A Fuzzy-Genetic Multi-Objective Optimization Method Applied to
Deployment of Routers in Agricultural Crop Areas
P. H. G. Coelho
, J. F. M. Amaral
, T. M. Carvalho
, R. A. Gomes
, I. S. Cardoso
and T. N. Souza
State Univ. of Rio de Janeiro, FEN/UERJ, R. S. Francisco Xavier, 524/Sala 5001E, Maracanã, RJ,20550-900, Brazil
Pontifical Catholic University of Rio de Janeiro, ELE, R. Marquês de São Vincente, 225, Gávea, RJ, 22453-900, Brazil
Keywords: Fuzzy-Genetic Systems, Multi-Objective Optimization, Precision Agriculture, AI Applications.
Abstract: High technology is increasingly applied to improving crop fields and coined an area as Precision Agriculture.
The main focus of this work is to increase production by performing data acquisition from an agricultural
crop area, monitoring sensor devices to measure temperature, humidity, etc. This allows the administrator of
the field to make good decisions related to the land management. This paper proposes a hybrid fuzzy-genetic
multi-objective intelligent method to place routers in an agricultural crop area so that to cover the sensor
monitoring devices spread over it. The method combines a genetic algorithm with a fuzzy aggregation
technique to evaluate multiples objectives, in order to determine an adequate location of the routers
considering the designer´s preferences. Case studies are presented and show the proposal results.
Family farming is at the origin of important debates,
both academic and political, and can refer to a
diversity of subjects in the collective imagination.
Family farming represents a production model
structured around the family and which is integrated
into different types of markets, whether acquiring
inputs and new technologies, or selling the food and
raw materials they produce. It is not, therefore, a
social group that predominated in the past and
remained relatively distant from the market, averse to
technology and poorly integrated into society. The
family farmer in Brazil typically owns a portion of
land ranging from 5 to 110 hectares (one hectare is
equivalent to 10 thousand m²). At least half of the
labor used in the activity of the property must be
family-owned, and income must come predominantly
of rural activity. Management must be strictly family-
based. According to IBGE (Brazilian Institute of
Geography and Statistics), responsible for the census,
family farming occupies 23% of the total cultivated
area in the country.
The use of technology is already part of several
segments in our society, and agriculture would be no
different. To seek greater revenue and productivity in
the field, the Brazilian farmers need to be increasingly
connected with what happens inside and outside their
property. Precision agriculture (PA) is largely
responsible for bringing agriculture into everyday life
in the field. Until a few years ago, they were restricted
to certain places and properties, because they were
impacted due to the high investment and financial
availability of the owners. How can we imagine this
in the current scenario, in which the demand for food
and its quality grow as the world population
increases? It is impossible not to use technology. The
term Agriculture 4.0 refers to the industry’s
upcoming significant trends, such as the internet of
things (IoT), using big data and machine learning to
make businesses more efficient amid the challenges
of population growth and climate change to improve
output, efficiency, and support sustainable agriculture
by using accurate information to make strategic
decisions (Tjhin et al., 2022).
By 2050, it is estimated that there will be 9 billion
people on the planet, which will require more
production, smaller costs and preservation of natural
resources. It is planned that atypical occurrences and
climate change represent serious risks to agricultural
production. As a result, an increase of 70% or more is
expected in food production. The agricultural
industry is changing as a result of the adoption of
emerging technologies. Using cutting-edge
technology like IoT, AI and other sensors, smart
Coelho, P., Amaral, J., Carvalho, T., Gomes, R., Cardoso, I. and Souza, T.
A Fuzzy-Genetic Multi-Objective Optimization Method Applied to Deployment of Routers in Agricultural Crop Areas.
DOI: 10.5220/0012696000003690
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 26th International Conference on Enterprise Information Systems (ICEIS 2024) - Volume 1, pages 792-799
ISBN: 978-989-758-692-7; ISSN: 2184-4992
Proceedings Copyright © 2024 by SCITEPRESS Science and Technology Publications, Lda.
agriculture will transform traditional farming
methods production and international agricultural
policies. Agriculture 4.0 looks at its possible benefits
and drawbacks of the implementation methodologies,
compatibility, reliability, and investigates the several
digital tools that are being utilized to change the
agriculture industry and how to mitigate the
challenges (Gyamfi et al., 2024).
