Optimization of Fuzzy Regression Transfer Learning using Genetic
Algorithm for Cross-Domain Mapping
MENGCHUN XIE
Department of Electrical and Computer Engineering,
National Institute of Technology, Wakayama College,
77 Noshima, Nada, Gobo, Wakayama, 644-0023,
JAPAN
Abstract: - Artificial intelligence and big data have become widely utilized in industry and thus machine
learning has been extensively researched. However, it is challenging to apply existing data-driven methods
when the amount of data is insufficient. Therefore, transfer learning, which reuses knowledge acquired from
domains with similar data characteristics and tasks, has gained attention for achieving fast and accurate model
learning in new domains. Although numerous transfer learning methods have been proposed for classification
problems, few have been proposed for regression problems. Moreover, conventional fuzzy regression transfer
learning tends to work well only in limited domain environments with extremely limited target data, making its
application to real-world data challenging. The present study applies a combination of regression models based
on Takagi-Sugeno fuzzy theory and transfers learning to regression problems in domains with incomplete
knowledge. We propose two methods, one based on a genetic algorithm and one based on differential evolution
combined with a genetic algorithm, for optimizing mapping for input space modification and applying them to
real datasets. The results of evaluation experiments demonstrate that the proposed methods have higher
efficiency and learning accuracy than those of conventional methods.
Key-Words: - Transfer learning, Fuzzy, Regression, Genetic algorithm, optimization, cross-domain mapping,
input space modification, Differential Evolution.
Received: August 14, 2023. Revised: October 29, 2023. Accepted: December 2, 2023. Published: December 31, 2023.
1 Introduction
Data science focuses on the processes and systems
involved in extracting knowledge from vast amounts
of data. Many machine learning methods assume
that training data are collected from a similar feature
space or distribution as that for the target domain.
When the data distribution changes, most statistical
models require the collection of new training data
and a complete reconstruction of the model.
However, these tasks are costly and sometimes
impossible.
Transfer learning, a machine learning method,
addresses this issue by leveraging knowledge from
models built in a source domain where extensive
data can be collected and applying this knowledge
to construct models for the target domain. Transfer
learning thus offers the potential for high-precision
learning with minimal data and a short training time.
Currently, transfer learning is applied to tasks
such as the classification of product reviews, spam
emails, and web documents and the estimation of
Wi-Fi location. Numerous methods have been
proposed, particularly for text and image
classification, [1], [2]. However, research on
transfer learning for regression problems remains
limited.
Transfer learning is often combined with deep
neural networks; however, domains with insufficient
information can introduce uncertainty in predictions.
Fuzzy systems, capable of efficiently handling
uncertainty, have gained attention in such situations.
Traditional regression transfer learning based on the
Takagi-Sugeno fuzzy theory is effective only when
the target domain has extremely limited training
data, [3]. This indicates a highly restricted domain
environment, making application to real datasets
challenging. Moreover, only particle swarm
optimization and differential evolution (DE)
methods have been used for optimizing mapping for
input space modification, [4], [5].
The present study first verifies the relationships
between learning data in different domains using a
regression transfer learning method based on the
Takagi-Sugeno fuzzy theory for domains with
incomplete knowledge. Then, two methods, one
based on a genetic algorithm (GA) and one based on
DE combined with a GA, are proposed for
optimizing mapping for input space modification.
WSEAS TRANSACTIONS on COMPUTERS
DOI: 10.37394/23205.2023.22.36
Mengchun Xie
E-ISSN: 2224-2872
316
Volume 22, 2023
We apply these methods to some real datasets and
assess their effectiveness through evaluation
experiments.
2 Related Research
2.1 Transfer Learning
Transfer learning is a machine learning approach
distinct from conventional machine learning, where
training and testing are typically conducted within
the same task. In transfer learning, the knowledge
gained from learning a given task is utilized for a
new task. In other words, transfer learning
effectively and efficiently addresses the data
scarcity problem by reusing data and learning
outcomes for a related problem, [1], [2].
In transfer learning, the source domain (where
knowledge is transferred from) and the target
domain (where knowledge is transferred to) are
defined. The applicability of transfer learning
depends on the strength of the relationship between
the source and target domains; specifically, when
there is a strong correlation between the tasks, data
features, and distributions across domains, transfer
learning is viable.
