https://doi.org/10.31449/inf.v47i4.4531 Informatica 47 (2023) 569–576 569 
A Modified Spider Monkey Optimization Algorithm Based on Good-
Point Set and Enhancing Position Update 
Sabreen Fawzi Raheem
1
, Maytham Alabbas
2*
 
1
 Basra Technical Institute, Southern Technical University, Basrah, Iraq 
2
 Department of Computer Science, College of Computer Science and Information Technology, University of Basrah, 
Basrah, Iraq 
E-mail: sabreen.fawzi@stu.edu.iq
1
, ma@uobasrah.edu.iq
2*
   
*
 Corresponding author   
                                  
Keywords: good-point-set method, swarm intelligence, enhancing position update, spider monkey optimization 
Received: November 23, 2022 
Spider monkey optimization (SMO), developed based on the behavior of spider monkeys, is a recently 
added swarm intelligence algorithm. SMO is a stochastic population-based metaheuristic algorithm. 
Spider monkeys have a fission-fusion social structure. In addition to being an excellent tool for solving 
optimization problems, SMO provides good exploration and exploitation capabilities. In this work, we 
present a modified strategy for improving the performance of the basic SMO in two ways: (a) we use the 
good-point-set method instead of random initial population generation; and (b) by changing both the 
local leader and global leader phases, we modify the SMO position update approach to increase global 
convergence while avoiding local optima. We evaluate the proposed modified SMO algorithm on 20 
popular benchmark functions. The current findings prove that the proposed approach outperforms the 
standard SMO regarding result quality and convergence rate. 
Povzetek: Predstavljeni SMO, stohastičen algoritem, ki temelji na socialni strukturi pajkovih opic, 
izboljšuje osnovno različico z dvema pristopoma: metodo dobre točke in modificiranim posodabljanjem 
položaja za večjo globalno konvergenco. 
1 Introduction  
Nature has inspired many researchers and is therefore 
considered a rich source of inspiration. Nowadays, most 
algorithms are inspired by nature. These algorithms 
depend primarily on one of the successful properties of a 
biological system. Numerous natural phenomena have 
inspired academics to create population-based 
optimization (PBO) methods. Because these PBO 
methods evaluate fitness, the population of possible 
solutions is expected to gravitate toward the areas of the 
potential search spaces with the best fitness. In PBO 
algorithms, natural selection offers near-optimal 
solutions to complex optimization problems. 
In recent years, researchers have gained interest in swarm 
intelligence (SI). Studies have proven that algorithms 
based on SI have enormous potential for numerical 
optimization. The last few years have seen the 
development of many related algorithms. In this regard, 
there are several algorithms available, but not limited to 
particle swarm optimization (PSO) [1], ant colony 
optimization (ACO) [2], cuckoo search [3], bacteria 
foraging optimization (BFO) [4], bat algorithm [5], and 
artificial bee colony (ABC) [6]. 
Among the latest techniques to be developed is spider 
monkey optimization (SMO) [7], a newcomer to the class 
of SI algorithms. Spider monkey foraging behavior based  
on fission-fusion social structure (FFSS), which they use 
to find great food sources and mate, served as the model  
 
 
for this SMO algorithm. In the same way as any other 
PBO strategy, it includes the intrinsic population solution 
that denotes the spider monkey food source. 
While searching for the best solution, the SMO algorithm 
tries to find a suitable balance between exploration and 
exploitation. It ensures that the local optimal solution is 
traversed correctly during exploitation, and it explores 
the global search space to prevent the problem of 
entrapment in the local optimum during exploration. It 
has been discovered that SMO effectively explores local 
search [8]. 
As SMO is a relatively new algorithm, there is little 
literature available on it. The authors in [9] developed a 
modified position update in the SMO method, which 
includes two revisions to the basic SMO algorithm. The 
golden section search (GSS) technique was used to 
modify both the local leader phase (LLP) and the global 
leader phase (GLP). In [10], Kumar et al. proposed 
individual fitness as a new technique for updating the 
position of spider monkeys in the LLP, GLP, and local 
leader decision (LLD) phases. In [11], Kavita and Kusum 
proposed a modified version of SMO (TS-SMO), which 
uses tournament selection to increase the exploration 
capabilities of SMO and prevent premature convergence. 
Urvinder and Rohit [12] introduced a modified SMO 
(MSMO) method based on a dual-search technique for 
linear antenna array synthesis (LAA). Singh et al. [13] 
suggested a modified version of SMO (SMONM), which 
uses Nelder-Mead (NM) transformations to improve the 
ability of the LLP. The proposed SMONM approach has 