Summing up, precision agriculture combines
artificial intelligence, the internet of things and GPS,
making the farmer's life easier to achieve greater
productivity and efficiency in the field, saving inputs,
optimizing the soil and practical operation. Precision
agriculture uses an agricultural management system
that considers the particularities of each point on the
property. Its application was intensified with the
improvement of GPS, which made it possible to
install receivers in seeders, harvesters and sprayers,
associating productivity data with geographic
coordinates using satellites. On the other hand, digital
agriculture or agriculture 4.0 is a set of technologies
that help the producer to monitor rural activities more
closely, such as software and devices responsible for
collecting and processing data about the farm.
Research in the area of computational intelligence
applied to farming is intense currently and there are a
large number of papers reporting an increase in crop
productivity. Recent works include (Ketheneni et al.,
2023) which uses an ensemble model, with four
classifiers, to recommending the fertilizer and a
sequential convolution neural network to
recommending the pesticide for the appropriate crop.
In the recent past, 3D machine vision techniques
have been widely employed in agriculture and food
systems, leveraging advanced deep learning
technologies. Following this path (Xiang et al., 2023)
published a survey of 3D vision techniques in food
and agriculture applications. (Karunathilake et al.,
2023) review recent innovations, challenges and
future prospects of precision agriculture and smart
For a sustainable production environment
(Mallinger et al., 2023) discusses the impact of AI in
farming concerning the fusion of AI and autonomous
farming machinery (e.g., drones and field robots) in
the daily work experience of farmers.
The purpose of this paper is to position a set of
routers so to cover the sensor monitoring devices
spread in an agricultural crop area, sending data such
as temperature, soil humidity, and the like, giving the
family farmer the chance of optimal decisions
regarding his/her crop. It is intuitive that random
positioning of router nodes is not a good choice as can
result in poor communication performance with the
sensor monitoring devices. Besides, the actual
deployment may have restrictions and geographic
characteristics of the area in question, making it
essential to seek for different topologies to distribute
them. Such a problem is of the NP hard type, so that is
a good indication for looking for the optimal solution
following an approach using evolutionary techniques
that includes genetic algorithms with fuzzy
aggregation. The placement of routers in a network is
not a trivial problem. Usually, such a problem can be
solved using traditional evolutionary techniques such
as weighted-sum approach genetic algorithms or
Pareto-based techniques. Weighted-sum evaluation for
genetic algorithms leads to difficult assignment of
appropriate weights, while Pareto techniques require
the designer to select the most suitable solution among
the set of presented solutions.
Research using intelligent computational systems
have been taken continuous attention in universities
and research centers around the globe. (Waqas et al.,
2022) presents an optimal sensor node placement
problem in Structural Health Monitoring (SHM)
application based on an optimized Wireless sensor
network (WSN). The sensor node placement problem
is formulated in multi-objective form by considering
the energy consumption, sensitivity area and network
lifetime. A hybrid optimization algorithm was used
by a combination of Chaotic Particle Swarm
Optimization (CPSO) with Gravitational Search
Algorithm (GSA) to provide optimal sensor node
placement in WSN based SHM system. The optimal
solution is achieved in the Pareto environment case,
which makes the algorithm multi-objective.
In (Akram et al., 2023), a meta-heuristic multi-
objective firefly algorithm (MOFA) is presented to
solve the layout optimization problem. Their main
goal is to cover a number of objectives related to
optimal layouts of homogeneous WSNs, which
includes coverage, connectivity, lifetime, energy
consumption and the number of sensor nodes.
Router Nodes Placement Using Artificial Immune
Systems is used in (Coelho et al., 2017), and (Coelho
et al., 2015) for industrial applications.
In this paper, we use genetic algorithms to
determine the location of routers in a mesh network
through evolutionary techniques associated with a
new Takagi-Sugeno-Kang (TSK) fuzzy aggregation
method inspired by Mamdani system aggregation
presented in (Coelho et al., 2019) and (Coelho et al.,
This paper is organized into four sections. The
second section deals with the new hybrid fuzzy-
genetic proposed model followed by discussion of the
case studies in section three. Finally, section four
closes the article with conclusions.
A Fuzzy-Genetic Multi-Objective Optimization Method Applied to Deployment of Routers in Agricultural Crop Areas
In this article, we utilized a fuzzy-based system for
optimizing router positioning. Fuzzy systems provide
a more intuitive and flexible approach to handling
imprecise data, which can be easily modeled by the
user. Through the implementation of a hybrid fuzzy-
genetic strategy, we facilitate the development and
adjustment of the objective function, while preserving
the optimization strategy of the Genetic Algorithm.
The method to optimize the placement of the
routers in the crop area must consider the multiple
objective aspects of this issue. For instance, besides
the necessity to full coverage of the sensor monitoring
devices in the area, it may impose restrictions on
positioning the routers due to high cost involved or,
in the limit, preventing prohibitive installation costs.