Many transfer learning methods have been
developed. Instance-based methods attempt to select
related source instances for transfer, [6], [7], [8],
[9]. One study investigated the transferability of
features within deep learning networks and the
potential reuse of features across various tasks and
domains, [10]. An unsupervised domain adaptation
method that employs backpropagation has been
developed, [11]. The amalgamation of transfer
learning and semi-supervised learning, with model
sharing across disparate tasks, has been investigated,
[12]. A method for the efficient transfer of data
across distinct domains using GAs for multiple-
kernel learning has been proposed, [13].
2.2 Fuzzy Regression Transfer Learning
The regression model based on the Takagi-Sugeno
fuzzy theory predicts outcomes according to the
following fuzzy rules, [3], [14]:
󰇛󰇜󰇛󰇜󰇛󰇜
where is a cluster centroid and is the
coefficient of a linear function.
This equation is constructed by forming a
membership function that represents the degree
of membership of the input to each cluster and
estimating the parameters of the linear function in
the conclusion part of the rule. The fuzzy regression
model predicts the output .
Fuzzy regression transfer learning combines the
Takagi-Sugeno fuzzy regression model and transfer
learning, [3]. Figure 1 shows the relationship
between the source and target domains. The
characteristics of the target domain should approach
those of the source domain because the
characteristics of the two domains are similar but
never the same. Therefore, the feature quantity of
the target domain is made to approach the feature
quantity of the source domain by passing the
mapping Φ.
Fig. 1: Relationship between source domain and
target domain
3 Fuzzy Regression Transfer
Learning Using Genetic Algorithm
In fuzzy regression transfer learning, when applying
the fuzzy regression model M constructed based on
the Takagi-Sugeno fuzzy theory to the target
domain, it is necessary to modify the input space.
3.1 Modification of Input Space
In the present study, the input space is modified as
shown in Figure 2 to bring the characteristics of the
target domain data closer to those of the source
domain data.
Fig. 2: Modification of input space using nonlinear
continuous mapping
WSEAS TRANSACTIONS on COMPUTERS
DOI: 10.37394/23205.2023.22.36
Mengchun Xie
E-ISSN: 2224-2872
317
Volume 22, 2023
Here, M is a model built in the source domain.
Model M' is model M combined with the nonlinear
continuous mapping Φ.
Modifying the input space specifically means
that the number of features in the input data in the
target domain is modified so as to be adapted to
model M. The input space 󰆒for the target domain is
modified by obtaining the mapping󰇛
󰆒) of each
input variable in the following equation:
󰇛󰆒󰇜
󰇛󰆒󰇜
󰇛󰆒󰇜
󰇛󰆒󰇜






󰇛󰇜
where  is the ith input variable of 󰆒. The
mapping for each input variable is constructed
through a network that is composed of P nodes
() located in the middle layer and
a single node located in the output layer. The nodes
in the middle layer are a sigmoid function consisting
of the two parameters in the following equation:

󰆓󰇛󰇜
 
When modifying the input space, it is important
to optimize the parameters α and β in the sigmoid
function and the weight W. In the present study, we
adopt a GA to optimize these parameters and
evaluate the improvement of the resulting limited
domain environment.
3.2 Optimization of Mapping using Genetic
Algorithm
GAs are optimization algorithms inspired by natural
selection and genetics. They belong to the broader
category of evolutionary algorithms and have been
widely used to find approximate solutions to
optimization and search problems. GAs are based on
the principles of evolution, including selection,
crossover (recombination), and mutation, [15], [16],
[17], [18], [19], [20].
In this study, we apply a GA to optimize the
parameters for the mapping Φ. The representation of
individuals in the GA uses a matrix whose size is
determined by the number of attributes and the
number of nodes. The representation of an
individual for parameter α is shown in Figure 3.
Similar representations are used for β and W. Here,
since we use a real-valued GA, each element in the
matrix is a random real number within a specified
range.
Fig. 3: Representation of individual for parameter α
in genetic algorithm
The fitness function uses the mean squared error
(MSE):

󰇛󰇜
 󰇛󰇜
where is a predicted value based on the input
space modified using the parameters of the
individual in the current generation and is a
target value.
Finally, for genetic manipulation, single-point
crossover is performed, as shown in Figure 4. Each
element of the matrix is stochastically mutated one
by one. The individuals are then compared and the
one with the best fitness is selected. Additional
individuals are selected by roulette selection. These
individuals make up the next generation.
