Shubert 函数的全局最小值：最优解与坐标

我们需要知道 Shubert 函数的形式：/n$$ f(x)=/prod_{i=1}^5/left(/sum_{j=1}^5j/cos/left((j+1)x_i+j/right)/right) $$ /n全局最小值在5维空间中共有18个，它们的坐标分别为：/n/n$$ //begin{array}{c|c} //text{最优解} & //text{函数值} ////hline (4.858, 4.858, 4.858, 4.858, 4.858) & -186.7309 //// (-4.858, -4.858, -4.858, -4.858, -4.858) & -186.7309 //// (4.858, 4.858, 4.858, 4.858, -4.858) & -186.7309 //// (-4.858, -4.858, -4.858, -4.858, 4.858) & -186.7309 //// (4.858, 4.858, 4.858, -4.858, 4.858) & -186.7309 //// (-4.858, -4.858, -4.858, 4.858, -4.858) & -186.7309 //// (4.858, 4.858, -4.858, 4.858, 4.858) & -186.7309 //// (-4.858, -4.858, 4.858, -4.858, -4.858) & -186.7309 //// (4.858, -4.858, 4.858, 4.858, 4.858) & -186.7309 //// (-4.858, 4.858, -4.858, -4.858, -4.858) & -186.7309 //// (4.858, -4.858, -4.858, -4.858, 4.858) & -186.7309 //// (-4.858, 4.858, 4.858, 4.858, -4.858) & -186.7309 //// (4.858, -4.858, 4.858, -4.858, -4.858) & -186.7309 //// (-4.858, 4.858, -4.858, 4.858, 4.858) & -186.7309 //// (4.858, -4.858, -4.858, 4.858, -4.858) & -186.7309 //// (-4.858, 4.858, 4.858, -4.858, 4.858) & -186.7309 //// (-7.0835, -7.0835, -7.0835, -7.0835, -7.0835) & -186.7309 //// (7.0835, 7.0835, 7.0835, 7.0835, 7.0835) & -186.7309 //// //end{array} $$ /n其中，前17个是在$[-10,10]^5$中的全局最小值，最后两个是在$[-20,20]^5$中的全局最小值。函数值为$-186.7309$。