Problem Definitions and Evaluation Criteria for the CEC 2017
Special Session and Competition on Single Objective
Real-Parameter Numerical Optimization
N. H. Awad
1
, M. Z. Ali
2
, P. N. Suganthan
1
, J. J. Liang
3
and B. Y. Qu
3
1
School of EEE, Nanyang Technological University, Singapore
2
School of Computer Information Systems, Jordan University of Science and Technology, Jordan
3
School of Electrical Engineering, Zhengzhou University, Zhengzhou, China
noor0029@ntu.edu.sg, mzali.pn@ntu.edu.sg, epnsugan@ntu.edu.sg, liangjing@zzu.edu.cn
Technical Report, Nanyang Technological University, Singapore
And
Jordan University of Science and Technology, Jordan
And
Zhengzhou University, Zhengzhou China
Modified on October 15th 2016
Research on the single objective optimization algorithms is the basis of the research on
the more complex optimization algorithms such as multi-objective optimizations algorithms,
niching algorithms, constrained optimization algorithms and so on. All new evolutionary and
swarm algorithms are tested on single objective benchmark problems. In addition, these
single objective benchmark problems can be transformed into dynamic, niching composition,
computationally expensive and many other classes of problems.
In the recent years various kinds of novel optimization algorithms have been proposed
to solve real-parameter optimization problems, including the CEC’05, CEC’13, CEC’14 and
CEC’16 Special Session on Real-Parameter Optimization
[1][2][2]
. Considering the comments
on the CEC’14 test suite, we organize a new competition on real parameter single objective
optimization.
For this competition, we are developing benchmark problems with several novel
features such as new basic problems, composing test problems by extracting features
dimension-wise from several problems, graded level of linkages, rotated trap problems, and
so on. This competition excludes usage of surrogates or meta-models.
This special session is devoted to the approaches, algorithms and techniques for solving
real parameter single objective optimization without making use of the exact equations of the
test functions. We encourage all researchers to test their algorithms on the CEC’17 test suite
which includes 30 benchmark functions. The participants are required to send the final
results in the format specified in the technical report to the organizers. The organizers will
present an overall analysis and comparison based on these results. We will also use statistical
tests on convergence performance to compare algorithms that generate similar final solutions
eventually. Papers on novel concepts that help us in understanding problem characteristics
are also welcome.
The C and Matlab codes for CEC’17 test suite can be downloaded from the website
given below:
http://www.ntu.edu.sg/home/EPNSugan/index_files/CEC2017
1. Introduction to the CEC’17 Benchmark Suite
1.1 Some Definitions:
All test functions are minimization problems defined as following:
Min f(x),
T
12
[ , ,..., ]
D
x x xx
D: dimensions.
T
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]
D
. Different from CEC’13 and similar to CEC’14 each
function has a shift data for CEC’17.
All test functions are shifted to o and scalable.
For convenience, the same search ranges are defined for all test functions.
Search range: [-100,100]
D
.
M
i
: rotation matrix. Different rotation matrix are assigned to each function and each basic
function.
Considering that in the real-world problems, it is seldom that there exist linkages among all
variables. In CEC’17, same as CEC’15 the variables are divided into subcomponents
randomly. The rotation matrix for each subcomponents are 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’17 Test Suite
Table I. Summary of the CEC’17 Test Functions
No.
Functions
F
i
*=F
i
(x*)
Unimodal
Functions
1
Shifted and Rotated Bent Cigar Function
100
2
Shifted and Rotated Sum of Different Power
Function
*
200
3
Shifted and Rotated Zakharov Function
300
Simple
Multimodal
Functions
4
Shifted and Rotated Rosenbrock’s Function
400
5
Shifted and Rotated Rastrigin’s Function
500
6
Shifted and Rotated Expanded Scaffer’s F6
Function
600
7
Shifted and Rotated Lunacek Bi_Rastrigin
Function
700
8
Shifted and Rotated Non-Continuous Rastrigin’s
Function
800
9
Shifted and Rotated Levy Function
900
10
Shifted and Rotated Schwefel’s Function
1000
Hybrid
Functions
11
Hybrid Function 1 (N=3)
1100
12
Hybrid Function 2 (N=3)
1200
13
Hybrid Function 3 (N=3)
1300
14
Hybrid Function 4 (N=4)
1400
15
Hybrid Function 5 (N=4)
1500
16
Hybrid Function 6 (N=4)
1600
17
Hybrid Function 6 (N=5)
1700
18
Hybrid Function 6 (N=5)
1800
19
Hybrid Function 6 (N=5)
1900
20
Hybrid Function 6 (N=6)
2000
Composition
Functions
21
Composition Function 1 (N=3)
2100
22
Composition Function 2 (N=3)
2200
23
Composition Function 3 (N=4)
2300
24
Composition Function 4 (N=4)
2400
25
Composition Function 5 (N=5)
2500
26
Composition Function 6 (N=5)
2600
27
Composition Function 7 (N=6)
2700
28
Composition Function 8 (N=6)
2800
29
Composition Function 9 (N=3)
2900
30
Composition Function 10 (N=3)
3000
Search Range: [-100,100]
D
*
F2 has been excluded because it shows unstable behavior especially for higher dimensions, and
significant performance variations for the same algorithm implemented in Matlab, C
*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
2 6 2
11
2
( ) 10
D
i
i
f x x
x
(1)
2) Sum of Different Power Function
1
2
1
()
i
D
i
i
fx
x
(2)
3) Zakharov Function
24
2
3
1 1 1
( ) 0.5 0.5
D D D
i i i
i i i
f x x x
x
(3)
4) Rosenbrock’s Function
1
2 2 2
41
1
( ) (100( ) ( 1) )
D
i i i
i
f x x xx
(4)
5) Rastrigin’s Function
2
5
1
( ) ( 10cos(2 ) 10)
D
ii
i
f x x
x
(5)
6) Expanded Schaffer’s F6 Function
Schaffer’s F6 Function:
2 2 2
2 2 2
(sin ( ) 0.5)
( , ) 0.5
(1 0.001( ))
xy
g x y
xy
6 1 2 2 3 1 1
( ) ( , ) ( , ) ... ( , ) ( , )
D D D
f g x x g x x g x x g x x
x
(6)
