测试函数D图.doc

1、一维函数一维单峰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2、二维函数2.1二维单峰函数2.2 二维多峰单全局最优解函数2.2.1 SHUBERT FUNCTIONDescription: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 Function2.2.2 EGGHOLDER FUNCTIONDescription: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-dimensional Levy 5 functionGlobal optimum: for .2.2.4 LANGERMANN FUNCTIONDescription: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 & Smutnicki (2005) are (for d = 2): m = 5, c = (1, 2, 5, 2, 3) and:Input Domain:The function is usually evaluated on the hypercube xi 0, 10, for all i = 1, , d. Global optimum: for class go_benchmark.XinSheYang01(dimensions=2)2.2.5 Xin-She Yang 1 test objective function.This class defines the Xin-She Yang 1 global optimization problem. This is a multimodal minimization problem defined as follows:The variable is a random variable uniformly distributed in .Here, represents the number of dimensions and for .Two-dimensional Xin-She Yang 1 functionGlobal optimum: for for 2.2.6 XinSheYang02(dimensions=2)Xin-She Yang 2 test objective function.This class defines the Xin-She Yang 2 global optimization problem. This is a multimodal minimization problem defined as follows:Here, represents the number of dimensions and for .Two-dimensional Xin-She Yang 2 functionGlobal optimum: for for 2.2.7 XinSheYang03(dimensions=2)Xin-She Yang 3 test objective function.This class defines the Xin-She Yang 3 global optimization problem. This is a multimodal minimization problem defined as follows:Where, in this exercise, and .Here, represents the number of dimensions and for .Two-dimensional Xin-She Yang 3 functionGlobal optimum: for for 2.2.8 XinSheYang04(dimensions=2)Xin-She Yang 4 test objective function.This class defines the Xin-She Yang 4 global optimization problem. This is a multimodal minimization problem defined as follows:Here, represents the number of dimensions and for .Two-dimensional Xin-She Yang 4 functionGlobal optimum: for for 2.2.9 Damavandi(dimensions=2)Damavandi test objective function.This class defines the Damavandi global optimization problem. This is a multimodal minimization problem defined as follows:Here, represents the number of dimensions and for .Two-dimensional Damavandi functionGlobal optimum: for for class go_benchmark.SineEnvelope(dimensions=2)SineEnvelope test objective function.This class defines the SineEnvelope global optimization problem. This is a multimodal minimization problem defined as follows:Here, represents the number of dimensions and for .Two-dimensional SineEnvelope functionGlobal optimum: for for 2.3 二维多峰多全局最优解函数3、多维函数3.1多维单峰函数3.2多维多峰单全局最优解函数3.2.1 Ackley3.2.2 MICHALEWICZ FUNCTIONDescription:Dimensions: d The Michalewicz function has d! local minima, and it is multimodal. The parameter m defines the steepness of they valleys and ridges; a larger m leads to a more difficult search. The recommended value of m is m = 10. The functions 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STYBLINSKI-TANG FUNCTIONDescription:Dimensions: d The Styblinski-Tang function is shown here in its two-dimensional form. Input D