# Multiobjective RFID Network Optimization Using Multiobjective Evolutionary and Swarm Intelligence Approaches

Authors: Hanning Chen; Yunlong Zhu; Lianbo Ma; Ben Niu
Journal: Mathematical Problems in Engineering
 (2014)

---

## Abstract

The development of radio frequency identification (RFID) technology generates the most challenging RFID network planning (RNP) problem, which needs to be solved in order to operate the large-scale RFID network in an optimal fashion. RNP involves many objectives and constraints and has been proven to be a NP-hard multi-objective problem. The application of evolutionary algorithm (EA) and swarm intelligence (SI) for solving multiobjective RNP (MORNP) has gained significant attention in the literature, but these algorithms always transform multiple objectives into a single objective by weighted coefficient approach. In this paper, we use multiobjective EA and SI algorithms to find all the Pareto optimal solutions and to achieve the optimal planning solutions by simultaneously optimizing four conflicting objectives in MORNP, instead of transforming multiobjective functions into a single objective function. The experiment presents an exhaustive comparison of three successful multiobjective EA and SI, namely, the recently developed multiobjective artificial bee colony algorithm (MOABC), the nondominated sorting genetic algorithm II (NSGA-II), and the multiobjective particle swarm optimization (MOPSO), on MORNP instances of different nature, namely, the two-objective and three-objective MORNP. Simulation results show that MOABC proves to be more superior for planning RFID networks than NSGA-II and MOPSO in terms of optimization accuracy and computation robustness.


---

## Body

## 1. Introduction

Academic research into radio frequency identification (RFID) has increased significantly over the last ten years, to the point that RFID is used to build up an “internet of things”—a network connects physical things to the Internet that makes it possible to access remote sensor data and to control the physical world from a distance [1]. An RFID system consists of four types of important components (see Figure 1): (1) RFID tags, each placed on an object and consisting of a microchip and an embedded antenna containing a unique identity, which is called Electronic Product Code (EPC); (2) RFID readers, each having more than one antenna and is responsible to send and receive data to and from the tag via radio frequency waves; (3) RFID middleware, which manages readers, as well as filtering and formatting the RFID raw tag data; and (4) RFID database, which records RFID raw tag data that contains information such as reading time, location, and tag EPC.Figure 1
RFID system.In many real-world RIFD applications, such as production, logistics, supply chain management, and asset tracking, a sufficient number of readers are deployed in order to provide complete coverage of all the tags in the given areas [2, 3]. This gives rise to some challenging issues in the deployment of an RFID network, such as optimal tag coverage, quality of service (QoS), and cost efficiency. Therefore, our previous pioneering work pointed out that the RFID network planning (RNP) problem in RFID system is a key issue that has to meet many requires of the RFID system in order to operate the large-scale network of RFID readers in an optimal fashion [4]. In general, we defined that the RNP aims to optimize a set of objectives (coverage, load balance, economic efficiency and interference between readers, etc.) simultaneously by adjusting the control variables (the coordinates of the readers, the number of the readers, and the antenna parameters, etc.) of the system. As a result, in the large-scale deployment environment, the RNP problem is a high-dimensional NP-hard optimization problem with a large number of variables and uncertain parameters.Obviously, optimization of the RNP is essentially a typical multiobjective problem (MOP). However, the methods used in the previous studies to solve the multiobjective RNP (MORNP) are always weighted coefficient approaches used to transform multiple objectives into a single objective [4–8]. Most of these methods are based on evolutionary algorithm (EA) and swarm intelligence (SI) optimization techniques, such as genetic algorithms (GA) [6, 9], evolutionary strategy (ES) [10], differential evolution (DE) [7], particle swarm optimization (PSO) [4, 5, 10], and bacterial foraging algorithm (BFA) [11]. Notice that these works considered only one object in RFID network planning or a single objective function that linearly composed several planning objectives and none of them can generate the tradeoffs between objectives. However, it is hard for users to determine these coefficients for optimization in RFID network. On the other hand, what can be acquired using a combination of coefficients is a single optimal solution instead of all the optimal solutions, namely, Pareto optimal solutions. Therefore, transformation of multiobjective functions into a single objective function is not the best choice for optimizing the real-world MORNP problem.This paper substantially extends the previous work on RNP and can be distinguished from it from three aspects as follows.(1)
A MORNP optimization approach is conducted in this work. In MORNP approach, four objectives, namely, coverage, load balance, economic efficiency, and interference, are considered simultaneously in optimization process. A fuzzy decision-making process for selection of the final solution from the available optimal points on Pareto frontier is also presented here.
(2)
Due to conflicts between different goals of the existing MORNP model, an efficient solution method should be used to search in the feasible solution space with the hope of finding the ideal RFID network layout while extracting a set of Pareto optimal solutions. Hence, this paper provides recommendations and guidance for the utilization of multiobjective EA and SI optimization techniques, such as the recently developed multiobjective artificial bee colony algorithm (MOABC), the nondominated sorting genetic algorithm II (NSGA-II), and the multiobjective particle swarm optimization (MOPSO). The success of multiobjective EA and SI is due to their ability of finding a set of representative Pareto optimal solutions in a single run.
(3)
By applying multiobjective approaches for solving the MORNP problem, a new framework was established that could handle different objectives and would enable the planner to find the optimal RFID network plan based on multiobjective EA and SI. Specifically, we formulated MORNP as two types of multiobjective problems, namely, two- and three-objective problems, whereas each two- or three-objective functions in RFID system are optimized simultaneously.The rest of this paper is organized as follows. Section2 gives the formulation of the MORNP problem. Section 3 presents the brief review of MOABC, NSGA-II, and MOPSO algorithms. In Section 4, the comparative study is performed for the three nature-inspired algorithms on solving the MORNP problem. Finally, Section 5 outlines the conclusions.


## 2. Problem Formulation

### 2.1. Multiobjective Optimization Problems

In many real-world optimization applications, the decision maker is always faced with the presence of multiple noncommensurable and often competing objectives. The solutions for the multiobjective problem (MOP) often result from both the optimization and decision making process [12]. When trying to solve an MOP, a set of trade-off solutions is the target of the solution algorithm and the one that will be chosen depends on the needs of the decision maker.An MOP can be defined as:(1)
Min
⁡
f
(
x
)
=
[
f
1
(
x
)
,
f
2
(
x
)
,
…
,
f
k
(
x
)
]
Τ
iii
s
.
t
.
h
(
x
)
=
0
i
i
i
i
i
i
i
g
(
x
)
≤
0
,
where multiobjective function f includes k
(
k
≥
2
) objective functions, constraints h
(
x
) and g
(
x
) are equality and inequality functions, and x is control variable.In order to optimize the vector function, the concept tied to an MOP called “Pareto Optimal” is defined as follows. For (1), let α
=
(
α
1
,
…
,
α
k
), β
=
(
β
1
,
…
,
β
k
)
∈
R
k (R
k is the objective space) be two vectors, α is said to dominate β if α
i
≤
β
i for all i
=
1
,
…
,
k, and α
≠
β. A point x
*
∈
X (X is the objective space) is called (globally) Pareto optimal if there is no x
∈
X such that f
(
x
) dominates f
(
x
*
). The set of all the Pareto optimal solutions, denoted by PS, is called the Pareto set. The set of all the Pareto objectives vectors, PF
=
{
f
(
x
)
∈
R
k
∣
x
∈
PS
}, is called the Pareto front. Illustrative example can be seen in Figure 2.Figure 2
Illustrative example of Pareto front.