A hybrid fuzzy-genetic approach was used based on
Genetic Algorithm (GA) and Fuzzy Inference System
Genetic algorithms are inspired by biological
evolution and some aspects of genetics. Optimization
problems are the main application of GAs,
particularly in problems with complex or large search
areas. In a searching problem, the idea is to establish
an analogy between the evolution of the species and
the problem. A set of possible solutions (population
of individuals) are evaluated, and each individual is
associated with a fitness value (quality of the
individual). The population is subjected to a process
of simulated evolution, through genetic operators
(selection and reproduction) for many generations. At
the end of the evolutionary simulated process, the best
individual (higher fitness value) is associated with the
The fitness evaluation function, also called
objective function, is conceived based on problem
specification and is very important for obtaining a
good result. The traditional GA involves a single
criterion, but many real-world optimization problems
involve multiples objectives. To deal with multiple
objectives, one possible approach is to convert vector
quantities (objectives) into a scalar (only one fitness
value considering all objectives) by using techniques
like the weighted-sum approach or Mamdani fuzzy
The utilization of a Fuzzy Inference System (FIS)
to aggregate the objectives allows the evaluation of
all objectives, integrating designer´s preferences in
relation to each objective and for each particular
problem. The proposed hybrid method offers an
advantage over Pareto optimization techniques
because it does not require that the designer chooses
the best solution at the end of the optimization
process. Specifications and preferences are
established a-priori and entered before evolution in a
simpler way through the fuzzy system, to guide the
evolution process in the direction of pre-established
It is worth mentioning that each GA individual
represents a possible solution to the search problem.
During the evaluation process each GA individual is
submitted to a particular objective function that
represents one aspect of the problem and the results
are used as inputs to the fuzzy inference system. The
fuzzy aggregation method is applied to each
individual in the population in order to produce a
single scalar overall fitness value. Figure 1 illustrates
the evaluation model using a Takagi-Sugeno-Kang
(TSK) Fuzzy Aggregation Method.
Figure 1: TSK Fuzzy System applied to fitness evaluation.
The values for GA parameters (selection,
crossover, mutation, population size and maximum
number of generations) must be defined by the
designer. The rules for the fuzzy aggregator system
are conceived according to the designer´s preferences
to solve the problem by considering each objective.
To stop the evolution, a certain stopping criterion also
must be specified. The most common ones are related
to the maximum number of generations and a certain
fitness value to be reached.
The fuzzy aggregation method uses an ordinary
FIS in which each input corresponds to a particular
objective and the membership functions are triangular
or trapezoidal in shape for simplicity. The Multiple-
objective GA with the TSK Fuzzy aggregator system
used in this work is presented in Figure 2.
In this study, we explored three scenarios as case
studies, aiming to strategically position low-power,
battery-operated routers in a mesh network for data
ICEIS 2024 - 26th International Conference on Enterprise Information Systems
acquisition in an agricultural environment, with
different size and number of sensors. Throughout the
investigations, we leveraged the MATLAB Fuzzy
Toolbox. For all experiments, the main objective is to
cover all sensors using the routers, while avoiding the
positioning in forbidden areas, which might represent
places such as rivers, houses, and so on.
Figure 2: Optimization flowchart with TSK Fuzzy
Figure 3: Membership functions for Cost variable.
To investigate the effectiveness of the TSK Fuzzy
Aggregator, we compare the results against those
obtained using the Mamdani Fuzzy Aggregator
(Coelho et al., 2023) across all of the used
scenarios in this article. To facilitate a meaningful
comparison of results, we configured both the TSK
(Takagi-Sugeno-Kang) fuzzy aggregator and the
Mamdani fuzzy aggregator to exhibit similar
behaviors. This involved maintaining consistency in
the information related to the input, specifically the
linguistic variables and their associated fuzzy sets.
The fuzzy sets for the number of points covered
by routers (SenCovered) are depicted in Figure 3,
while Figure 4 illustrates the fuzzy sets for the cost
variable (Cost).
Figure 4: Membership functions for SenCovered variable.
Figure 5: Membership functions for evaluation variable.
Despite the different specifications for the TSK
and Mamdani output, both methods employ a
common evaluation scale ranging from 0 to 10.