570 Informatica 47 (2023) 569–576 S.F. Raheem et al. 
the same number of phases as the conventional SMO, 
except for the LLP, which is modified using the NM 
reflection, expansion, and contraction transformations. If 
there is no improvement in the fitness function value 
after updating the solution with the original LLP, NM 
modifications are applied. 
The rest of this paper is organized as follows: Section 2 
briefly explains the fundamental SMO algorithm. Section 
3 describes the primary concept of the proposed 
approach. Section 4 discusses the test functions, 
simulation results, and comparison outcomes. Section 5 
provides a comprehensive explanation. 
 
2 Spider monkey optimization 
(SMO) 
Bansal et al. [7] introduced the SMO algorithm, a nature-
inspired evolutionary algorithm. The fission-fusion social 
structure (FFSS) of spider monkeys (SMs) is modeled in 
SMO. SMs live in groups of forty to fifty monkeys and 
separate into subgroups to look for food to reduce 
competition. The group is led by the most senior female, 
who is responsible for finding food sources. If she cannot 
find enough food for the group, she divides it into small 
subgroups of three to eight individuals. The local leader 
(LL) leads the subgroups and plans their foraging paths 
each day. The members of this group are responsible for 
finding food sources and adjusting their location 
according to the distance to the food source. It is 
important for these group members to interact with each 
other to maintain social bonds, especially if they 
encounter a stalemate. 
 
2.1 The SMO algorithm's phases 
SMO consists of seven phases. Below is a detailed 
description of each phase of SMO. The steps of the SMO 
algorithm's phases are given in Algorithm 1. 
2.1.1 Initialization phase 
Initially, SMO produces N of SMs with uniform 
distribution. Each SM i = 1, .., N is a D-dimensional 
vector. The number D indicates how many variables are 
involved in the optimization problem, and SM i is the i
th
 
individual in the population. Each individual is generated 
using Eq. 1. 
𝑆𝑀
𝑖 = 𝐿𝑏
𝑗 + 𝑟𝑎𝑛𝑑 (0,1)∗ (𝑈𝑏
𝑗 − 𝐿𝑏
𝑗 ),∀𝑗 ∈
{1,… ,𝐷 },∀𝑖 = {1,…,𝑁 },                                                  (1) 
                                                                      
where rand(0,1) is a random number between 0 and 1, 
the lower bound of the solution location is given by Lb j, 
and the upper bound of the solution location is given by 
Ub j. 
2.1.2 Local leader phase (LLP) 
During LLP, SMs change their present positions 
depending on information from the LL's experience as 
well as the experience of local group members. The 
fitness value of the newly acquired location is computed. 
If the new position's fitness value exceeds the old 
position's, the SM replaces its position with the new one. 
In this phase, the position update equation for the i
th
 SM 
(member of the k
th
 local group) is calculated as follows: 
 