### 2.2. Problem Formulation on Multiobjective RFID Network Planning

In this section, a mathematical multiobjective optimization model for the MORNP problem based on RFID middleware is proposed. The model is constructed from several different aspects. The deployment region of hotspots is supposed as a two-dimension square domain. The tags here are passive and based on the Class-1 Generation 2 UHF standard specification [13]. It means that they can only be powered by radio frequency energy from readers. The proposed multiobjective model aims to improve the QoS of RFID networks by simultaneously optimizing the objects including coverage, interference, load balance, and aggregate efficiency via regulating the parameters of RFID networks, including the number, location, and radiated power of readers. Generally the problem is formulated as follows.


#### 2.2.1. Optimal Tag Coverage (f
c)

The first objective function represents the level of coverage, which is most important in an RFID system. In this paper, if the radio signal received at a tag is higher than the thresholdδ
=
-
10 dBm, the communication between reader and tag can be established. Then the function is formulated as the sum of the difference between the desired power level δ and the actual received power P
i
j of each tag i in the interrogation region of reader j:
(2)
Min
⁡
f
c
=
∑
i
∈
TS
∑
j
∈
R
S
i
(
P
i
j
-
δ
)
,
where TS and RS is the tag and reader set that deployed in the working area, respectively, and R
S
i represents the set of readers which has the tag i in its interrogation region. This object function ensures that the received power P
i
j at the tag i from the reader j in R
S
i, which is mainly determined by the relative distance and radiated power of the reader j, is higher than the threshold δ, which guarantees that the tag is activated. That is, by regulating the locations and radiated power of the readers, the optimization algorithm should locate the RFID readers close to the regions where the desired coverage level is higher, while the areas requiring lower coverage are taken into account by the proper radiated power increases of the readers.


#### 2.2.2. Reader Interference (f
i)

Reader collision mainly occurs in a dense reader environment, where several readers try to interrogate tags at the same time in the same area. This results in an unacceptable level of misreads. The main feature of our approach is that the interference is not solved by traditional ways, such as frequency assignment and reader scheduling [4, 13], but in a more precautionary way. This objective function is formulated as
(3)
Min
⁡
f
i
=
∑
k
∈
RS
∑
i
∈
T
S
k
(
δ
-
(
P
i
k
-
∑
j
∈
R
S
i
j
≠
k
P
i
j
)
)
,
where T
S
k is the tag set in the interrogation region of reader k. For each tag i, this objective considers all the readers except the best one as interfering sources. That is, by changing reader positions and powers according to this functional the algorithm tries to locate the readers far from each other to reduce the interference.


#### 2.2.3. Economic Efficiency (f
e)

This aspect could be approached from various points of view. For example, due to the stochastic noise, multipath effect, and attenuation in the propagation channel, readers should be located closely to the center of tags in the hotspots. From this perspective, this objective can be reached by weighing the distances of each center of tag clusters from its best served reader. Here we employK-means clustering algorithm to find the tag cluster. It can be defined below:
(4)
Min
⁡
f
e
=
∑
k
∈
RS
dist
⁡
(
R
k
,
θ
k
)
,
where dist() is the distance between the k
th reader and the k
th tag center and θ
k and R
k are the position of k
th cluster center and its best served reader, respectively. In this way the algorithm tries to reduce the distance from the readers to the elements with high tag densities.


#### 2.2.4. Load Balance

A network with a homogeneous distribution of reader cost can give a better performance than an unbalanced configuration. Thus, in large-scale RFID system, the set of tags to be monitored needs to be properly balanced among all readers. This objective function is formulated as(5)
Min
⁡
f
l
=
∏
k
∈
RS
(
C
k
max
⁡
C
k
)
,
where C
k  is the assigned tags number to reader k and C
k
max
⁡ is the maximum number of tags which can be read by the reader k in unit time. It should be noticed that the C
k
max
⁡ take different values according to the different types of readers used in the network. This object aims to minimize the variance of load conditions by changing the locations and radiated power of readers.


### 2.3. Objective Constraint

All the tags in working area must be covered by a reader. This constraint can be formally expressed by the following formula:(6)
s
.
t
.
P
i
j
-
δ
≥
0
∀
i
∈
TS
,
j
∈
R
S
i
i
i
i
∑
k
∈
RS
λ
i
k
≥
1
∀
i
∈
TS
where λ
i
k is a binary variable that λ
i
k
=
1 if the reader k
∈
R
S
i; otherwise λ
i
k
=
0. So this constraint can maintain the power efficiency of network and ensure a complete coverage deployment.


## 2.1. Multiobjective Optimization Problems

In many real-world optimization applications, the decision maker is always faced with the presence of multiple noncommensurable and often competing objectives. The solutions for the multiobjective problem (MOP) often result from both the optimization and decision making process [12]. When trying to solve an MOP, a set of trade-off solutions is the target of the solution algorithm and the one that will be chosen depends on the needs of the decision maker.An MOP can be defined as:(1)
Min
⁡
f
(
x
)
=
[
f
1
(
x
)
,
f
2
(
x
)
,
…
,
f
k
(
x
)
]
Τ
iii
s
.
t
.
h
(
x
)
=
0
i
i
i
i
i
i
i
g
(
x
)
≤
0
,
where multiobjective function f includes k
(
k
≥
2
) objective functions, constraints h
(
x
) and g
(
x
) are equality and inequality functions, and x is control variable.In order to optimize the vector function, the concept tied to an MOP called “Pareto Optimal” is defined as follows. For (1), let α
=
(
α
1
,
…
,
α
k
), β
=
(
β
1
,
…
,
β
k
)
∈
R
k (R
k is the objective space) be two vectors, α is said to dominate β if α
i
≤
β
i for all i
=
1
,
…
,
k, and α
≠
β. A point x
*
∈
X (X is the objective space) is called (globally) Pareto optimal if there is no x
∈
X such that f
(
x
) dominates f
(
x
*
). The set of all the Pareto optimal solutions, denoted by PS, is called the Pareto set. The set of all the Pareto objectives vectors, PF
=
{
f
(
x
)
∈
R
k
∣
x
∈
PS
}, is called the Pareto front. Illustrative example can be seen in Figure 2.Figure 2
Illustrative example of Pareto front.


## 2.2. Problem Formulation on Multiobjective RFID Network Planning

In this section, a mathematical multiobjective optimization model for the MORNP problem based on RFID middleware is proposed. The model is constructed from several different aspects. The deployment region of hotspots is supposed as a two-dimension square domain. The tags here are passive and based on the Class-1 Generation 2 UHF standard specification [13]. It means that they can only be powered by radio frequency energy from readers. The proposed multiobjective model aims to improve the QoS of RFID networks by simultaneously optimizing the objects including coverage, interference, load balance, and aggregate efficiency via regulating the parameters of RFID networks, including the number, location, and radiated power of readers. Generally the problem is formulated as follows.