Fig. 4: Diagram of single-point crossover
3.3 Optimization of Mapping Using
Differential Evolution Combined with
Genetic Algorithm
In the optimization of mapping using a GA, it is
considered that in a real-valued GA, the fitness of
the initial individuals has a significant impact on the
final accuracy. Increasing the population size,
mutation probability, and number of generations in
the GA can enhance the coverage of the search
space; however, this may also increase the
computation time.
DE is a population-based optimization algorithm
that falls under evolutionary algorithms. It
iteratively evolves a population of candidate
WSEAS TRANSACTIONS on COMPUTERS
DOI: 10.37394/23205.2023.22.36
Mengchun Xie
E-ISSN: 2224-2872
318
Volume 22, 2023
solutions through processes such as mutation,
crossover, and selection. DE is known for its
simplicity and effectiveness in solving optimization
problems across various domains, [21], [22], [23],
[24].
In this study, we propose a mapping optimization
method that combines DE and GA, denoted as DE-
GA. Initially, optimization is conducted using DE.
Then, further optimization is conducted by applying
a GA to the solution set obtained from DE. In this
approach, the initial optimization using DE is
performed to enhance the fitness of the initial
individuals for the real-valued GA. It is expected
that combining DE with a GA will improve the
prediction accuracy (even though a smaller solution
set and fewer generations are used compared to
those for GA alone) and reduce the computation
time.
3.4 Proposed Model and Evaluation Metric
In this study, we propose five patterns for model M'
in the target domain, where the model is transferred
from the constructed model in the source domain.
: model built with only target data (Φ=1)
: model built with only source data (Φ=1)
: Φ and M optimized using DE
: Φ and M optimized using GA
: Φ and M optimized using DE-GA
The evaluation metric used in the validation
experiments on a real dataset is the root-mean-
square error (RMSE) between the target values
and the predicted values 󰆒, as defined in (5). In
addition, the standard deviation (SD) of the
prediction errors, defined in (6), is calculated to
assess the variability of the predictions.
󰆒
represents the mean value of the predicted values.
Furthermore, to assess the efficiency of the models,
a comparison of the computation time from model
learning to prediction is conducted for , ,
and .

󰇛󰇜
 󰇛󰇜


 󰇛󰇜
4 Experiment and Results
Validation experiments were conducted using the
proposed five models on real datasets. The five
models were applied to various tasks for real
datasets. The proposed method was evaluated in
terms of prediction accuracy and computation time.
Cross-validation was also performed. The
experimental conditions are shown in Table 1.
Table 1. Experimental conditions
Fuzzy Regression
DE
*
Solution Group
200
*
Generation
200
Mapping
Scaling Factor F
*
3
Crossover Rate CR
*
GA
DE-GA
50
Solution Group
(Individuals)
50
1000
DE generation
100
0.2
GA generation
100
0.05
No other changes
Since did not require five-fold cross-
validation, all target data were used as the test data
for this model. In addition, the parameters were set
to values believed to be sufficient for the learning of
each model based on preliminary experiments. For
parameters C and m for the fuzzy regression model
and parameters F and CR for DE, the values were
set to accommodate the given dataset.
4.1 Experiment 1: Boston Housing Dataset
In this experiment, the Boston housing dataset, an
open dataset for regression problems, was utilized.
For the transfer learning process, the input space
was constructed using two attributes from this
dataset, namely ROOM (average number of rooms
in each neighborhood) and DISTANCE (distance
from each neighborhood to five employment centers
in Boston).
The target variable was the median housing price
in each neighborhood. For the transfer learning task,
instances with the attribute TAX (property tax rate
per $10,000) below 600 were considered as the
source data (one dataset with 370 instances) and
those with TAX equal to or above 600 were
considered as the target data (three datasets with 30,
60, and 90 instances, respectively). The input space
for the two domains is shown in Figure 5. As
shown, the two domains have different data
distributions.
