CEC基准函数——用于算法的测试_cec基准测试函数,cec2020测试函数资源-CSDN下载

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CEC（Competition on Evolutionary Computation）基准函数是一系列设计用于评估和比较不同智能优化算法性能的标准测试集。这些函数通常由国际会议或研讨会，如CEC（Congress on Evolutionary Computation）发布，旨在推动进化计算和相关领域的研究发展。在给定的压缩包中，包含了从2014年到2020年的CEC基准函数定义文件，对于理解这些函数以及如何利用它们来测试优化算法具有重要的价值。 1. CEC2014基准函数：这部分文档主要涵盖了CEC2014年发布的基准函数，可能包括单目标和多目标优化问题，以及各种不同的约束条件。这些函数设计时考虑了复杂性、多样性以及全局优化的挑战性，旨在全面评估算法的性能。Part A可能详细介绍了无界和有界优化问题的不同函数类别及其特点。 2. CEC2015基准函数：CEC2015重点关注学习基础的基准函数，这可能意味着这些函数部分基于真实世界问题或学习过程中的优化挑战。20141228的文件可能包含更新和改进的函数定义，以便更好地反映实际应用中的问题。 3. CEC2017基准函数：2017年的版本可能引入了新的函数类别和更复杂的优化场景，以反映算法技术的发展。"final version updated"表明这是经过多次迭代和修订后的最终版本，包含了对先前版本的反馈和改进。 4. CEC2019基准函数：随着优化算法的不断进步，CEC2019基准可能更加注重高维度问题、大规模问题和混合变量类型的挑战。该文件将详细阐述这些新特性，并提供测试实例和性能指标。 5. CEC2020基准函数：2020年的版本可能会继续提升难度，包括更具挑战性的优化任务，例如非线性、非凸和多模态问题。"Bound Constrained"可能特别关注在特定边界条件下的优化问题，这对于实际应用中的约束优化问题至关重要。通过深入研究这些文档，研究者和开发者可以了解每个函数的数学模型、性能指标、评价标准以及如何在算法测试中应用它们。这不仅有助于评估现有算法的优劣，还能激发新的算法设计思路，推动智能优化领域的创新。在进行算法开发和优化时，选择合适的CEC基准函数进行测试，能够确保算法在处理不同类型问题时具有较好的泛化能力和性能表现。

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测试函数.rar （5个子文件）

Definitions of CEC2020 benchmark suite Bound Constrained.pdf 5.65MB

Definitions of CEC2019 Benchmark Sute.pdf 1MB

Definitions of CEC2017 benchmark suite final version updated.pdf 2.72MB

Definitions of CEC2014 benchmark suite Part A.pdf 752KB

Definitions of CEC2015 benchmark learning-based 20141228.pdf 3.28MB

Problem Definitions and Evaluation Criteria for the CEC 2020

Special Session and Competition on Single Objective Bound

Constrained Numerical Optimization

C. T. Yue

, K. V. Price

, P. N. Suganthan

, J. J. Liang

M. Z. Ali

, B. Y. Qu

N. H. Awad

and Partha P Biswas

School of Electrical Engineering, Zhengzhou University, Zhengzhou, China

836 Owl Circle, Vacaville, CA, U.S.A.

School of EEE, Nanyang Technological University, Singapore

School of Computer Information Systems, Jordan University of Science and Technology, Jordan

School of Electric and Information Engineering, Zhongyuan University of Technology, Zhengzhou, China

Department of Computer Science, Faculty of Engineering, University of Freiburg

Advanced Digital Science Center, Singapore

zzuyuecaitong@163.com, kvprice@pacbell.net, [email protected]g, [email protected].cn,

[email protected], [email protected]m, [email protected]freiburg.de, partha.b@adsc-create.edu.sg

Technical Report 201911, Computational Intelligence Laboratory,

Zhengzhou University, Zhengzhou China

And

Technical Report, Nanyang Technological University, Singapore

November 2019

Single objective optimization algorithms are the foundation upon which more complex methods, like

multi-objective, niching and constrained optimization algorithms, are built. Consequently,

improvements to single objective optimization algorithms are important because they can impact other

domains as well. These algorithmic improvements depend in part on feedback from trials conducted

with single objective benchmark functions, which themselves are the elemental building blocks for

more complex tasks, like dynamic, niching, composition and computationally expensive problems. As

algorithms improve, ever more challenging functions must be developed. This interplay between

methods and problems drives progress, so we have developed the CEC’20 Special Session on Real-

Parameter Optimization to promote this symbiosis.

Improved methods and problems sometimes require updating traditional testing criteria. In recent

years, many novel optimization algorithms have been proposed to solve the bound-constrained, single

objective problems offered in the CEC’05

[1]

, CEC’13

[2]

, CEC’14

[3]

and CEC’17

[4]

Special Sessions on

Real-Parameter Optimization. In those competitions, the maximum allowed number of function

evaluations—unlike problem complexity—did not scale exponentially with dimension. To address this

disparity, this competition significantly increases the maximum number of allowed function evaluations

for 10 scalable benchmark problems beyond their prior contest limits, with the goal of determining the

extent to which this extra time translates into improved solution accuracy.

Participants are required to send their final results to the organizers in the format specified in this

technical report. Based on these results, organizers will present a comparative analysis that includes

statistical tests on convergence performance to compare algorithms with similar final solutions.