### 2.2.1. Optimal Tag Coverage (f
c)

The first objective function represents the level of coverage, which is most important in an RFID system. In this paper, if the radio signal received at a tag is higher than the thresholdδ
=
-
10 dBm, the communication between reader and tag can be established. Then the function is formulated as the sum of the difference between the desired power level δ and the actual received power P
i
j of each tag i in the interrogation region of reader j:
(2)
Min
⁡
f
c
=
∑
i
∈
TS
∑
j
∈
R
S
i
(
P
i
j
-
δ
)
,
where TS and RS is the tag and reader set that deployed in the working area, respectively, and R
S
i represents the set of readers which has the tag i in its interrogation region. This object function ensures that the received power P
i
j at the tag i from the reader j in R
S
i, which is mainly determined by the relative distance and radiated power of the reader j, is higher than the threshold δ, which guarantees that the tag is activated. That is, by regulating the locations and radiated power of the readers, the optimization algorithm should locate the RFID readers close to the regions where the desired coverage level is higher, while the areas requiring lower coverage are taken into account by the proper radiated power increases of the readers.


### 2.2.2. Reader Interference (f
i)

Reader collision mainly occurs in a dense reader environment, where several readers try to interrogate tags at the same time in the same area. This results in an unacceptable level of misreads. The main feature of our approach is that the interference is not solved by traditional ways, such as frequency assignment and reader scheduling [4, 13], but in a more precautionary way. This objective function is formulated as
(3)
Min
⁡
f
i
=
∑
k
∈
RS
∑
i
∈
T
S
k
(
δ
-
(
P
i
k
-
∑
j
∈
R
S
i
j
≠
k
P
i
j
)
)
,
where T
S
k is the tag set in the interrogation region of reader k. For each tag i, this objective considers all the readers except the best one as interfering sources. That is, by changing reader positions and powers according to this functional the algorithm tries to locate the readers far from each other to reduce the interference.


### 2.2.3. Economic Efficiency (f
e)

This aspect could be approached from various points of view. For example, due to the stochastic noise, multipath effect, and attenuation in the propagation channel, readers should be located closely to the center of tags in the hotspots. From this perspective, this objective can be reached by weighing the distances of each center of tag clusters from its best served reader. Here we employK-means clustering algorithm to find the tag cluster. It can be defined below:
(4)
Min
⁡
f
e
=
∑
k
∈
RS
dist
⁡
(
R
k
,
θ
k
)
,
where dist() is the distance between the k
th reader and the k
th tag center and θ
k and R
k are the position of k
th cluster center and its best served reader, respectively. In this way the algorithm tries to reduce the distance from the readers to the elements with high tag densities.


### 2.2.4. Load Balance

A network with a homogeneous distribution of reader cost can give a better performance than an unbalanced configuration. Thus, in large-scale RFID system, the set of tags to be monitored needs to be properly balanced among all readers. This objective function is formulated as(5)
Min
⁡
f
l
=
∏
k
∈
RS
(
C
k
max
⁡
C
k
)
,
where C
k  is the assigned tags number to reader k and C
k
max
⁡ is the maximum number of tags which can be read by the reader k in unit time. It should be noticed that the C
k
max
⁡ take different values according to the different types of readers used in the network. This object aims to minimize the variance of load conditions by changing the locations and radiated power of readers.


## 2.2.1. Optimal Tag Coverage (f
c)

The first objective function represents the level of coverage, which is most important in an RFID system. In this paper, if the radio signal received at a tag is higher than the thresholdδ
=
-
10 dBm, the communication between reader and tag can be established. Then the function is formulated as the sum of the difference between the desired power level δ and the actual received power P
i
j of each tag i in the interrogation region of reader j:
(2)
Min
⁡
f
c
=
∑
i
∈
TS
∑
j
∈
R
S
i
(
P
i
j
-
δ
)
,
where TS and RS is the tag and reader set that deployed in the working area, respectively, and R
S
i represents the set of readers which has the tag i in its interrogation region. This object function ensures that the received power P
i
j at the tag i from the reader j in R
S
i, which is mainly determined by the relative distance and radiated power of the reader j, is higher than the threshold δ, which guarantees that the tag is activated. That is, by regulating the locations and radiated power of the readers, the optimization algorithm should locate the RFID readers close to the regions where the desired coverage level is higher, while the areas requiring lower coverage are taken into account by the proper radiated power increases of the readers.


## 2.2.2. Reader Interference (f
i)

Reader collision mainly occurs in a dense reader environment, where several readers try to interrogate tags at the same time in the same area. This results in an unacceptable level of misreads. The main feature of our approach is that the interference is not solved by traditional ways, such as frequency assignment and reader scheduling [4, 13], but in a more precautionary way. This objective function is formulated as
(3)
Min
⁡
f
i
=
∑
k
∈
RS
∑
i
∈
T
S
k
(
δ
-
(
P
i
k
-
∑
j
∈
R
S
i
j
≠
k
P
i
j
)
)
,
where T
S
k is the tag set in the interrogation region of reader k. For each tag i, this objective considers all the readers except the best one as interfering sources. That is, by changing reader positions and powers according to this functional the algorithm tries to locate the readers far from each other to reduce the interference.


## 2.2.3. Economic Efficiency (f
e)

This aspect could be approached from various points of view. For example, due to the stochastic noise, multipath effect, and attenuation in the propagation channel, readers should be located closely to the center of tags in the hotspots. From this perspective, this objective can be reached by weighing the distances of each center of tag clusters from its best served reader. Here we employK-means clustering algorithm to find the tag cluster. It can be defined below:
(4)
Min
⁡
f
e
=
∑
k
∈
RS
dist
⁡
(
R
k
,
θ
k
)
,
where dist() is the distance between the k
th reader and the k
th tag center and θ
k and R
k are the position of k
th cluster center and its best served reader, respectively. In this way the algorithm tries to reduce the distance from the readers to the elements with high tag densities.


## 2.2.4. Load Balance

A network with a homogeneous distribution of reader cost can give a better performance than an unbalanced configuration. Thus, in large-scale RFID system, the set of tags to be monitored needs to be properly balanced among all readers. This objective function is formulated as(5)
Min
⁡
f
l
=
∏
k
∈
RS
(
C
k
max
⁡
C
k
)
,
where C
k  is the assigned tags number to reader k and C
k
max
⁡ is the maximum number of tags which can be read by the reader k in unit time. It should be noticed that the C
k
max
⁡ take different values according to the different types of readers used in the network. This object aims to minimize the variance of load conditions by changing the locations and radiated power of readers.


## 2.3. Objective Constraint

All the tags in working area must be covered by a reader. This constraint can be formally expressed by the following formula:(6)
s
.
t
.
P
i
j
-
δ
≥
0
∀
i
∈
TS
,
j
∈
R
S
i
i
i
i
∑
k
∈
RS
λ
i
k
≥
1
∀
i
∈
TS
where λ
i
k is a binary variable that λ
i
k
=
1 if the reader k
∈
R
S
i; otherwise λ
i
k
=
0. So this constraint can maintain the power efficiency of network and ensure a complete coverage deployment.


