Combination of Adaptive Fuzzy Inference System and Simulated Annealing Algorithm-Based for Malaria Susceptibility Mapping in Daknong Province

VNU Journal of Science: Earth and Environmental Sciences, Vol. 34, No. 4 (2018) 80-88 
 80 
Combination of Adaptive Fuzzy Inference System 
 and Simulated Annealing Algorithm-based for Malaria 
Susceptibility Mapping in Daknong Province 
Bui Quang Thanh* 
Faculty of Geography, VNU University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam 
Received 23 September 2018 
Revised 07 December 2018; Accepted 11 December 2018 
Abstract: Adaptive Neuro-Inference system (Anfis) has been widely used in recent studies aiming 
at generating probabilities of unseen data in binary classification application. It is normally used in 
combination with optimization algorithms for tuning its parameters to generate optimal objective 
values. This study proposed a state-of-the-art method using Simulated Annealing to improve Anfis 
performance. Malaria occurrences and spatial variation of environmental, socio-economic factors in 
Daknong province, Vietnam were selected for case study. For accuracy assessment, Receiver 
Operating Characteristic curve, Cost curve were used and the predicted map was compared to 
several benchmark classifiers. The results showed that the S-Anfis (AUC = 0.912, RMSE =0.335) 
outperformed Support Vector Machine (AUC = 0.902, RMSE =0.364), Multiple Layer Perceptron 
(AUC = 0.868, RMSE =0.430). Although, the performance of S-Anfis depended on proper selection 
of input factors and geographic variations of those, we concluded that this method could be an 
alternative in mapping susceptibility of malaria. 
Keywords: Anfis, Simulated annealing, malaria. 
1. Introduction 
As report by [1], risk of Plasmodium 
falciparum (P.f) and Plasmodium vivax (P.v) 
malaria was significantly worsening in less 
developed and isolated regions around the world. 
The most prominent regions are those which 
have limited accessibility to health services or 
________ 
 Tel.: 84-943672345. 
 Email: qthanh.bui@gmail.com 
 https://doi.org/10.25073/2588-1094/vnuees.4304 
disease preparedness programs. In which 
community susceptibility to malaria is one of the 
key index for disease control and prevention 
program in every country. Transmission of this 
disease is mostly influenced by physical 
environment, climatic and socioeconomic 
condition. 
 https://doi.org/10.25073/2588-1094/vnuees.4304 
B.Q. Thanh / VNU Journal of Science: Earth and Environmental Sciences, Vol. 34, No. 4 (2018) 80-88 
81 
Currently, the relation of those variables has 
been studied with support of recent development 
of spatial technology and data mining 
techniques. Specifically, susceptible mapping is 
widely used as it provides probability variations 
of malaria infection rate as consequence of non-
linear modelling of physical and social 
influential factors. Most recent researches on 
spatial variation of malaria focused on 
application of data mining classifiers and their 
tweeted versions. In which neural network 
family, support vector machine, decision rules 
are among common techniques. 
Another approach is aiming at exploring 
natural reasoning with application of fuzzy 
logics. Fuzzy logic relies on human 
understanding in defining membership relation 
between input variables. It is customized to 
match diversity of input data. Among all fuzzy 
logic tools, Adaptive Neuro Fuzzy Inference 
System (Anfis) is one of the most common 
algorithm in classification application. It is one 
of the greatest tradeoff among Artificial Neural 
Networks and fuzzy logic systems. There were 
many theoretical researches and pratical works 
aiming at exploring the predictive capability of 
Anfis, in which the system parameters were 
tuned by optimization algorithms. There were 
also several studies on community diseases but 
few focused on tuning Anfis parameters. 
This study proposed a new hybrid method 
named S-Anfis, using Simulated Annealing 
optimization algorithm to maximize 
performance of regular Anfis. Malaria 
occurrences and independent variables in 
Dakong provine, Viet Nam were selected as 
input database for training and validating the 
proposed model. The rest of the paper is 
organized as follows: the next section provides 
description of the study area and data used; the 
third one introduces research methodology; the 
fourth includes results and discussions; 
conclusion and final remarks are in the last 
section. 