𝑆𝑀𝑛𝑒𝑤 𝑖𝑗
= 𝑆𝑀
𝑖𝑗
+ 𝑟𝑎𝑛𝑑 (0,1)∗ (𝐿𝐿
𝑘𝑗
− 𝑆𝑀
𝑖𝑗
)+
𝑟𝑎𝑛𝑑 (−1,1)∗ (𝑆𝑀
𝑟𝑗
− 𝑆𝑀
𝑖𝑗
),                                      (2) 
 
where LL kj stands for the j
th
 dimension of the k
th
 local 
group leader position, SM ij stands for the j
th
 dimension of 
the i
th
 SM, and SM rj is the j
th
 dimension of the k
th
 SM that 
is selected at random within the k
th
 group, such that (r≠i). 
2.1.3 Global leader phase (GLP)  
The GLP phase begins once the LLP is completed. 
During this phase, each SM updates its position using Eq. 
3, considering the experience of the global leader (GL) 
and local group members. 
 
𝑆𝑀𝑛𝑒𝑤 𝑖𝑗
= 𝑆𝑀
𝑖𝑗
+ 𝑟𝑎𝑛𝑑 (0,1)∗ (𝐺𝐿
𝑗 − 𝑆𝑀
𝑖𝑗
)+
𝑟𝑎𝑛𝑑 (−1,1)∗ (𝑆𝑀
𝑟𝑗
− 𝑆𝑀
𝑖𝑗
),                                      (3) 
 
where GL j is the j
th
 dimension of the GL position and 𝑗 ∈
{1,2,…,𝐷 } is a randomly selected index. 
 
SM i's location is updated throughout this phase based on 
the probability prob i that can be calculated using Eq. 4. 
 
𝑃𝑟𝑜𝑏 𝑖 = 
𝑓𝑖𝑡𝑛𝑒𝑠𝑠 𝑖 ∑ 𝑓𝑖𝑡𝑛𝑒𝑠𝑠 𝑖 𝑁 𝑖 =1
.                                                   (4) 
2.1.4 Global leader learning (GLL)  
A greedy selection is used to update the GL's position. 
Consequently, the GL's position is updated based on the 
SM's position that has the best fitness. In addition, the 
GlobalLimitCount (GLLimit) is increased by one if the 
GL's position has not been updated. 
2.1.5 Local leader learning (LLL) 
A greedy selection method is used to update the position 
of the LL in that group, i.e., to reflect the position of the 
new LL. Selection is made based on the position of the 
SM in the group with the best fitness. A comparison is 
then conducted between the new position of the LL and 
the earlier one, and LocalLimitCount (LLLimit) is 
increased by one if no changes are made. 
2.1.6 Local leader decision (LLD) 
As long as no LL position has changed above a 
LocalLeaderLimit threshold, whether it is random or 
using Eq. 5, all group members are updated. This is 
determined by the perturbation rate (pr), which specifies 
how much perturbation is in the current position. 
 
If   rand(0,1) >= pr  then 
     Using Eq. 1. 
Else 

A Modified Spider Monkey Optimization Algorithm Based on… Informatica 47 (2023) 569–576 571 
𝑆𝑀𝑛𝑒𝑤 𝑖𝑗
= 𝑆𝑀
𝑖𝑗
+ 𝑟𝑎𝑛𝑑 (0,1)∗ (𝐺𝐿
𝑗 − 𝑆𝑀
𝑖𝑗
)+
𝑟𝑎𝑛𝑑 (0,1)∗ (𝑆𝑀
𝑖𝑗
− 𝐿𝐿
𝑘𝑗
).                                         (5) 
 
2.1.7 Global leader decision (GLD) 
After a certain number of iterations, the global leader's 
(GL's) position is observed. If it is not changed, the GL 
divides the population into subgroups. Initially, two 
groups are separated from the population, and the 
number of groups is increased until it reaches the 
maximum number of groups (MG). 
 
The pseudocode for the SMO algorithm is presented in 
Algorithm 1 [7]. 
 