## 3. Multiobjective EA and SI Algorithms for MORNP

In this section, we detail the representation of the individual solutions and give a brief description of the multiobjective EA and SI algorithms compared in this work.


### 3.1. Solution Representation

In this work, the task of RFID network planning is to deploy several RFID readers in the working area in order to achieve four goals described in Section2. Figure 3 shows an example of a working area containing 100 RFID tags and 1 RFID reader, where the following three decision variables are chosen in this work:X: thex-axis coordinate value of the RFID reader,
Y: they-axis coordinate value of the RFID reader,
P: the read range (i.e., radiated power level) of the RFID reader.Figure 3
Example of a 30 m × 30 m working area with one RFID reader and 100 tags. The radiated power level (dBm) is marked on the right diagram sidebar and the green cycle represents the read range of the RFID reader.These variables can be encoded into solution’s representation shown in Table1. We employ a representation that each solution is characterized by a D
=
3
N
r (N
r is the total number of readers that deployed in the network) dimensional real number vector. In the representation, 2
N
r dimensions indicate the coordinates of the readers in the 2-dimensional working area, and the other 1
N
r dimensions denote the interrogation range of each reader (which is determined by the radiated power).Table 1
Representation of an individual solutioni. N
r is the max. number of RFID readers that deployed in the working area.
Reader 1 variables
Reader 2 variables
⋯
ReaderN
r variables
Solutio
n
i
X
i
1
Y
i
1
P
i
1
X
i
2
Y
i
2
P
i
2
⋯
X
i
N
r
Y
i
N
r
P
i
N
r


### 3.2. Multiobjective Artificial Bee Colony (MOABC)

ABC is a swarm intelligence algorithm developed by Karaboga motivated by the intelligent behavior of honeybees colony [14]. In ABC model, the colony of artificial bees contains three groups of individuals, namely, the employed, onlookers, and scouts bees [15]. Employed bees go to their food source and come back to hive and dance on this area. The employed bee whose food source has been abandoned becomes a scout and starts to search for finding a new food source. Onlookers watch the dances of employed bees and choose food sources depending on them. Since the original ABC is formulated as a single objective problem optimizer, we defined a new multiobjective algorithm in [16] named as MOABC. This algorithm incorporates two changes that allow its application in multiobjective optimization problems. The first modification applied is based on nondominated sorting strategy. That is, the MOABC algorithm uses the concept of Pareto dominance to determine the flight direction of a bee and it maintains nondominated solution vectors which have been found in an external archive. Secondly, the MOABC uses comprehensive learning strategy which is inspired by comprehensive learning particle swarm optimizer (CLPSO) [9] to ensure the diversity of population. Additionally, MOABC applies the crowding distance concept to calculate the corresponding value for all the solutions of the conflicting Pareto front and choose the sources of the best crowding distances. For further information about the MOABC algorithm please refer to [16].


### 3.3. Nondominated Sorting Genetic Algorithm (NSGA-II)

Deb developed the nondominated sorting genetic algorithm (NSGA) based on the classification of the population at various levels [17]. In this algorithm, before the selection, NSGA ranks the population by using the dominance concept. All nondominated individuals are classified into a category with a dummy fitness proportional to the population size. In order to maintain the diversity of the population, these individuals are distributed according to their fitness, subject to a distribution parameter (sharing parameter). This classified group is removed of the population and the remaining individuals are reclassified by the same procedure. This process continues until all individuals in the population are classified. Since the first individuals are of best quality, they always get more copies than the rest of the population, allowing the search in nondominated regions. NSGA got promising results; however, it was criticized for computational complexity problem. To repair this limitation, Deb et al. proposed an enhanced version of this method, called NSGA-II [18]. It solves the computational complexity problem through a fast nondominated sorting mechanism and a selection operator to combine the parent and child populations and select the N best solutions taking into account their quality and their distribution in the Pareto front. NSGA-II has become a standard multiobjective algorithm that has solved a lot of multiobjective problems. For further information about the NSGA/NSGA-II algorithms see [17, 18].


### 3.4. Multiobjective Particle Swarm Optimization (MOPSO)

Particle swarm optimization (PSO) has established itself as a successful swarm intelligence algorithm in a variety of optimization contexts. The rules of particle dynamics that govern this movement are inspired by models of swarming and flocking [19]. In PSO population, each particle has a position and a velocity and experiences linear spring-like attractions towards two attractors: its previous best position (pbest) and the best position of its neighbors (gbest). Until now there have been several proposals for extending PSO to multiobjective problems and these methods are called multiobjective particles swarm optimization (MOPSO) [20]. The greatest challenge in extending the PSO to multiobjective problems is deciphering the notion of guide and selection ofpbest andgbest as in multiobjective scenario. In this work, we considered a Pareto-based MOPSO [21] to solve MORNP. This algorithm incorporates the main mechanisms of NSGA-II to a PSO algorithm. In this approach, once a particle has updated its position, instead of comparing the new position only against thepbest position of the particle, all thepbest positions of the swarm and all the new positions recently obtained are combined in just one set. Then, MOPSO selects the best solutions among them to construct the next swarm (by means of a nondominated sorting). This approach also selects the leaders randomly from the leaders set (stored in an external archive) among the best of them, based on two different mechanisms: a niche count and a nearest neighbor density estimator. For further information about this MOPSO algorithm see [21].


### 3.5. Optimization Procedure

The overall operating process of MORNP based on MOEA and MOSI algorithms can be described as follows:Step 1 (initialization).
The positions of all individuals of each algorithm are randomly generated, with each(
X
i
k
,
Y
i
k
) being a random point in the working area and P
i
k being a random value within the transmitted power range of readers (
k
=
1,2
,
…
,
N
r
).Step 2 (fitness evaluation).
As described in Section2, the individuals should be evaluated on all the objectives of MORNP including maximizing tag coverage (defined by (2)), minimizing interference (defined by (3)), maximizing economic efficiency (defined by (4)), and maintaining an optimal load balance (defined by (5)), in an order of decreasing importance. Accordingly, the algorithm handles these four objectives in a multiobjective manner in the next step.Step 3 (population evolution).
Compare the evaluated fitness values and update the position of each individual according to specific rules of MOABC, NSGA-II, and MOPSO, respectively.Step 4 (termination condition).
The computation is repeated until the maximum number of iterations is met or the system requirement is researched.


