 50～100 to about 30 times. New method can effectively avoid degeneration and failure in the calculation, and can be successfully used in the engineering optimum and data processing.