2. Data and methods 
2.1. Study area and Malaria incidences 
The study area is located in the south western 
part of the central highlands region of Viet Nam, 
geographically defined between 11o45’ to 12o50’ 
northern latitudes and between 107o13’to 
108o10’ eastern longitudes (Figure 1). The 
province is characterized by moderate 
temperature and complex topography that 
spatially varies from 600m to 1982m. According 
to provincial information portal 
(daknong.gov.vn), the province is home for 
several ethnic minority groups, of which 65% of 
total population is Kinh (largest community in 
Viet Nam). The combination of population and 
physical environment has shaped the livelihoods 
of local community, education levels as well as 
attitudes towards disease control and prevention. 
The prediction of malaria susceptibility is 
mostly influenced by input databases. The 
proper selection of input data affects prediction 
accuracy how malaria incidences spatially vary. 
In fact, there are two way to measure malaria 
occurrences, in which malaria occurrences are 
measured by point-based locations as in [2, 3] or 
aggregated data (polygon – based aggregated 
data) as in [4]. The first manner requires exact 
coordinates of individual surveys and prediction 
map are usually measured for every single 
locations. The second one use average data 
within certain boundaries (administrative 
boundaries are usually used) and risk probability 
is unique for the whole polygon. 
Due to limitation in data colle ...  
2.3. Methods 
Since application of data mining techniques 
in malaria susceptibility mapping is still rare, 
particularly hybrid method that combines single 
classifier and an optimization algorithm. This 
study verifies the capability of simulated 
annealing optimization in selecting the optimal 
parameters for Anfis through minimizing the 
Root Mean Square Error as the objective 
functions.
Adaptive Fuzzy Inference System (Anfis) 
Figure 3. Adaptive Neuro-Inference System 
This techniques was first introduced in early 
1990s and has been widely used in variation of 
research topics. Anfis takes advantages of neural 
network and Takagi-Sugeno/ Mandanni rules in 
fuzzy logics. 
Simulated Annealing 
Taking idea of the state of physical process 
of crystallization aiming at bring the state to 
minimum energy state, SA was developed to 
minimize or maximize the global optimum of a 
function [5]. The optimization process involves 
permutation of new position that inspires new 
state with new energy value. This new value is 
compared to the previous one by pre-defined 
conditions. If passed, the new state is kept as 
current state and the iteration continues until 
meeting maximum number of iteration or 
desirable energy value. Typical pseudocode 
presents simulated annealing heuristic as follow: 
 Start initial state with value = f0 
 i = 1 
 Repeat until Lmax iteration or State level 
reached 
Pick a random state 
If fi<fi−1 then value = fiElse 
If exp (
fi−1−fi
si−1
)> random[0,1] then value = fi 
 si = r ∗ si−1 
i = i + 1 
 Ouptut: the final state with valuefi 
3. Proposed S-Anfis for malaria susceptibility 
mapping 
3.1. Dataset standardization 
Depending on characteristics of data mining 
algorithms, real values of input datasets might be 
directly used as in [6] or can be classified into 
classes as in [7] before further analysis. 
Normally, for the first choice, variables are 
measured in different units and scales. It is 
difficult to use this type in some classifiers or 
performance of classification model might be 
reduced. Decision to choose the second type 
depends on how many classes are determined 
and how to select threshold values to separate the 
classes. To some extent, this type generalizes 
nature of dataset and data detail might be lost. In 
this study, we used absolute value for the dataset 
and standardize it into similar unit by using this 
conversion equation. 
𝑥𝑖𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑧𝑒𝑑 = (𝑥𝑖 − min) (max − min)⁄
B.Q. Thanh / VNU Journal of Science: Earth and Environmental Sciences, Vol. 34, No. 4 (2018) 80-88 
85 
Figure 4. Simulated annealing diagram. 
3.2. Initialization of S-anfis 
Proposed workflow of S-Anfis is showed in 
(Figure 4), in which 448 samples were divided 
into two packs: 70% for training data and 30% 
for validation. Each sample consisted of 13 
controlling factors that were clearly defined in 
above section (Figure 2). One of the key issues 
for good performance of S-Anfis is a proper 
selection of number of rules (or numbers of clusters 
prior to further processes). Normally, a clustering 
algorithm is used to define number of clusters if 
there is no prior understanding of the dataset. 
