常见的新算法的标准测试函数

标准测试函数相关详细介绍请参考测试函数集：http://www.sfu.ca/~ssurjano/index.html。

1、优化测试问题【Optimization Test Problems】

1）许多局部极小值【Many Local Minima】

2）碗状【Bowl-Shaped】

3）板状【Plate-Shaped】

4）山谷状【Valley-Shaped】

5）陡峭的山脊/瀑布【Steep Ridges/Drops】

6）其他【Other】

2、仿真/预测测试问题【Emulation/Prediction Test Problems】

1） Physical Models

2） Qualitative and Quantitative Inputs

3） Trigonometric

4） Exponential/Logarithmic

5） Rational

6） Other

3、不确定度量化测试问题【Uncertainty Quantification Test Problems】

1）Physical Models

2）Other

4、多保真仿真测试问题【Multi Fidelity Simulation Test Problems】

1） Physical Models

2） Other

5、校准/调谐测试问题【Calibration/Tuning Test Problems】

1）Physical Models

2）Other

6、筛选测试问题【Screening Test Problems】

1）Physical Models

2）Strong Interactions

3）High Dimensionality

4）Qualitative and Quantitative Inputs

5）Product Integrand Functions

6）Other

7、集成测试问题【Integration Test Problems】

1）Genz (1984) Integrand Families

2）Product Functions

3）Other

8、功能数据测试问题【Functional Data Test Problems】

1）Physical Models

9、其他测试功能及代码【Other Test Functions and Code】

1） Computer Codes & Datasets

2） Optimization Test Functions

10.单目标优化标准测试函数

11.常见多目标测试函数

1）ZDT1

2）ZDT2

3）ZDT3

4）ZDT4

12.高维多目标进化领域测试函数

1）DTLZ测试函数

2）收敛性评价指标IGD

3）覆盖率指标C

测试函数一般分类大概分为以下9个大类

1、优化测试问题【Optimization Test Problems】

1）许多局部极小值【Many Local Minima】

1.阿克力函数【Ackley Function】

2.bukin函数【Bukin Function N. 6】

3.交叉进纸盘函数【Cross-in-Tray Function】

4.滴波函数【Drop-Wave Function】

5.茄子架函数【Eggholder Function】

6.Gramacy&Lee（2012）函数【Gramacy & Lee (2012) Function】

7.格栅函数【Griewank Function】

8.支架台函数【Holder Table Function】

9.朗格曼函数【Langermann Function】

10.征收函数【Levy Function】

11.征费函数13【Levy Function N. 13】

12.rastrigin函数【Rastrigin Function】

13.Schaffer函数n.2【Schaffer Function N. 2】

14.Schaffer函数n.4【Schaffer Function N. 4】

15.Schwefel函数【 Schwefel Function】

16.舒伯特函数【Shubert Function】

2）碗状【Bowl-Shaped】

17.Bohachevsky Functions

18.Perm Function 0, d, β

19.Rotated Hyper-Ellipsoid Function

20.Sphere Function

21.Sum of Different Powers Function

22.Sum Squares Function

23.Trid Function

3）板状【Plate-Shaped】

24.Booth Function

25.Matyas Function

26.McCormick Function

27.Power Sum Function

28.Zakharov Function

4）山谷状【Valley-Shaped】

29.Three-Hump Camel Function

30.Six-Hump Camel Function

31.Dixon-Price Function

32.Rosenbrock Function

5）陡峭的山脊/瀑布【Steep Ridges/Drops】

33.De Jong Function N. 5

34.Easom Function

35.Michalewicz Function

6）其他【Other】

36.Beale Function

37.Branin Function

38.Colville Function

39.Forrester et al. (2008) Function

40.Goldstein-Price Function

41.Hartmann 3-D Function

42.Hartmann 4-D Function

43.Hartmann 6-D Function

44.Perm Function d, β

45.Powell Function

46.Shekel Function

47.Styblinski-Tang Function

2、仿真/预测测试问题【Emulation/Prediction Test Problems】

1） Physical Models

Borehole Function
MARTHE Dataset
OTL Circuit Function
Piston Simulation Function
Robot Arm Function
Wing Weight Function

2） Qualitative and Quantitative Inputs

Han et al. (2009) Function
Qian et al. (2008) Function
Zhou et al. (2011) Function

3） Trigonometric

Branin Function
Cheng & Sandu (2010) Function
Currin et al. (1988) Sinusoidal Function
Forrester et al. (2008) Function
Friedman Function
Gramacy & Lee (2009) Function
Gramacy & Lee (2012) Function
Higdon (2002) Function
Higdon (2002) and Gramacy & Lee (2008) Function
Holsclaw et al. (2013) Sinusoidal Function
Lim et al. (2002) Nonpolynomial Function
Santner et al. (2003) Damped Cosine Function

4） Exponential/Logarithmic

Currin et al. (1988) Exponential Function
Currin et al. (1988) Survival Function
Dette & Pepelyshev (2010) 8-Dimensional Function
Dette & Pepelyshev (2010) Exponential Function
Franke's Function
Gramacy & Lee (2008) Function
Holsclaw et al. (2013) Logarithmic Function
Zhou (1998) Function