## 3.1. Solution Representation

In this work, the task of RFID network planning is to deploy several RFID readers in the working area in order to achieve four goals described in Section2. Figure 3 shows an example of a working area containing 100 RFID tags and 1 RFID reader, where the following three decision variables are chosen in this work:X: thex-axis coordinate value of the RFID reader,
Y: they-axis coordinate value of the RFID reader,
P: the read range (i.e., radiated power level) of the RFID reader.Figure 3
Example of a 30 m × 30 m working area with one RFID reader and 100 tags. The radiated power level (dBm) is marked on the right diagram sidebar and the green cycle represents the read range of the RFID reader.These variables can be encoded into solution’s representation shown in Table1. We employ a representation that each solution is characterized by a D
=
3
N
r (N
r is the total number of readers that deployed in the network) dimensional real number vector. In the representation, 2
N
r dimensions indicate the coordinates of the readers in the 2-dimensional working area, and the other 1
N
r dimensions denote the interrogation range of each reader (which is determined by the radiated power).Table 1
Representation of an individual solutioni. N
r is the max. number of RFID readers that deployed in the working area.
Reader 1 variables
Reader 2 variables
⋯
ReaderN
r variables
Solutio
n
i
X
i
1
Y
i
1
P
i
1
X
i
2
Y
i
2
P
i
2
⋯
X
i
N
r
Y
i
N
r
P
i
N
r


## 3.2. Multiobjective Artificial Bee Colony (MOABC)

ABC is a swarm intelligence algorithm developed by Karaboga motivated by the intelligent behavior of honeybees colony [14]. In ABC model, the colony of artificial bees contains three groups of individuals, namely, the employed, onlookers, and scouts bees [15]. Employed bees go to their food source and come back to hive and dance on this area. The employed bee whose food source has been abandoned becomes a scout and starts to search for finding a new food source. Onlookers watch the dances of employed bees and choose food sources depending on them. Since the original ABC is formulated as a single objective problem optimizer, we defined a new multiobjective algorithm in [16] named as MOABC. This algorithm incorporates two changes that allow its application in multiobjective optimization problems. The first modification applied is based on nondominated sorting strategy. That is, the MOABC algorithm uses the concept of Pareto dominance to determine the flight direction of a bee and it maintains nondominated solution vectors which have been found in an external archive. Secondly, the MOABC uses comprehensive learning strategy which is inspired by comprehensive learning particle swarm optimizer (CLPSO) [9] to ensure the diversity of population. Additionally, MOABC applies the crowding distance concept to calculate the corresponding value for all the solutions of the conflicting Pareto front and choose the sources of the best crowding distances. For further information about the MOABC algorithm please refer to [16].


## 3.3. Nondominated Sorting Genetic Algorithm (NSGA-II)

Deb developed the nondominated sorting genetic algorithm (NSGA) based on the classification of the population at various levels [17]. In this algorithm, before the selection, NSGA ranks the population by using the dominance concept. All nondominated individuals are classified into a category with a dummy fitness proportional to the population size. In order to maintain the diversity of the population, these individuals are distributed according to their fitness, subject to a distribution parameter (sharing parameter). This classified group is removed of the population and the remaining individuals are reclassified by the same procedure. This process continues until all individuals in the population are classified. Since the first individuals are of best quality, they always get more copies than the rest of the population, allowing the search in nondominated regions. NSGA got promising results; however, it was criticized for computational complexity problem. To repair this limitation, Deb et al. proposed an enhanced version of this method, called NSGA-II [18]. It solves the computational complexity problem through a fast nondominated sorting mechanism and a selection operator to combine the parent and child populations and select the N best solutions taking into account their quality and their distribution in the Pareto front. NSGA-II has become a standard multiobjective algorithm that has solved a lot of multiobjective problems. For further information about the NSGA/NSGA-II algorithms see [17, 18].


## 3.4. Multiobjective Particle Swarm Optimization (MOPSO)

Particle swarm optimization (PSO) has established itself as a successful swarm intelligence algorithm in a variety of optimization contexts. The rules of particle dynamics that govern this movement are inspired by models of swarming and flocking [19]. In PSO population, each particle has a position and a velocity and experiences linear spring-like attractions towards two attractors: its previous best position (pbest) and the best position of its neighbors (gbest). Until now there have been several proposals for extending PSO to multiobjective problems and these methods are called multiobjective particles swarm optimization (MOPSO) [20]. The greatest challenge in extending the PSO to multiobjective problems is deciphering the notion of guide and selection ofpbest andgbest as in multiobjective scenario. In this work, we considered a Pareto-based MOPSO [21] to solve MORNP. This algorithm incorporates the main mechanisms of NSGA-II to a PSO algorithm. In this approach, once a particle has updated its position, instead of comparing the new position only against thepbest position of the particle, all thepbest positions of the swarm and all the new positions recently obtained are combined in just one set. Then, MOPSO selects the best solutions among them to construct the next swarm (by means of a nondominated sorting). This approach also selects the leaders randomly from the leaders set (stored in an external archive) among the best of them, based on two different mechanisms: a niche count and a nearest neighbor density estimator. For further information about this MOPSO algorithm see [21].


## 3.5. Optimization Procedure

The overall operating process of MORNP based on MOEA and MOSI algorithms can be described as follows:Step 1 (initialization).
The positions of all individuals of each algorithm are randomly generated, with each(
X
i
k
,
Y
i
k
) being a random point in the working area and P
i
k being a random value within the transmitted power range of readers (
k
=
1,2
,
…
,
N
r
).Step 2 (fitness evaluation).
As described in Section2, the individuals should be evaluated on all the objectives of MORNP including maximizing tag coverage (defined by (2)), minimizing interference (defined by (3)), maximizing economic efficiency (defined by (4)), and maintaining an optimal load balance (defined by (5)), in an order of decreasing importance. Accordingly, the algorithm handles these four objectives in a multiobjective manner in the next step.Step 3 (population evolution).
Compare the evaluated fitness values and update the position of each individual according to specific rules of MOABC, NSGA-II, and MOPSO, respectively.Step 4 (termination condition).
The computation is repeated until the maximum number of iterations is met or the system requirement is researched.


## 4. Experiment

### 4.1. Experimental Setup

We consider an idea example shown in Table2 [4]. That is, the proposed algorithm is evaluated against a test working area: a 30 m × 30 m working space with 100 tags that are distributed by a specific topology (shown in Figure 4). Ten RFID readers, whose radiated power is adjustable in the range from 0.1 to 2 watt, are considered to serve this area. Here the interrogation range according to the reader radiated power is computed as in [4].Table 2
The example setting of a RFID network.
Reader specification
Topology specification
Reader number
10
Dimension
30
m
×
30
m
Radiated power
0.1–2 watt
Tag number
100
Interrogation range
3-4 m
Tag distribution
Uniform
Interference range
3.5–4.5 m
Tag power threshold
−10 dBmFigure 4
The test working area with 100 tags.In this experiment, the performance of three multiobjective EA and SI algorithms, namely, the MOABC, NSGA-II, and MOPSO, is compared on two- and three-objective MORNP cases. The maximum generation for each algorithm is 1000. The initialized population size of 100 individuals is the same for all tested algorithms. For MOABC, archive sizeA
=
100, elitism probability is 0.4. For NSGA-II, crossover probability p
c
=
0.9, mutation probability p
m
=
1
/
n (where n is the number of decision variables), and distribution indices for crossover and mutation operators η
c
=
20 and η
m
=
20, respectively. For MOPSO, the inertia weight ω started at 0.9 and ended at 0.5 and the learning rate c
1
=
c
2
=
2.0, and for the other parameters set for MOPSO please refer to [21].