Figure 5 displays the fuzzy sets associated with the
Mamdani fuzzy aggregator, while the TSK fuzzy
aggregator output is described in terms of linear
equations for the linguistic variables:
𝑜𝑣𝑒𝑟𝑎𝑙𝑙𝑏𝑎𝑑 0.006 𝑆𝑒𝑛𝐶𝑜𝑣𝑒𝑑 0.4 𝐶𝑜𝑠𝑡  4
𝑎𝑡𝑡𝑒𝑛𝑑𝑏𝑎𝑑 4.5
𝑐𝑜𝑠𝑡𝑏𝑎𝑑 0.006 𝑆𝑒𝑛𝐶𝑜𝑣𝑒𝑟𝑒𝑑  0.4 𝐶𝑜𝑠𝑡  7
𝑔𝑜𝑜𝑑 0.04 𝑆𝑒𝑛𝐶𝑜𝑣𝑒𝑟𝑒𝑑  0.8 𝐶𝑜𝑠𝑡  2
Throughout all case studies, we maintained the
rules of the FIS, considering the problem as
essentially the same across scenarios. Figure 6
displays the rules for the TSK system, while Figure 7
illustrates the rules for the Mamdani fuzzy
aggregator. It is noteworthy that the rules used in the
Mamdani system can be simplified to 5 rules.
Figure 6: Rules for TSK Fuzzy Aggregator.
Figure 7: Rules for Mamdani Fuzzy Aggregator.
A Fuzzy-Genetic Multi-Objective Optimization Method Applied to Deployment of Routers in Agricultural Crop Areas
Figure 8: Surface for TSK Fuzzy Aggregator.
The TSK system was designed to progressively
reach toward an optimal solution, as illustrated in
Figure 8. This approach may be considered an
advantageous feature of the TSK system, offering
simplicity and precision in its rule-based outputs.
For each case study, we ran the optimization
strategy ten times, and compared the results in terms
of convergence (basically looking at the output
score). As the objective and evaluation for both
strategies were tailored to have similar behavior, we
compare how good the fuzzy aggregation might be
into finding the optimal solution. Also, we aim to
observe the consistency of the results provided by the
optimization strategies.
3.1 First Case Study
In the initial case study, the scenario unfolds in an
agricultural expanse covering 2500 (50 m x 50 m),
necessitating a strategic spatial layout of routers.
Monitoring devices (sensors), with a reach of 13 m,
are strategically positioned to achieve two primary
objectives: ensuring each monitoring point is covered
by at least one router and minimizing installation
costs by avoiding high-cost areas. The parameters
employed in this experiment using genetic algorithm
are outlined in Table 1.
Table 1: GA Parameters for the Case Study 1.
Parameter Value
Generations 300
Population 50
Mutation 0.01
The results of the first case study are illustrated in
Figure 9, showcasing the optimization outcomes
employing TSK and Mamdani as fuzzy aggregation
strategies. Notably, TSK and Mamdani exhibited
similar behaviors in terms of consistency. Both TSK
and Mamdani strategies converged to solutions with
similar fitness values, which showed that there might
be no difference in terms of robustness to achieve an
optimal solution. However, it is important to note that
the first case study can be considerably easier to
obtain a solution that fulfill the requirements.
Figure 9: Fitness curve for Case Study 1.
Figure 10: Routers’ deployment using TSK Fuzzy
Aggregator in Case Study 1.
Figure 10 provides a visual representation of the
monitored points and router positions for the best
individual identified by the GA. In this depiction,
smaller blue circles denote monitoring points, large
blue circles represent the coverage area of each
router, routers are marked by a red "x," the obstacles
are illustrated as red rectangles, and the crop limit
area is highlighted in green.
A visual inspection affirms the optimal solution
achieved through the optimization strategy. All
routers were strategically positioned to enable sensor
reach, avoiding forbidden areas, albeit with some
proximity to them.
ICEIS 2024 - 26th International Conference on Enterprise Information Systems
3.2 Second Case Study
For the second case study, we created one more
obstacle in the router position, which simulates the
obstacle of a house and a river crossing the
environment. In this experiment, we kept the
experimental setup, except for the number of
individuals, as presented in Table 2. The rationale
behind this change is based on the complexity of the
Table 2: GA Parameters for the Case Study 2.
Parameter Value
Generations 300
Population 150
Mutation 0.01
The results of the optimization strategies can be
seen in Figure 11. We observed that the Mamdani
fuzzy aggregator obtained more unstable results and,
in average, noticeable worse results than the TSK
strategy. In a more complex scenario (if compared to
the previous case study), the TSK fuzzy aggregator
obtained results closer to the optimal, which may
indicate a more appropriate approach to achieve the
desired router placement configuration. We also
observed that the Mamdani-type fuzzy aggregator did
not converge gradually, but rather took some jumps
between the fitness values. For both observations in
this case study, the simplified building of the
Mamdani fuzzy system may led to worse
optimization results, which requires a much larger
number of estimates than for the TSK fuzzy
aggregator to achieve the best solutions in the
optimization process.