5） Rational

Currin et al. (1991) Function
Lim et al. (2002) Polynomial Function
Welch et al. (1992) Function

6） Other

Dette & Pepelyshev (2010) Curved Function

3、不确定度量化测试问题【Uncertainty Quantification Test Problems】

1）Physical Models

Borehole Function
Cantilever Beam Functions
MARTHE Dataset
Short Column Function
Steel Column Function
Sulfur Model Function

2）Other

Eldred et al. (2007) Lognormal Ratio Function
G-Function
Ishigami Function
Oakley & O'Hagan (2002) 1-D Function
Oakley & O'Hagan (2002) 2-D Function
Oakley & O'Hagan (2004) Function
Webster et al. (1996) Function

4、多保真仿真测试问题【Multi Fidelity Simulation Test Problems】

1） Physical Models

Borehole Function
Currin et al. (1988) Exponential Function
Park (1991) Function 1

2） Other

Park (1991) Function 2

5、校准/调谐测试问题【Calibration/Tuning Test Problems】

1）Physical Models

Environmental Model Function

2）Other

Park (1991) Function 1
Park (1991) Function 2

6、筛选测试问题【Screening Test Problems】

1）Physical Models

Borehole Function
MARTHE Dataset
Moon et al. (2012) Function
OTL Circuit Function
Piston Simulation Function
Wing Weight Function

2）Strong Interactions

Moon (2010) High-Dimensionality Function
Moon (2010) Low-Dimensionality Function
Welch et al. (1992) Function

3）High Dimensionality

Linkletter et al. (2006) Decreasing Coefficients Function
Linkletter et al. (2006) No Signal Function
Linkletter et al. (2006) Simple Function
Linkletter et al. (2006) Sinusoidal Function
Loeppky et al. (2013) Function
Morris et al. (2006) Function
Oakley & O'Hagan (2004) Function

4）Qualitative and Quantitative Inputs

Moon (2010) Mixed Function

5）Product Integrand Functions

G-Function
Morokoff & Caflisch (1995) Function 1
Roos & Arnold (1963) Function

6）Other

Bratley et al. (1992) Function
Ishigami Function
Sobol' & Levitan (1999) Function
Williams et al. (2006) Function

7、集成测试问题【Integration Test Problems】

1）Genz (1984) Integrand Families

Continuous Integrand Family
Corner Peak Integrand Family
Discontinuous Integrand Family
Gaussian Peak Integrand Family
Oscillatory Integrand Family
Product Peak Integrand Family

2）Product Functions

G-Function
Morokoff & Caflisch (1995) Function 1
Morokoff & Caflisch (1995) Function 2
Roos & Arnold (1963) Function

3）Other

Bratley et al. (1992) Function
Zhou (1998) Function

8、功能数据测试问题【Functional Data Test Problems】

1）Physical Models

Environmental Model Function

9、其他测试功能及代码【Other Test Functions and Code】

1） Computer Codes & Datasets

Argonne's Software for Applications (contains several models):
http://www.mcs.anl.gov/software/science-engineering-applications-software

Benchmark Proposals of GdR MASCOT-NUM:
http://www.gdr-mascotnum.fr/benchmarks.html

FOAM: The Fast Ocean Atmosphere Model:
http://www.mcs.anl.gov/research/projects/foam/index.html

OOMMF/NIST Software:
http://math.nist.gov/oommf/software.html

TESTPACK, for Testing Multidimensional Integration Routines:
http://people.sc.fsu.edu/~jburkardt/m_src/testpack/testpack.html

2） Optimization Test Functions

Adorio, E. P., & Diliman, U. P. MVF - Multivariate Test Functions Library in C for Unconstrained Global Optimization (2005):
http://www.geocities.ws/eadorio/mvf.pdf

Global Optimization Test Functions Index:
http://infinity77.net/global_optimization/test_functions.html#test-functions-index

Global Optimization Test Problems:
http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO.htm

Laguna, M., & Marti, R. Experimental Testing of Advanced Scatter Search Designs for Global Optimization of Multimodal Functions (2002):
http://www.uv.es/rmarti/paper/docs/global1.pdf

Molga, M., & Smutnicki, C. Test Functions for Optimization Needs (2005):
http://www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf

10.单目标优化标准测试函数

11.常见多目标测试函数

1）ZDT1

2）ZDT2

3）ZDT3

4）ZDT4

12.高维多目标进化领域测试函数

1）DTLZ测试函数

DTLZ1 ~~~~~~DTLZ7

2）收敛性评价指标IGD

3）覆盖率指标C

本文在罗列测试函数的相关介绍基础上，增加展示了部分测试函数的图像展示以及高维多目标评价相关知识，基于测试函数收集总站的基础上，又统计了其他相关博主jj_千寻的相关内容，做一个相对全面总结统计，以备使用相关知识时更加方便。