WSEAS TRANSACTIONS on COMPUTERS
DOI: 10.37394/23205.2023.22.36
Mengchun Xie
E-ISSN: 2224-2872
319
Volume 22, 2023
Table 2. Results for Boston housing dataset
Target
M'T
M'S
M'DE
M'GA
M'DE_GA
30
104.32
8.44
5.38
9.75
50.24
6.65
12.69
4.71
37.80
26.33
32.47
33.61
32.50
34.54
18.61
17.51
24.85
39.33
20.00
35.51
Mean
49.94±28.42
16.71
23.06±13.34
17.83±8.96
20.22±12.41
60
13.32
9.20
6.52
7.21
27.63
24.47
21.94
22.40
11.80
4.83
6.70
4.05
5.64
7.46
4.96
10.39
9.58
6.42
9.18
6.77
Mean
13.59±7.48
13.62
10.48±7.14
9.86±6.19
13.37±5.27
90
24.71
25.68
21.08
19.53
17.21
12.86
12.58
11.33
7.35
9.13
7.86
9.05
5.32
4.85
5.57
4.14
5.12
4.78
5.27
4.43
Mean
11.94±7.78
12.22
11.46±7.72
10.47±5.92
9.70±5.63
Time Ratio
1.00
4.66
0.56
Fig. 5: Input space for source and target domains in
Experiment 1
Table 2 shows the results of five-fold cross-
validation for each trial, including the RMSE,
average, and SD for various target data sizes and the
ratio of the average computation time. The
parameters used were C = 6, m = 1.8, F = 0.5, and
CR = 0.9. As shown in the table, and 
often have smaller errors than those for the other
models, indicating higher prediction accuracy.
However, for the target dataset with 30 instances,
both and  are inferior to .
4.2 Experiment 2: Diabetes Dataset
In this experiment, we utilized an open dataset
related to diabetes for regression analysis. The input
space was constructed using three attributes, namely
BMI (body mass index indicating obesity), BP
(blood pressure), and GLU (blood glucose level).
The target variable was the progression of diabetes
after 1 year.
Here, instances with ages below 60 were used as
source data (one dataset with 339 instances) and
those with ages equal to or above 60 were used as
target data (three datasets with 30, 60, and 90
instances, respectively). The input space for the two
domains is shown in Figure 6. In contrast to
Experiment 1, the two domains have similar data
distributions.
Fig. 6: Input space for source and target domains in
Experiment 2
Table 3 shows the results of five-fold cross-
validation for each trial. The parameters used were
C = 6, m = 1.8, F = 0.5, and CR = 0.7. A shown in
the table, depending on the data split, there are cases
where and have smaller errors than
those for the other models. However, on average,
regardless of the number of instances in the target
dataset,  has the best prediction accuracy in all
cases.
WSEAS TRANSACTIONS on COMPUTERS
DOI: 10.37394/23205.2023.22.36
Mengchun Xie
E-ISSN: 2224-2872
320
Volume 22, 2023
Table 3. Results for diabetes dataset
Target
M'T
M'S
M'DE
M'GA
M'DE_GA
30
4376.53
62.83
84.05
52.41
678.69
149.21
128.89
114.99
193.28
62.55
42.67
47.36
5554.48
89.92
76.84
75.85
91.44
87.94
48.28
51.75
Mean
2178.88±2314.08
60.60
90.49±31.63
76.15±30.79
68.47±25.30
60
73.64
66.10
63.60
62.93
64.41
66.77
61.50
65.95
56.75
65.61
65.63
73.66
70.60
64.17
67.98
54.82
74.97
63.10
59.24
52.68
Mean
68.08±6.73
56.63
65.15±1.33
63.59±3.06
62.01±7.63
90
68.49
72.35
57.32
55.19
54.30
61.14
69.75
67.02
54.44
62.46
64.66
54.76
47.18
44.61
55.29
42.57
64.67
49.48
59.45
54.22
Mean
57.82±7.72
53.61
58.01±9.88
61.29±5.26
54.75±7.74
Time Ratio
1.00
3.60
0.48
Table 4. Results for cancer dataset
Target
M'T
M'S
M'DE
M'GA
M'DE_GA
30
50.42
27.58
29.54
25.53
60.93
44.51
38.29
39.71
2362.65
71.81
63.92
100.46
2208.44
27.60
42.51
40.22
208.68
46.50
46.06
44.37
Mean
978.22±1070.00
38.32
43.60±16.24
44.06±11.36
50.06±25.99
60
33.38
37.10
36.22
34.87
31.84
33.11
34.61
35.92
35.80
40.33
39.39
34.37
503.46
26.89
23.15
26.33
48.28
23.07
35.52
32.59
Mean
130.55±186.54
36.15
32.10±6.36
33.78±5.55
32.81±3.42
90
39.58
36.71
32.96
32.02
37.47
36.54
36.75
35.01
34.56
28.12
32.62
28.18
31.91
29.18
36.90
28.04
36.59
29.28
28.99
28.08
Mean
36.02±2.61
34.67
31.97±3.82
33.64±2.95
30.27±2.81
Time Ratio
1.00
3.36
0.42
4.3 Experiment 3: Cancer Dataset
In this experiment, a dataset related to cancer
incidence rates by county in the United States was
utilized. The input space was constructed using two
attributes, namely IR (cancer diagnosis rate per
capita for each county) and INCOME (median
income of residents in each county). The target
variable was the per capita cancer mortality rate for
each county. Instances with a poverty rate of less
than 30% were used as source data (one dataset with
2930 instances) and those with a poverty rate equal
to or above 30% were used as target data (three
datasets with 30, 60, and 90 instances, respectively).