Algorithm 1: SMO algorithm  
1: Initialize the population, the Local Leader Limit (LLlimit), 
the Global Leader Limit (GLlimit), and the perturbation 
rate (pr).       
2:  Calculate fitness  
3: Choose leaders (both global and local) through greedy 
selection. 
4: While (termination criteria is not) do 
5: Create new locations for all group members based on 
your own experience, local leader experience, and group 
member experience. Using Eq. (2) 
6: Use the greedy selection process to choose between an 
existing location and a newly generated location based 
on fitness, and then choose the better one.   
7: Using Eq. (4), compute the probability pi for each group 
member. 
8: Create new locations for all group members based on 
pi's selection, using self-experience, global leader 
experience, and group member experiences. Using Eq. 
(3). 
9:  By applying the greedy selection process to all groups, 
you can update the position of local and global leaders. 
10: If a Local group leader does not update her position 
after a set number of times (LLLimit), the algorithm will 
re-direct all members of that group to foraging. 
11:   If the Global Leader does not update her position for a 
set number of times (GLLimit), she divides the group into 
smaller groups using the steps below. 
12: End while      
 
3 The current work 
In the current work, two modifications have been made 
to make the basic SMO algorithm work better. The first 
modification is that we used the good-point-set method 
to generate a suitable initial population for the SMO 
algorithm. Then, we modified both LLP and GLP of the 
basic SMO algorithm. 
3.1 Modification of the initial population 
Initializing the population is one of the most crucial steps 
in metaheuristic optimization. A successful initial 
population can generate reasonable solutions faster and 
accelerate convergence. The basic SMO algorithm 
randomly generates the initial population using the 
stochastic method. However, the initial solutions do not 
cover the entire search space in quality and may be good 
or bad. To address these challenges, we used the good-
point-set (GPS) method [14] to generate the initial 
population of the SMO algorithm. GPS is generally used 
to create several individuals with uniform distributions to 
preserve the population's diversity. The GPS pseudocode 
is presented in Algorithm 2 [15, 16,17,18]. 
Algorithm 2: Pseudocode of the GPS method 
P is the lower prime number with P ≥ 2*D +3. 
 
1: For i=0 to N do 
2:     For j=0 to D do  
3:           𝑥 = 2 ∗ 𝑛 + 3, 
4:          While P ≠ x do 
5:                Set individual counter k = 2 
6:                For k = 2 to x – 1 do 
7:                       If mod(x , i) == 0 then 
8:                            x = x + 1 
9:                       Else  
10:                          P = x 
11:                     End if 
12:              End for 
13:          End while 
14:          𝐺𝑃𝑆
𝑖 ,𝑗 = i ∗ 2 ∗ cos(2 ∗ 𝜋 ∗
𝑗 𝑃 )      
15:          𝑋 𝑖𝑗
= 𝐿𝑏
𝑗 + 𝐺𝑃𝑆
𝑖 ,𝑗 ∗ (𝑈𝑏
𝑗 − 𝐿𝑏
𝑗 )    
16:    End for 
17: End for               
3.2 Modification of the position update in 
SMO  
Maintaining diversity in the LLP and GLP of SMO can 
balance exploring the entire search space and exploiting 
the best solutions found nearby. To achieve this balance, 
the proposed algorithm modifies both LLP and GLP of 
the basic SMO algorithm using the modified Eqs. 6 and 
7, respectively. 
 
𝑆𝑀𝑛𝑒𝑤 𝑖𝑗
= 𝑆𝑀
𝑖𝑗
+ 𝑟𝑎𝑛𝑑 (0,1)∗ (𝐿𝐿
𝑘𝑗
− 𝑆𝑀
𝑖𝑗
)+
𝑟𝑎𝑛𝑑 (−1,1)∗ (𝑆𝑀
𝑟 1𝑗 − 𝑆𝑀
𝑟 2𝑗 ).                                  (6) 
                                
𝑆𝑀𝑛𝑒𝑤 𝑖𝑗
= 𝑆𝑀
𝑖𝑗
+ 𝑟𝑎𝑛𝑑 (0,1)∗ (𝐺𝐿
𝑘𝑗
− 𝑆𝑀
𝑖𝑗
)+
𝑟𝑎𝑛𝑑 (−1,1)∗ (𝑆𝑀
𝑟 1𝑗 − 𝑆𝑀
𝑟 2𝑗 ).                                  (7) 
 
Where 𝑟 1 ∈ {1,2,…,𝑁 } is a different index from i that 
was chosen at random from the population, and 𝑟 2 ∈
{1,2,…,𝑁 } is a different index from i, where r1≠r2. 