This algorithm usually generates high number of 
clusters that makes model complicated and time-
consuming. Literature has showed that by 
reducing the clusters, model performance will be 
increased [7]. Through several trials by comparing 
RMSEs we came up to alternatively run the 
model with 4,5,8 clusters. The best performance 
would be selected to produce malaria susceptible 
map. 
One of the options in running the model is to 
define constraint bounds for parameters. Since 
value ranges of all variables are limited within 
[0,1]. As a consequence, 𝑎𝑖, 𝑏𝑖, 𝑐𝑖 are also fallen 
within the similar [0,1] range. Parameters𝑝𝑖 of 
linear transformation in layer 5 have no bounds, 
but we decided to limit those within [0,1] for 
easy calculation. 
On the other hand, the Simulated annealing 
required proper selection of initial parameters, in 
which initial temperature, temperature cooling 
function are the most important parameters. 
These values define acceptance probability of 
new states. Higher initial temperature avoids 
sudden jump of accepted new state. Through 
several trial, we finally used default value for 
initial temperature at 100, exponential function 
for temperature cooling process and maximum 
iteration at 300. The model started with 
initializing 𝑎𝑖 , 𝑏𝑖, 𝑐𝑖, 𝑝𝑖 and those parameters 
were used to generate RMSE for the first 
iteration. The result was checked if it met 
predefined threshold or number of iteration 
exceeded 300. The model continued until 
stopping condition was met and the final model 
was validated by validation data. 
(Figure 5) shows decreasing trend of RMSE 
values since the best function values of RMSE 
were plotted again each iteration. RMSEs had 
sudden jumps in all three tests and kept 
unchanged after around the 200th and the 250th 
iteration. Models with 5 clusters resulted in 
smallest RMSE values and were used for 
generating malaria susceptible map (Figure 7). 
Figure 5. RMSE after 300 iterations. 
B.Q. Thanh / VNU Journal of Science: Earth and Environmental Sciences, Vol. 34, No. 4 (2018) 80-88 
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Figure 6. ROCs and AUC values for validation data. 
3.3. Performance assessment 
For accuracy assessment, Receiver 
Operating Curve (ROC), Area under ROC 
(AUC), Cost Curve are widely used for 
performance assessment of classifications 
models. (Figure 6) shows ROC curves by 
validation data for S-Anfis and two benchmark 
classifiers Support Vector Machine (SVM) and 
Multilayer Perceptron network (MLP). The 
results shows that the proposed model out-
performed both SVM and MLP in all indications 
as showed in (Table 1). RMSE rapidly decreased 
in the first 120 iterations and kept horizontal 
trend from that point with stable value at 0.265. 
This value was lower than two RMSEs of two 
benchmark SVM and MLP. 
Table 1. Performance comparison by validation data 
 Statistical indicators MLP SVM S-Anfis 
Kappa statistic 0.541 0.621 0.653 
Mean absolute error (MAE) 0.236 0.273 0.239 
Root mean squared error (RMSE) 0.430 0.364 0.335 
Relative absolute error (%) 47.04 54.36 47.64 
AUC 0.868 0.902 0.912 
4. Discussions and remarks 
The selection of proper variables 
significantly contributed to the performance of 
the proposed model. In fact, in many researches 
focusing on spatial variations of malaria, social 
– economic factors were have been scored with 
highest predictive capabilities among other. 
Normally, those variables were used as 
aggregated data that provided average value 
across administrative boundary. This 
summation, however, results in inaccurate 
variation patterns as every location within 
predefined boundary has the same probability 
values. This study used individual locations of 
malaria cases to produce susceptible maps 
providing probability of each pixel within study 
area. Thirteen variables were selected, of which 
distances from man-made features can be 
classified as social – economic factors. 
Population data (including demography, 
density) was valuable information but was not 
put into input database, because there was no 
significant way to assign those values into single 
locations. Instead, distance to roads could be 
used as replacement to population density as the 
local communities (as well as the Vietnamese) 
tend to live as close to the roads as possible. 
Simulated annealing is single solution - 
based solution for searching for global optimal, 
in which model performance is improved over 
the course of iterations. The main goal of this 
paper was to investigate whether the 
combination of Anfis and simulated annealing 
was capable for optimizing large number of 
parameters and for solving non-linear functions. 