### 4.2. Best Compromise Solution Based on Fuzzy Decision

Upon having the Pareto-optimal set of nondominated solution, the proposed approach presents one solution to the decision maker in RFID middleware as the best compromise solution. In this work, a fuzzy-based mechanism is employed to extract the best compromise solution over the trade-off curve and assist the decision maker to adjust the generation levels efficiently [22]. Due to imprecise nature of the decision maker’s judgment, each objective function of the ith solution is represented by a membership function μ
i defined as follows:
(7)
μ
i
=
{
1
,
F
i
≤
F
i
min
⁡
,
F
i
max
⁡
-
F
i
F
i
max
⁡
-
F
i
min
⁡
,
F
i
min
⁡
≤
F
i
≤
F
i
max
⁡
0
,
F
i
≥
F
i
max
⁡
,
,
where F
i
min
⁡ and F
i
max
⁡ are lower and upper bounds of ith objective function. The higher the values of the membership function are, the greater the solution satisfaction is.For each nondominated solution, the normalized membership functionμ
k is calculated as
(8)
μ
k
=
∑
i
=
1
N
obj
μ
i
k
∑
k
=
1
M
∑
i
=
1
N
obj
μ
i
k
,
where M is the number of nondominated solutions and N
obj is the number of object. The best compromise solution is the one having the maximum of μ
k.


### 4.3. Two-Objective MORNP Optimization Results

In this case, the RFID network planning is handled as a multiobjective optimization problem, where each two objective functions are optimized simultaneously. According to thetag coverage-reader interference,tag coverage-load balance,tag coverage-economic efficiency,reader interference-load balance,reader interference-economic efficiency, andload balance-economic efficiencypairs, all obtained Pareto fronts by the MOABC, NSGA-II, and MOPSO algorithms are shown in Figures 5, 6, 7, 8, 9, and 10, respectively. Table 3 shows the best compromise solutions for each objective in the two-dimensional Pareto front.Table 3
The best compromise solutions for each two-objective pair from the Pareto front based on different multiobjective algorithms.
f
1-f
2: tag coverage-reader interference
f
1-f
2: tag coverage-load balance
f
1-f
2: tag coverage-economic efficiency
f
1-f
2: reader interference-load balance
f
1-f
2: reader interference-economic efficiency
f
1-f
2: load balance-economic efficiency
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
X
1
14.6668
14.9591
23.6603
8.0243
14.3741
3.0968
22.1271
12.0735
25.7203
15.0263
16.2267
11.6752
17.2808
11.9258
15.2901
13.5976
14.8326
26.9110
Y
1
14.2470
14.1992
15.3618
8.1933
13.2948
18.8718
16.0752
13.0334
19.2306
15.4210
15.8344
21.2025
15.9344
12.2486
15.7009
11.7350
2.7473
19.0259
X
2
14.4493
14.6396
14.8650
23.8009
14.6396
22.0302
3.0673
16.8770
6.2154
16.9529
15.7222
15.8465
16.1994
12.2200
18.8190
28.2506
17.4607
6.6272
Y
2
14.2839
14.1494
15.4898
13.3678
3.2982
15.4898
12.6043
3.3217
13.6645
15.2430
15.1584
12.4404
17.5005
12.2523
20.9882
18.8189
17.5964
13.0753
X
3
7.5738
14.8056
14.4811
22.4914
22.5116
14.4811
12.2238
23.1667
8.0651
12.5142
15.0240
20.5168
15.3896
16.1644
13.8571
16.4754
12.0461
26.1841
Y
3
14.8167
13.8212
15.5783
18.4790
7.9865
27.6549
12.0984
18.9583
21.8078
12.6226
15.5996
15.8852
11.9416
15.7955
13.2327
2.3578
12.1474
17.4291
X
4
14.1844
21.2353
13.9386
10.8805
6.4234
13.4249
17.0103
21.7660
19.1332
12.2440
14.6418
13.6673
12.2466
13.2044
14.8848
28.1157
8.9226
18.3752
Y
4
14.7374
13.2745
15.3881
0
21.5524
7.1051
1.7632
14.8215
18.6486
13.9441
15.8820
12.5367
12.1589
16.3929
20.4061
16.2639
22.6934
16.9155
X
5
21.8309
16.8342
14.8401
16.7345
25.4174
13.0661
15.6573
7.7429
14.8634
16.8370
15.5021
9.4594
12.2530
16.1182
13.4459
12.1106
6.6118
27.7083
Y
5
15.6692
9.5623
14.8721
2.6244
19.8279
21.5497
2.6164
12.2108
2.9496
16.2388
16.5136
13.8324
12.1940
16.0794
15.4850
3.0829
24.8726
15.9665
X
6
13.7471
17.0190
7.4532
19.4920
24.9699
29.9945
26.0054
24.7067
10.6806
16.3634
15.7880
12.0369
6.9216
9.1411
16.8075
4.8475
6.7352
25.8685
Y
6
22.4647
18.9882
9.1349
29.4010
17.7300
21.6393
16.5819
17.424
16.8855
9.3519
21.7933
12.0127
22.3016
23.9233
9.2303
12.5767
20.9216
17.0771
X
7
21.4122
17.7159
22.2261
12.7520
18.0847
13.4248
10.7506
7.5776
18.4566
28.6247
17.3494
24.9182
2.5598
28.7307
9.0639
26.0313
27.2525
28.2079
Y
7
29.5893
18.7159
9.0002
9.7634
22.5299
18.5291
4.2459
22.2473
29.0428
23.5482
14.6977
10.4249
13.6075
18.0936
12.2212
16.5968
17.2175
16.3333
X
8
23.7329
17.9861
12.7217
1.9005
7.6897
0.6968
7.7477
10.8887
18.7944
11.7648
19.2868
23.6823
9.3788
8.8868
11.5189
10.8501
3.0391
29.5283
Y
8
30.0000
13.7097
1.4773
10.5770
12.3945
27.2645
22.1314
12.2439
12.4288
11.3147
14.2619
19.3590
21.9164
22.6378
0.5988
12.4080
12.6008
15.2288
X
9
0.0394
20.4814
22.5273
0
21.0586
24.5199
28.4301
13.3601
12.1297
29.2736
20.3418
9.8239
27.3754
14.7298
12.8665
7.7341
5.5630
7.9657
Y
9
0.5512
15.7414
7.2266
13.2954
6.2764
10.6532
17.6250
12.0000
14.3425
29.1248
20.5881
8.9728
17.0486
2.5995
14.4691
22.1321
22.9728
21.8465
X
1
0
0.9966
22.9037
3.7019
12.1615
26.1840
19.1473
16.3310
2.8480
2.5991
18.6003
16.1876
4.1920
18.9171
6.5382
26.6609
17.5415
9.6663
13.4027
Y
1
0
25.4693
17.9346
20.9468
23.4485
21.2759
15.3933
18.1338
11.1619
15.7726
2.1852
13.2425
9.9108
18.5032
21.0702
17.8097
17.5877
20.3473
7.7711
P
1
29.6831
25.4623
16.2849
30.0000
22.9925
21.8565
29.1985
7.3709
19.9079
30.0000
20.7485
29.9531
30.0000
28.1238
20.0529
15.7997
21.2355
17.4112
P
2
30.0000
23.9497
22.9714
2.6086
12.4009
16.4076
12.6566
18.7052
19.9648
30.0000
24.2889
28.9745
30.0000
26.9935
21.3541
29.9113
17.1525
8.5656
P
3
29.9923
21.5273
16.2968
30.0000
18.0682
25.2165
1.6545
14.5860
0.7097
29.9835
18.8867
16.2649
30.0000
28.5281
27.7953
29.5788
17.0314
19.7733
P
4
30.0000
24.1162
27.3476
24.5835
25.4954
13.6050
0.0006
9.4255
5.3374
29.9908
21.8553
29.9507
29.9048
28.3914
19.3609
7.3992
22.3946
28.3690
P
5
29.8647
20.9584
27.8525
20.1886
21.6631
29.4136
0
22.4140
15.8294
30.0000
19.6825
20.7239
29.9968
30.0000
18.6862
30.0000
23.1712
7.1341
P
6
29.2786
22.0590
18.9056
29.9921
13.5260
20.3225
29.9308
17.3120
15.2129
29.5915
20.7426
29.8516
30.0000
30.0000
29.9661
30.0000
21.1680
6.6785
P
7
29.9781
28.7987
29.3736
18.0392
11.0446
23.8474
0.0052
17.8124
7.4149
28.1585
24.1357
14.3184
30.0000
29.9349
29.9941
13.0170
16.2818
5.6323
P
8
29.8020
25.3925
25.5862
24.1827
11.9192
12.0720
30.0000
18.6012
5.3309
30.0000
17.9936
29.3191
29.9373
28.4198
30.0000
29.9472
10.7081
10.5206
P
9
29.8250
27.5284
29.9612
7.8134
16.7762
29.8577
0.1760
14.3726
1.7169
30.0000
17.2945
25.0529
29.9955
29.1151
29.7016
29.6526
17.7010
10.4884
P
1
0
29.4446
28.4619
29.5342
30.0000
14.1121
27.6338
29.9470
22.2466
13.1698
30.0000
17.3401
230523
29.9822
30.0000
16.8744
29.9478
11.4670
18.0714
f
1
0.0944
0.1257
0.1816
0.0272
0.1461
0.0262
0.0592
0.0481
0.1704
0.4648
0.5083
0.5471
0.4756
0.4766
0.5256
0
0
0
f
2
0.4998
0.5208
0.5163
0
0
0
0.0244
0.1026
0.0516
0
0.0138
0
0.0971
0.1468
0.2450
0.0124
0.0043
0.0432
WhereX
i and Y
i represent the position of the ith RFID reader in the working area and P
i represents the radiated power of the ith RFID reader.Figure 5
Pareto fronts for tag coverage-reader interference.Figure 6
Pareto fronts for tag coverage-load balance.Figure 7
Pareto fronts for tag coverage-economic efficiency.Figure 8
Pareto fronts for reader interference-load balance.Figure 9
Pareto fronts for reader interference-economic efficiency.Figure 10
Pareto fronts for load balance-economic efficiency.From the results, we can observe that the trade-off among two selected competing objectives is obtained by emphasizing on nondominated solutions and getting a well-distributed set of solutions, respectively. From Figures5–11, it is clear that the MOABC algorithm is able to obtain well-distributed Pareto-optimal fronts. From Table 3, we can see that MOABC gets the best convergence solutions for most of objective pairs.Figure 11
Pareto fronts for tag coverage-reader interference-load balance.