572 Informatica 47 (2023) 569–576 S.F. Raheem et al. 
4 Experiments 
4.1 Test functions  
The improved SMO algorithm is evaluated using 20 
well-known benchmark optimization functions, f 1-f 20, as 
shown in Table 1. These continuous optimization 
problems cover a range of difficulties, search spaces, and 
multimodality. 
 
 
Table 1: The current 20 benchmark optimization functions for testing 
 
NO Function type 
 Search 
Range 
optimal value Formulation 
f 1 Rosenbrock UN [-50,50] 0 
𝑓 1
(𝑥 )= ∑ 100 (𝑥 𝑖 +1 
𝐷 −1
𝑖 =1
− 𝑥 𝑖 2
) 
2
+ (𝑥 𝑖 − 1)
2
 
f 2 sphere US [-100,100] 0 𝑓 2
(𝑥 )= ∑𝑥 𝑖 2
𝐷 𝑖 =1
 
f 3 Elliptic UN [-100,100] 0 𝑓 3
(𝑥 )= ∑(10
6
)
(𝑖 −1)/(𝐷 −1)
𝑥 𝑖 2
𝐷 𝑖 =1
 
f 4 Sum Squares US [-10,10] 0 𝑓 4
(𝑥 )= ∑𝑖 𝑥 𝑖 2
𝐷 𝑖 =1
 
f 5 Quartic US [-1.28,1.28] 0 𝑓 5
(𝑥 )= ∑𝑖 𝑥 𝑖 4
𝐷 𝑖 =1
 
f 6 kowalik MS [-5,5] 0.0003075 𝑓 6
(𝑥 )= ∑[𝑎 𝑖 −
𝑥 1
(𝑏 𝑖 2
+ 𝑏 𝑖 𝑥 2
)
𝑏 𝑖 2
+ 𝑏 𝑖 𝑥 3
+ 𝑥 4
]
2 11
𝑖 =1
 
f 7 Scaffer’s F6 MN [-100,100] 0 
𝑓 7
(𝑥 )
= 0.5 + 
 𝑠𝑖𝑛 2  
(√∑ 𝑥 𝑖 2 𝐷 𝑖 =1
) − 0.5
( 1 + 0.001 (√∑ 𝑥 𝑖 2 𝐷 𝑖 =1
))
2
 
f 8 Rastrigin MS [-5.12,5.12] 0 𝑓 8
(𝑥 )= ∑(𝑥 𝑖 2
− 10 cos (2𝜋 𝑥 𝑖 )
𝐷 𝑖 =1
+ 10) 
f 9 Griewank MN [-600,600] 0 
𝑓 9
(𝑥 )=
1
4000
∑𝑥 𝑖 2
𝐷 𝑖 =1
− ∏cos(
𝑥 𝑖 √𝑖 )
𝐷 𝑖 =1
 
+ 1 
f 10 Ackley MN 
[-
32.768,32.7
68] 
0 
𝑓 10
(𝑥 )
= 20+ 𝑒 − 20𝑒𝑥𝑝 [
 
 
 
−0.2 √
1
𝐷 ∑𝑥 𝑖 2
𝐷 𝑖 =1
]
 
 
 
− 𝑒𝑥𝑝 [
1
𝐷 ∑cos(2𝜋 𝑥 𝑖 𝐷 𝑖 =1
)] 
 

