測試函數(shù)2D圖

1、1、一維函數(shù)一維單峰函數(shù)一維多峰單全局最優(yōu)解函數(shù)一維多峰多局部最優(yōu)解函數(shù)2、二維函數(shù)2.1二維單峰函數(shù)2.2 二維多峰單全局最優(yōu)解函數(shù)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 fun

2、ction 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

3、 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 follo

4、ws: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 &am

5、p; 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-S

6、he 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(dimensi

7、ons=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 XinSheY

8、ang03(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 fu

9、nctionGlobal 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-

10、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 Dama

11、vandi 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

12、-dimensional SineEnvelope functionGlobal optimum: for for 2.3 二維多峰多全局最優(yōu)解函數(shù)3、多維函數(shù)3.1多維單峰函數(shù)3.2多維多峰單全局最優(yōu)解函數(shù)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

13、; 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:多維多峰多局部最優(yōu)解函數(shù)STYBLINSKI-TANG FUNCTIONDescription:Dimensions: d The Styblinski-Tang function is