### 4.4. Three-Objective MORNP Optimization Results

In this case, three competing objectives are optimized simultaneously by the MOEA and MOSI algorithms. According to the three-objective combination set, namely,tag coverage-reader interference-load balance,tag coverage-reader interference-economic efficiency,tag coverage-load balance-economic efficiency, andreader interference-load balance-economic efficiency, all obtained Pareto fronts by the MOABC, NSGA-II, and MOPSO algorithms are shown in Figures 11, 12, 13, and 14, respectively. Table 4 shows the best compromise Pareto-optimal solutions for each objective in the three-dimensional Pareto front, respectively.Table 4
The best compromise solutions for each three-objective combination from the Pareto front based on different multiobjective algorithms.
f
1-f
2-f
3: tag coverage-reader interference-load balance
f
1-f
2-f
3: tag coverage-reader interference-economic efficiency
f
1-f
2-f
3: tag coverage-load balance-economic efficiency
f
1-f
2-f
3: reader interference-load balance-economic efficiency
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
X
1
30.0000
15.6458
20.3190
14.4420
11.8283
8.4442
26.8131
17.8148
17.5537
25.8946
22.6339
27.2339
Y
1
16.9790
14.3781
12.5002
0
18.3440
20.7029
16.5430
14.6978
17.6758
16.4923
16.1318
13.4871
X
2
11.6783
16.2336
18.2667
7.0450
17.0533
23.4947
12.0077
13.8891
7.9142
29.9279
14.4756
3.6646
Y
2
6.8240
10.2314
12.2365
24.7556
15.0016
17.5124
11.8382
7.9821
22.1609
18.4677
17.6092
19.5012
X
3
25.4676
18.2227
24.0731
26.9491
7.3295
7.7721
28.9775
16.5915
4.3063
17.5268
14.9108
21.3461
Y
3
14.1602
6.5977
19.6585
18.6439
16.4109
21.3357
18.2038
15.0106
5.9032
17.6167
14.0875
14.3025
X
4
5.9639
11.0810
14.0721
17.3119
16.4662
22.9025
8.1405
13.4403
12.2387
28.0962
13.8269
15.3770
Y
4
13.4280
23.6013
13.4354
18.3675
17.3788
16.5265
21.7743
23.5938
12.0325
16.4211
14.1824
25.2919
X
5
15.2744
14.6464
15.1293
12.4728
17.1886
8.2734
2.8157
22.4016
25.1392
12.6584
14.6806
12.7989
Y
5
17.3405
10.8091
6.9810
11.0377
17.4837
17.5023
11.3618
14.1959
12.8338
11.7092
15.0255
22.7917
X
6
20.2859
14.0696
13.3128
6.9209
17.6499
28.3456
27.2172
3.7468
14.6130
14.7326
13.2400
27.0443
Y
6
11.6031
9.2959
19.4163
20.6577
16.9948
18.6085
16.6506
12.6232
2.5993
2.6127
17.7407
19.0955
X
7
28.1739
21.6110
22.2639
4.3360
10.6829
25.4949
28.7175
14.7962
26.1424
29.9136
13.6599
12.9675
Y
7
29.6683
11.5423
9.9485
13.6199
16.8479
13.6055
16.1278
2.1734
15.7406
15.3185
6.6932
12.9054
X
8
20.9052
16.7326
10.6803
2.3055
15.4599
5.3180
17.7040
28.6417
26.2886
3.0762
15.0238
25.6991
Y
8
13.2269
11.8862
8.8565
10.7391
6.5395
27.2699
17.7577
18.8571
17.2283
12.6195
13.8859
13.8272
X
9
2.5844
17.4557
5.6418
9.9599
25.5618
12.3296
15.5689
9.0791
2.5127
7.9611
14.8855
23.1240
Y
9
30.0000
9.2592
29.6541
19.3121
16.3300
21.1540
2.6437
21.8757
13.5274
22.2376
15.1088
5.5600
X
1
0
6.9912
9.7717
26.9739
18.6074
12.3257
24.2924
3.5366
26.2076
27.2014
27.3023
12.2537
13.2477
Y
1
0
22.8135
12.3124
14.5397
15.6450
11.8818
10.9631
13.8447
16.4889
16.0260
18.4885
11.5432
6.3683
P
1
28.5994
10.2497
24.3570
29.3637
19.6143
9.7765
0
10.7962
5.3177
0
16.9192
9.1608
P
2
29.9048
14.8504
20.5618
28.9276
17.3447
11.2273
29.8120
12.8104
4.5570
29.4346
16.1668
8.1942
P
3
29.3810
15.5604
5.5342
28.4916
17.7065
22.6933
0.1976
18.7327
21.5341
20.5107
20.0453
19.8892
P
4
29.7105
18.3519
29.8482
29.9584
18.1298
0
30.0000
0
23.8859
0.2752
18.0065
10.7492
P
5
29.9965
12.0862
27.3747
30.0000
16.6680
6.0234
3.5911
0
29.4297
3.2871
21.4912
0
P
6
0
16.6213
7.2695
28.5306
19.4510
4.3180
0
7.3890
16.9454
27.9123
17.7692
20.0606
P
7
0
20.5853
0
29.1589
16.6647
22.7788
8.9367
17.8957
20.7766
0
12.4918
12.6108
P
8
30.0000
23.1314
12.8241
27.0217
21.8865
15.0980
26.6633
22.7678
25.9616
6.2084
17.1475
17.9766
P
9
0
15.1540
28.5495
30.0000
20.8408
28.6249
7.7588
20.7964
10.3521
28.7588
13.4188
28.7101
P
1
0
29.8938
16.5469
20.3087
29.1991
20.2684
16.3864
30.0000
14.7074
0.1723
29.5780
18.0411
23.8331
f
1
0.4300
0.2413
0.0400
0.2827
0.3225
0.1291
0.0281
0.0926
0.4132
0.3735
0.3489
0.0803
f
2
0.4583
0.5458
06788
0.6043
0.5522
0.7583
0
0
0.0698
0.3212
0.5562
0.6562
f
3
0
0
0
0.0627
0.2661
0.4006
0.0287
0.1211
0.0019
0.0082
0.3079
0.3542Figure 12
Pareto fronts for tag coverage-reader interference-economic efficiency.Figure 13
Pareto fronts for tag coverage-load balance-economic efficiency.Figure 14