The input space for the two domains is shown in
Figure 7. The two domains have different data
distributions.
Table 4 shows the results of five-fold cross-
validation for each trial. The parameters were set as
C = 6, m = 1.4, F = 0.5, and CR = 0.7. As shown in
the table, there are cases where  has smaller
errors than those for the other models. In
addition,  often has the smallest errors
(highest prediction accuracy). However, for the
target dataset with 30 instances,  has the best
results.
WSEAS TRANSACTIONS on COMPUTERS
DOI: 10.37394/23205.2023.22.36
Mengchun Xie
E-ISSN: 2224-2872
321
Volume 22, 2023
Fig. 7: Input space for source and target domains in
Experiment 3
The results for the three experiments confirm
that fuzzy regression transfer learning is effective
for real datasets. However, in Experiment 2, for
which the input space distributions of the source and
target domains overlapped, the modification of the
input space adversely affected the learning process.
In addition, due to the large variability in input data
in a real dataset, the method performed well even
with a large number of instances in the target
dataset. On the other hand, for a target dataset with
30 instances, learning was insufficient. These
observations suggest that depending on the
conditions (e.g., data distribution and the number of
instances), negative transfer through mapping may
occur.
Furthermore, a comparison of the computation
times indicates that  was approximately 3.5 to
4.5 times faster than  in all experiments. On
the other hand,  was about half as fast as
. Considering both prediction accuracy and
computation time, it can be concluded that 
is the best model, verifying the efficient
optimization of parameters with DE-GA.
Although the proposed method requires certain
conditions (e.g., the number and distribution of data
instances in the source and target domains) to be
met, it is applicable to various real-world regression
problems.
5 Conclusion
In the present study, we applied fuzzy regression
transfer learning to regression problems in domains
with incomplete knowledge. First, for the target
task, we found that the impact of the ratio of data
between the source and target domains was
negligible, but the distribution of data between the
two domains had a significant effect. Incorporating
a GA for optimizing the mapping for input space
modification improved prediction accuracy and
reduced computation time. The effectiveness of the
proposed method was confirmed on real-world
datasets. The proposed transfer learning method can
only be applied when the dimensions and attributes
of the input space are the same.
The following challenges will be considered in
future studies:
(1) Handling datasets with different dimensions
and attributes. The current method is applicable only
when the dimensions and attributes of the input
space are the same. Methods that can handle
datasets with different dimensions and attributes are
required.
(2) Experiments using more diverse domains.
Although the experiments in this study were
conducted on real-world datasets, the effectiveness
of the proposed method should be further verified
using more diverse domains and datasets.
(3) Automated parameter tuning. Some
parameters in the current method are manually set.
Methods for the automatic adjustment of these
parameters should be developed.
(4) Enhancing robustness to noise and missing
data. Real-world datasets often contain noise and/or
missing data. Improving the robustness of the
proposed method in such situations is important.
References:
[1] S. J. Pan and Q. Yang, A Survey on Transfer
Learning, IEEE Transactions on Knowledge
and Data Engineering, vol. 22, no. 10, 1345-
1359, October 2010.
[2] Weiss, K., Khoshgoftaar, T.M. & Wang, D. A
survey of transfer learning. J. Big Data, 3, no.
9, March 2016.
[3] H. Zuo, G. Zhang, W. Pedrycz, V. Behbood,
J. Lu, Fuzzy Regression Transfer Learning in
Takagi-Sugeno Fuzzy Models, IEEE
Transactions on Fuzzy Systems, vol.25, no.6
December 2017.
[4] Ahmed G. Gad, Particle swarm optimization
algorithm and its application: a systematic
review, Archives of Computational Methods
in Engineering, Springer Link, Vol. 29, 2531-
2561, April 2022.