A Modified Spider Monkey Optimization Algorithm Based on… Informatica 47 (2023) 569–576 573 
f 11 Himmelblau MS [-5,5] 78.3323 f
11
(x)=
1
D
∑(x
i
4
D
i=1
− 16 x
i
2
+ 5 x
i
 
f 12 Step US [-100,100] 0 
 
f
12
(x)= ∑(⌊x
i
+ 0.5⌋
i
)
2
D
i=1
 
f 13 Beale UN [- 4.5,4.5] 0 
 
𝑓 13
(𝑥 )= [1.5 − (1 − 𝑥 2
)]
2
+ [2.25− 𝑥 1
(1
− 𝑥 2
2
)]
2
+ [2.625− 𝑥 1
(1
− 𝑥 2
3
)]
2
 
f 14 Easom UN [-100,100] -1 
𝑓 14
(𝑥 )
= −cos𝑥 1
 cos𝑥 2
 𝑒 ((−(𝑥 1
−𝜋 )
2
( −(𝑥 2
−𝜋 )
2
)
 
 
f 15 Schwefel MS [-500,500] 0 
f
15
(x)= 418.9829∗ D
− ∑x
i
sin(√|x
i
|)
D
i=1
 
f 16 Levy N.13 MN [-10,10] 0 
f
16
(x)= sin
2
(3πx
1
)
+ (x
1
− 1)
2
(1
+ sin
2
(3πx
2
))
+ (x
2
− 1)
2
(1
+ sin
2
(2πx
2
)) 

574 Informatica 47 (2023) 569–576 S.F. Raheem et al. 
f 17 
Goldstein-
Price 
MN [-2,2] 3 
𝑓 17
(𝑥 )= [1 + (𝑥 1
+ 𝑥 2
+ 1)
2
 (19
− 14𝑥 1
+ 13𝑥 1
2
− 14𝑥 2
+ 6𝑥 1
𝑥 2
+ 3𝑥 2
2
)] ∗ [30
+ (2𝑥 1
− 3𝑥 2
)
2
 (18
− 32𝑥 1
+ 12𝑥 1
2
− 48𝑥 2
− 36𝑥 1
𝑥 2
+ 27𝑥 2
2
) 
f 18 Colville MN [-10,10] 0 
𝑓 18
(𝑥 )= [100(𝑥 1
2
− 𝑥 2
)
2
+ (𝑥 1
− 1)
2
+ (𝑥 3
− 1)
2
+ 90(𝑥 3
2
− 𝑥 4
)
2
+ 10.1((𝑥 2
− 1)
2
+ (𝑥 4
− 1)
2
)
+ 19.8(𝑥 2
− 1)(𝑥 4
− 1)] 
 
f 19 Booth UN [-10,10] 2 
 
f 20 
Dekkers and 
Aarts 
MN [-20,20] 2 
f
20
(x)= 10
5
+ x
1
2
+ x
2
2
− (x
1
2
+ x
2
2
)
2
+ 10
−5
(x
1
2
+ x
2
2
)
4
 
 
4.2 Parameter setting 
The present work and the basic SMO share the following 
primary control parameters: 
 
• The Swarm size (N) = 80, 
• The Minimum Group (MG) = 5 , 
• LocalLeaderLimit = N 
• GlobalLeaderLimit = D * N , 
• Pr grows linearly over iterations by Eq. 8, where 
initial pr ∈ [0.1, 0.4], 
 
𝑝𝑟 = 𝑝𝑟 + (0.4/𝑖𝑡𝑒𝑟 ).                                          (8)                                                       
4.3 Experimental results 
To evaluate the proposed approach, we compared it to 
the basic SMO algorithm on 20 popular benchmark 
functions. Table 2 shows the mean and standard 
deviation (SD) of the solutions obtained by each 
algorithm based on 15 runs. The best outcomes 
highlighted in bold typeface. 
 
