测试函数D图

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 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-dimensional Levy 5 function

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 & 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 in Here, . represents the number of dimensions and . for is a random variable uniformly distributed Two-dimensional Xin-She Yang 1 function Global 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 function

Global 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

.

for

Here, represents the number of dimensions and

.

Two-dimensional Xin-She Yang 3 function

Global 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 function

Global 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 function

Global 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

.

Two-dimensional SineEnvelope function

for

Global 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 Ackley

3.2.2 MICHALEWICZ FUNCTION

Description:

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 function's two-dimensional form is shown in the plot above.

Input Domain:

The function is usually evaluated on the hypercube xi ∈ [0, π], for all i = 1, …, d.

Global Minima:

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], for all i = 1, …, d.

Global Minimum:

Griewank

Michalewicz

Penalized

Penalized2

Rastrigin

Rosenbrock