测试函数2D图.doc

1 一维函数 一维函数 一维单峰函数一维单峰函数 一维多峰单全局最优解函数一维多峰单全局最优解函数 一维多峰多局部最优解函数一维多峰多局部最优解函数 2 二维函数 二维函数 2 1 二维单峰函数二维单峰函数 2 2 二维多峰单全局最优解函数二维多峰单全局最优解函数 2 2 1 SHUBERT FUNCTION Description Dimensions 2 The Shubert function has several local minima and many global minima The second plot shows the the function on a smaller input domain to allow for easier viewing Input Domain The function is usually evaluated on the square xi 10 10 for all i 1 2 although this may be restricted to the square xi 5 12 5 12 for all i 1 2 Global Minimum Schwefel Function 2 2 2 EGGHOLDER FUNCTION Description Dimensions 2 The Eggholder function is a difficult function to optimize because of the large number of local minima Input Domain The function is usually evaluated on the square xi 512 512 for all i 1 2 Global Minimum 2 2 3 Levy 5 test objective function This class defines the Levy 5 global optimization problem This is a multimodal minimization problem defined as follows Here represents the number of dimensions and for Two dimensionalTwo dimensional LevyLevy 5 5 functionfunction Global optimum for 2 2 4 LANGERMANN FUNCTION Description Dimensions d The Langermann function is multimodal with many unevenly distributed local minima The recommended values of m c and A as given by Molga a larger m leads to a more difficult search The recommended value of m is m 10 The function s two dimensional form is shown in the plot above Input Domain The function is usually evaluated on the hypercube xi 0 for all i 1 d Global Minima 多维多峰多局部最优解函数多维多峰多局部最优解函数 STYBLINSKI TANG FUNCTION Description Dimensions d The Styblinski Tang function is shown here in its two dimensional form Input Domain The function is usually evaluated on the hypercube xi 5 5 f