 
As shown in Table 2, the proposed approach outperforms 
the basic SMO algorithm in most cases in terms of 
convergence rate, convergence speed, and global 
optimization capability. 
5 Conclusions 
This work proposes two modifications to address the 
shortcomings of the basic SMO algorithm. The first 
modification improves the distribution of the initial 
population using the GPS method during the 
initialization phase. The second modification modifies 
the LLP and GLP phases to account for the intensified 
and diversified breathing space for local searches. We 
evaluated the proposed algorithm on 20 standard 
benchmark functions. The simulation results show that 
the proposed algorithm outperforms the basic SMO 
algorithm and provides accurate and robust solutions. 
We aim to improve the performance of the modified 
SMO algorithm in a number of ways using powerful soft 
computing tools. By using soft computing tools, we can 
control the parameters of the SMO algorithm, guide the 

A Modified Spider Monkey Optimization Algorithm Based on… Informatica 47 (2023) 569–576 575 
search process, and develop hybrid algorithms to create 
algorithms that are more efficient and effective than the  
basic SMO algorithm. 
 
 
Table 2: Comparison of test problem results
 
 
 
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Function D 
Basic SMO Modified SMO 
Mean SD Mean SD 
Rosenbrock 
10 967.95828 2311.63421 7.93559 0.34621
 
30 28.66994 1.93780 27.33593 0.36470 
sphere 
30 2.24285e-13 8.39023e-13 2.89926e-17 8.26299e-18 
60 7.85583e-17 7.66269e-18 2.63342e-17 7.62556e-18 
Elliptic 
30 5.75254e-17 9.29459e-17 2.78168e-17 7.55754e-18 
60 7.63723e-17 7.43771e-18 3.06328e-17 4.73009e-18 
Sum Squares 
30 7.62003e-10 2.85115e-09 3.04396e-17 7.97876e-18 
60 7.02444e-17 1.20772e-17 3.74735e-17 6.21793e-18 
Quartic 
30 1.16326e-23 4.03573e-23 1.49493e-23 4.31037e-23 
60 2.04903e-23 4.45292e-23 1.15639e-22 1.99527e-22 
Kowalik 4 0.00105094 0.0006879576 0.00032137 6.26241e-05 
Schaffer's F6 
10 0.03602 0.01491 0.00906 0.00242 
30 0.03327 0.00898 0.00972 1.03182e-09 
Rastrigin 
30 114.81071 19.08043 0 0 
60 103.08621 67.12331 0 0 
Griewank 
30 1.39276e-06 4.74962e-06 0 0 
60 9.75133e-11 2.09656e-10 0 0 
Ackley 
30 9.37203e-12 3.50519e-11 3.28626e-15 1.42108e-15 
60 4.23365e-15 8.86203e-16 3.99681e-15 0 
Himmelblau 100 - 78.3323 9.07 ×10
 -12
 - 78.3323 3.48 × 10 
-14
 
Step 30 0 0 0 0 
Beale 2 1.33 × 10 
-13
 4.00 × 10 
-16
 4.91 × 10 
-8
 2.36 × 10 
-8
 
Easom 2 -1 0 -1 9.05 ×10
 -13
 
Schwefel 30 3.82 × 10 
-4
 7.28 × 10 
-13
 3.82 ×10
 -4
 6.78 ×10
 -13
 
Levy N.13 2 9.03 × 10 
-20
 7.79 × 10 
-20
 1.97 ×10
 -20
 1.72 ×10
 -20
 
Goldstein-Price 2 3 4.81 × 10 
-8
 3 1.1 ×10
 -15
 
Colville 4 5.18 × 10 
-2
 5.59 × 10 
-2
 8.24 ×10
 -3
 1.83 ×10
 -2
 
Booth 2 1.75 ×10
 -18
 1.92 ×10
 -12
 1.33 ×10
 -18
 1.15 ×10
 -18
 
Dekkers and Aarts 2 -24776.52 7.27 ×10
 -12
 -24776.52 7.28 ×10
 -12
 

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