Participants may not explicitly use the equations of the test functions, e.g. to compute gradients. This

competition also excludes surrogate and meta-models. Papers on novel concepts that help us to

understand problem characteristics are also welcome. The C and Matlab codes for CEC’20 test suite

can be downloaded from the website below:

https://github.com/P-N-Suganthan

1. Introduction to the CEC’20 Benchmark Suite

1.1. Some Definitions:

All test functions are minimization problems defined as follows:

 

Min ( ), , , ,xx

f x x x

D: number of dimensions.

 

1 1 2

, , ,

i i i iD

o o oo

: the shifted global optimum (defined in “shift_data_x.txt”), which is randomly

distributed in [-80,80]

. All test functions are shifted to o and are scalable.

Search range: [-100,100]

. For convenience, the same search ranges are defined for all test functions.

: rotation matrix. Different rotation matrix are assigned to each function and each basic function.

Considering that linkages seldom exists among all variables in real-world problems, CEC’20 randomly

divides variables into subcomponents. The rotation matrix for each set of subcomponents is generated

from standard normally distributed entries by Gram-Schmidt ortho-normalization with condition

number c that is equal to 1 or 2.

1.2. Summary of the CEC’20 Test Suite

No.

Functions

= F

(x*)

Unimodal

Function

Shifted and Rotated Bent Cigar Function (CEC 2017

[4]

F1)

100

Basic

Functions

Shifted and Rotated Schwefel’s Function (CEC 2014

[3]

F11)

1100

Shifted and Rotated Lunacek bi-Rastrigin Function

(CEC 2017

[4]

F7)

700

Expanded Rosenbrock’s plus Griewangk’s Function (CEC2017

[4]

)

1900

Hybrid

Functions

Hybrid Function 1 (N = 3) (CEC 2014

[3]

F17)

1700

Hybrid Function 2 (N = 4) (CEC 2017

[4]

F16)

1600

Hybrid Function 3 (N = 5) (CEC 2014

[3]

F21)

2100

Composition

Functions

Composition Function 1 (N = 3) (CEC 2017

[4]

F22)

2200

Composition Function 2 (N = 4) (CEC 2017

[4]

F24)

2400

Composition Function 3 (N = 5) (CEC 2017

[4]

F25)

2500

Search range: [-100,100]

*Please Note: These problems should be treated as black-box problems. The explicit equations of

the problems are not to be used.

1.3. Definitions of the Basic Functions

1) Bent Cigar Function

( ) 10

f x x







(1)

2) Rastrigin’s Function

 

( ) 10cos 2 10

f x x x



   



(2)

3) High Conditioned Elliptic Function

 

( ) 10

f x x







(3)

4) HGBat Function

1/2

1 1 1 1

( ) 0.5 / 0.5

D D D D

i i i i

f x x x x D

   

     

    

     

     

   

(4)

5) Rosenbrock’s Function

 





5 1

( ) 100 1

i i i

f x x x







   



(5)

6) Griewank’s Function

( ) cos 1

4000





  









(6)

7) Ackley’s Function

 

( ) 20exp( 0.2 ) exp cos 2 20 e

f x x





      







(7)

8) Happycat Function

1/4

1 1 1

( ) 0.5 / 0.5

D D D

i i i

f x D x x D

  



    





  

(8)

9) Discus Function

6 2 2

( ) 10

f x x







(9)

10) Lunacek bi-Rastrigin Function

     

010 1

1 1 1

ˆ ˆ

( ) min , 10 cos 2

D D D

i i i

f x dD s x D z

  

   

      

   

   

  

(10)

 

100

2.5, , 1 , 1

2 20 8.2

10( )

, 2sign , for 1,2, ,

100



       





     

   

y x y i D

11) Modified Schwefel’s Function

 

( ) 418.9829

f x D g z



  



(11),

4.209687462275036e 002  

 

1/2

sin if 500

500

500 mod ,500 sin( 500 mod ,500 ) if 500

10000

500

mod ,500 500 sin( mod ,|,500 500 ) if 500

10000











    









    



i i i

i i i i

i i i

z z z

g z z z z

z z z

12) Expanded Schaffer’s Function

Schaffer’s Function:





 

2 2 2

sin ( ) 0.5

( , ) 0.5

1 0.001







g x y

 

   

1 2 2 3 112 1

( ) , , , ,

D D D

f g x x g x x g x x g x x



   x

(12)

13) Expanded Rosenbrock’s plus Griewangk’s Function

 

1 2 2 313 6 5 6116 5 6 5 5

( ) , , , ,

D D D

f f f x x f f x x f f x x f f x x



   x

(13)

14) Weierstrass Function

 

   

max max

1 0 0

( ) cos 2 0.5 cos 2 0.5

D k k

k k k k

i k k

f a b x D a b

  



   

    



   







  

(14)

0.5, 3, max 20  a b k

1.4. Definitions of the CEC’20 Test Suite

A. Basic Functions

1) Bent Cigar Function

 

( ) MFf Foxx

(15)

Properties:

 Unimodal

 Non-separable

 Smooth but narrow ridge

(a) 3-D map for 2-D function (b) Contour map for 2-D function

Figure 1 Bent Cigar Function

2) Shifted and Rotated Schwefel’s Function (the same as F11 in CEC2014

[3]

)

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