Figure 11: Fitness curve for Case Study 2.
Figure 12: Router’s deployment using TSK Fuzzy
Aggregator in Case Study 2.
To illustrate the best solutions found in the second
case study, Figure 12 shows one of the results using
the TSK fuzzy aggregator. As observed in the router
deployment, one of the difficulties is that some
routers probably need to be placed near one obstacle
to accomplish completely one of the objectives.
Nevertheless, it was possible to achieve a solution
that fulfilled all requirements, showing the
effectiveness of finding a set of routers’ deployment
for this case study.
3.3 Third Case Study
For the third case study, we increased the complexity
of the scenario by expanding: the number of sensors
(20), number of obstacles (3) and covered area
10000m² (100 m x 100 m). Due to that constraints, we
also increased the number of routers to be placed in
the environment from 5 to 9.
For the GA parameters, we also increased the
number of individuals of population, to balance the
increase in the search space. The parameters used in
this experiment can be seen in Table 3.
Table 3: GA Parameters for the Case Study 3.
Parameter Value
Generations 300
Population 300
Mutation 0.01
Figure 13 displays the fitness curve for the third
case study. Some of the aspects of the graphs are also
present in previous experiments, specifically the
predominance of TSK method over the Mamdani.
However, we noticed that the Mamdani fuzzy
A Fuzzy-Genetic Multi-Objective Optimization Method Applied to Deployment of Routers in Agricultural Crop Areas
aggregator did not obtain reasonable results, with
small increase of fitness score over the epochs.
As depicted in Figure 14, it was possible to obtain
a solution that completely achieves all requirements
for the router deployment. For a larger area and
random positioning of sensors, it is plausible to
observe that all routers were allocated to be in range
to at least one sensor.
Figure 13: Fitness curve for Case Study 3.
Figure 14: Routers’ deployment using TSK Fuzzy
Aggregator in Case Study 3.
This paper focused on the placement of routers in a
small crop area for data acquisition of sensor
monitoring devices to optimize the production of
family agriculture. Case studies were presented with
scenarios with restrictions closer to real applications.
These scenarios consider not only the need to cover
all sensors but also the avoidance of areas where
routers’ installation cost is high. A hybrid TSK fuzzy-
genetic multiple-objective optimization method was
applied to place the routers in a crop area taking into
account the number of covered sensors and the cost
objectives in the routing problem.
The multiple-objective technique based on fuzzy
aggregation allows the evaluation of the objectives
simultaneously, including designer´s preferences
before the evolution takes place. This a-priori method
offers an interesting advantage over Pareto method
because it does not require that the designer chooses
the solution at the end of the process. It´s worth noting
that both the fuzzy aggregation specifications and
designer´s preferences are integrated before evolution
in a simpler manner, so the evolution is guided to the
desired preferences.
The TSK fuzzy aggregation presented here
showed, in two case studies, better performance to
this kind of application in comparison with Mamdani
fuzzy aggregation (Coelho et al., 2023). It is up to the
designer to choose between these two fuzzy
inferences which one should be applied to a particular
problem. However, it should be stressed that the
Mamdani fuzzy aggregation may require a higher
effort to achieve a similar behavior, mostly adding
new fuzzy sets for inputs, outputs and new rules to
increase the granularity of evaluation.
We plan for future works on precision agriculture
run case studies with some other a-priori methods, for
instance, such as a weighted-sum, and also a-
posteriori based on Pareto traditional method for
comparison’s sake. We also plan to include new
objectives for fuzzy aggregation and conceive a
model that can also select the adequate minimum
number of routers for complete field coverage. In
addition, comparisons with other techniques such as
African Vulture Optimization Algorithm (AVOA)
(Abdollahzadeh et al., 2021), Bat Algorithm (BA)
(Yang et al., 2013), Whale Optimization Algorithm
(WOA) (Mirjalili et al., 2016) and Particle Swarm
Optimization (PSO) (Marinakis et al., 2008) are
foreseen in future works related to precision
This study was financed in part by the Coordenação
de Aperfeiçoamento de Pessoal de Nível Superior
Brasil (CAPES) – Finance Code 001, and FAPERJ.
ICEIS 2024 - 26th International Conference on Enterprise Information Systems
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A Fuzzy-Genetic Multi-Objective Optimization Method Applied to Deployment of Routers in Agricultural Crop Areas