Since the objective function (RMSE in this case) 
consists of premise and consequence parameters 
that vary depending on number of clusters 
defined in initial stages. With 5 clusters and 200 
parameters, the objective function was 
successfully solved. 
For the second verification in optimizing 
non-linear optimization problems, two 
benchmark classifiers MLP and SVM were 
selected and run with the same training and 
validation dataset. The two classifiers are widely 
used in non-linear problems [8]. The goodness-
of-fit of two classifiers are dominated by model 
complexity, such as number of hidden layers in 
MLP or Kernel function parameters in SVM. By 
using Grid search techniques, two classifiers 
with optimal parameters were trained and 
validated with similar training and validation 
datasets. Performance comparison of S-anfis 
model with two benchmark classifiers by using 
B.Q. Thanh / VNU Journal of Science: Earth and Environmental Sciences, Vol. 34, No. 4 (2018) 80-88 
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Kappa index, RMSE, ROC curve indicated that 
S-anfis outperformed the two in all indicators 
(Figure 6), (Table 1) 
Figure 7. Susceptible map by S-Anfis. 
Technically, the selection of Simulated 
annealing parameters, for instance, initial 
temperature, temperature decreasing function, 
function to generate new points only impact how 
the shape of the plot and how fast this model 
converge. From several trials, we found that 
even with different parameters, the models came 
to similar value after certain iterations. Another 
aspect should be taken into consideration is how 
membership function in Anfis is defined. In this 
study, Bell-shaped function was selected among 
two other, including Gauss and Sigmoil 
distribution. 
5. Conclusion 
This paper filled up the literature in spatial 
modelling of epidemiology studies, in which a 
classifier is combined with optimization 
algorithm. The result of the hybrid model shows 
a significant improvement of this combination 
against two benchmark classifiers in all 
comparing criteria such as RMSE, Kappa, Mean 
Absolute Error, AUC. Since only Simulated 
annealing was used in the study, performance of 
model might be improved if other optimization 
algorithms are employed such as population-
based optimization. More research on this 
direction should be performed in the future. 
The hotspot modelling based on hybrid 
model shows important risk factors relating to 
variation of socio-economic and environment 
condition. The output map provides preliminary 
understanding of susceptibility levels of the 
disease in the study area and it can be used as one 
of important indicators in malaria control and 
elimination program. 
Acknowledgments 
This research is funded by the Viet Nam 
National University, Hanoi (VNU) under project 
number QG.17.20 
References 
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[7] D. Tien Bui et al., “A hybrid artificial intelligence 
approach using GIS-based neural-fuzzy inference 
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Tích hợp hệ thống suy luận mờ (Anfis) và thuật toán 
tối ưu hóa Simulated annealing trong nghiên cứu nguy cơ 
sốt rét tại tỉnh Đắk Nông, Việt Nam 
Bùi Quang Thành 
Khoa Địa lý, Trường Đại học Khoa học Tự nhiên, ĐHQGHN, 334 Nguyễn Trãi, Hà Nội, Việt Nam 
Tóm tắt: Adaptive Neuro-Inference system (Anfis) được sử dụng nhiều trong các ứng dụng phân 
loại nhị phân. Phương pháp này thường xuyên được sử dụng cùng với thuật toán tối ưu hóa nhằm xác 
định các tham số tối ưu cho Anfis. Nghiên cứu này thử nghiệm thuật toán Simulated Annealing (SA) và 
Anfis trong nghiên cứu nguy cơ sốt rét tại tỉnh Đắk Nông, Việt Nam. Để đánh giá độ chính xác của mô 
hình, thông số ROC được sử dụng cùng với một số chỉ số thống kê khác. Kết quả nghiên cứu cho thấy 
độ chính xác của mô hình đề xuất so với các mô hình dùng để so sánh như sau S-Anfis (AUC = 0.912, 
RMSE =0.335) Support Vector Machine (AUC = 0.902, RMSE =0.364), Multiple LayerPerceptron 
(AUC = 0.868, RMSE =0.430). Kết quả này cho thấy mô hình kết hợp giữa SA và Anfis cho kết quả tốt 
hơn các phương pháp khác, và có thể được sử dụng cho nghiên cứu nguy cơ sốt rét tại các địa phương 
khác tại Việt Nam 
Từ khóa: Anfis, Simulated annealing, Sốt rét.