[5] F. zhao, C. Wang, H. Liu, Differential
evolution - based transfer rough clustering
algorithm, Vol. 9, 5033-5047, February 2023
[6] Y. Wang, J. Zhai, Y. Li, K. Chen, H. Xue,
Transfer learning with partial related
“instance-feature” knowledge,
Neurocomputing, 310, 115-124, 2018.
[7] J. Huang, A. J. Smola , A. Gretton, K.M.
Brorgwardt, B. Scholkopf, Correcting sample
WSEAS TRANSACTIONS on COMPUTERS
DOI: 10.37394/23205.2023.22.36
Mengchun Xie
E-ISSN: 2224-2872
322
Volume 22, 2023
selection bias by unlabeled data, Proceedings
of the International Conference on Neural
Information Processing Systems, 601-608,
2006.
[8] M.E. Taylor, P. Stone Transfer learning for
reinforcement learning domain: a survey, J.
Math. Learn, Res., no. 10 1633-1685, 2009.
[9] R.E. Schapire, Y. Freund, P. Bartlett, W.S.
Lee, Boosting the margin: a new explanation
for the effectiveness of voting methods, ICML
'97: Proceedings of the Fourteenth
International Conference on Machine
Learning, p.322-330, 1997.
[10] J. Yosinski, J. Clune, Y. Bengio, H. Lipson,
How transferable are features in deep neural
networks? In Advances in Neural Information
Processing Systems, vol. 27, 3320-3328, 2014
[11] Y. Ganin, V. Lempitsky, Unsupervised
domain adaptation by backpropagation. In
International Conference on Machine
Learning, p.1180-1189, 2015.
[12] S. Ruder, An overview of multi-task learning
in deep neural networks. arXiv preprint
arXiv:1706.05098, 2017
[13] W. Zhang, Z. Li, Y. Chen, Domain transfer
multiple kernel learning using genetically
evolved kernels. Neurocomputing, 171, 303-
312, 2016.
[14] T. Takagi, M. Sugeno, Fuzzy Identification of
Systems and Its Applications to Modeling and
Control, IEEE Transactions on System, Man,
and Cybernetics, vol. SMC-15, no.1, 1985.
[15] J. H. Holland, Adaptation in Natural and
Artificial Systems. University of Michigan
Press, 1975
[16] A. E. Eiben, J. E. Smith, Introduction to
Evolutionary Computing, Springer Link,
2015, https://doi.org/10.1007/978-3-662-
44874-8.
[17] M. Wooldridge, Intelligent Agents, Multiagent
Systems: A modern Approach to Distributed
Artifical Intelligence, edited by Gerhard
Weiss, The MIT Press, 2000
[18] M. Xie, H. Ogura, T. Odaka, J. Nishino,
“Application of Genetic Algorithm to Inter-
correlated Nonlinear Knapsack Problem”,
1996 International Symposium on Nonlinear
Theory and its Applications, p.145-148, 1996
[19] M.C. Xie, Cooperative Behavior Rule
Acquisition for Multi-Agent Systems Using a
Genetic Algorithm, Proceedings of the
IASTED International Conference on
Advances in Computer Science and
Technology, p.124-128 ,2006
[20] S. M. Elsayed, R. A Sarker, and D. L. Essam,
A new genetic algorithm for solving
optimization problems, Engineering
Application of Artificial Intelligence, Vol. 27,
p.57-69, 2014
[21] R. Storn, K. Price, Differential Evolution – A
Simple and Efficient Heuristic for Global
Optimization over Continuous Spaces,
Journal of Global Optimization, vol.11, no. 4,
341-359, 1997
[22] S. Das, P.N. Suganthan, Differential
Evolution: A Survey of the State-of-the-Art.
IEEE Transactions on Evolutionary
Computation, vol. 15, no.1, p.4-31, 2011.
[23] A.K. Qin, V. Huang, P.N. Suganthan,
Differential Evolution Algorithm with
Strategy Adaptation for Global Numerical
Optimization. IEEE Transactions on
Evolutionary Computation, vol. 13, no.2,
p.398-417, 2009.
[24] T. Eltaeib, A. Mahmood, Differential
Evolution: A Survey and Analysis, Applied
Sciences, vol.8, no.10, 2018,
https://doi.org/10.3390/app8101945.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The authors equally contributed in the present
research, at all stages from the formulation of the
problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on COMPUTERS
DOI: 10.37394/23205.2023.22.36
Mengchun Xie
E-ISSN: 2224-2872
323
Volume 22, 2023