Pareto fronts for reader interference-load balance-economic efficiency.It is clear that each RNP objective cannot be further improved without degrading the other related optimized objectives. Figures11–14 clearly show the relationships among all presented objective functions. Between the obtained Pareto-optimal solutions, it is necessary to choose one of them as a best compromise for implementation.Figures15(a)–15(l) show the reader locations and radiated power contours for the four three-objective MORNP instances, in which the best results obtained by MOABC, MOPSO, and NSGA-II are compared in a visible way. A contour in the figures represents the points with the same radiated power (which equals the value assigned to that contour). It can be seen in Figure 15 that the power peaks in the working area are the points where the readers are placed. Then, the signal strength decreases with respect to the distance to the readers. The figures clearly show that all the MO algorithms try to (1) generate an optimal reader network layout with high tag coverage rate; (2) maintain sufficient distances between RFID readers to reduce interference; (3) provide a satisfactory economic efficiency by increasing the best-server areas; and (4) configure the network in a load balance scheme so that each reader in the network serves the optimal amount of tags according to its capacity.Reader distribution and radiated power contour obtained by MOABC, MOPSO, and NSGA-II: (a)–(c) for tag coverage-reader interference-load balance; (d)–(f) for tag coverage-reader interference-economic efficiency; (g)–(h) for tag coverage-load balance-economic efficiency; (j)–(l) for reader interference-load balance-economic efficiency.
(a)
MOABC
(b)
MOPSO
(c)
NSGA-II
(d)
MOABC
(e)
MOPSO
(f)
NSGA-II
(g)
MOABC
(h)
MOPSO
(i)
NSGA-II
(j)
MOABC
(k)
MOPSO
(l)
NSGA-IIIt can once again be proved that the MOABC algorithm is giving better performance for four three-objective MORNP cases, while the other two algorithms sometimes have redundant readers and cannot provide full coverage. All the results confirm that the MOEA and MOSI methods are impressive tools for solving the multiobjective RFID network planning problem where multiple Pareto-optimal solutions can be obtained in a single run.


## 4.1. Experimental Setup

We consider an idea example shown in Table2 [4]. That is, the proposed algorithm is evaluated against a test working area: a 30 m × 30 m working space with 100 tags that are distributed by a specific topology (shown in Figure 4). Ten RFID readers, whose radiated power is adjustable in the range from 0.1 to 2 watt, are considered to serve this area. Here the interrogation range according to the reader radiated power is computed as in [4].Table 2
The example setting of a RFID network.
Reader specification
Topology specification
Reader number
10
Dimension
30
m
×
30
m
Radiated power
0.1–2 watt
Tag number
100
Interrogation range
3-4 m
Tag distribution
Uniform
Interference range
3.5–4.5 m
Tag power threshold
−10 dBmFigure 4
The test working area with 100 tags.In this experiment, the performance of three multiobjective EA and SI algorithms, namely, the MOABC, NSGA-II, and MOPSO, is compared on two- and three-objective MORNP cases. The maximum generation for each algorithm is 1000. The initialized population size of 100 individuals is the same for all tested algorithms. For MOABC, archive sizeA
=
100, elitism probability is 0.4. For NSGA-II, crossover probability p
c
=
0.9, mutation probability p
m
=
1
/
n (where n is the number of decision variables), and distribution indices for crossover and mutation operators η
c
=
20 and η
m
=
20, respectively. For MOPSO, the inertia weight ω started at 0.9 and ended at 0.5 and the learning rate c
1
=
c
2
=
2.0, and for the other parameters set for MOPSO please refer to [21].


## 4.2. Best Compromise Solution Based on Fuzzy Decision

Upon having the Pareto-optimal set of nondominated solution, the proposed approach presents one solution to the decision maker in RFID middleware as the best compromise solution. In this work, a fuzzy-based mechanism is employed to extract the best compromise solution over the trade-off curve and assist the decision maker to adjust the generation levels efficiently [22]. Due to imprecise nature of the decision maker’s judgment, each objective function of the ith solution is represented by a membership function μ
i defined as follows:
(7)
μ
i
=
{
1
,
F
i
≤
F
i
min
⁡
,
F
i
max
⁡
-
F
i
F
i
max
⁡
-
F
i
min
⁡
,
F
i
min
⁡
≤
F
i
≤
F
i
max
⁡
0
,
F
i
≥
F
i
max
⁡
,
,
where F
i
min
⁡ and F
i
max
⁡ are lower and upper bounds of ith objective function. The higher the values of the membership function are, the greater the solution satisfaction is.For each nondominated solution, the normalized membership functionμ
k is calculated as
(8)
μ
k
=
∑
i
=
1
N
obj
μ
i
k
∑
k
=
1
M
∑
i
=
1
N
obj
μ
i
k
,
where M is the number of nondominated solutions and N
obj is the number of object. The best compromise solution is the one having the maximum of μ
k.


## 4.3. Two-Objective MORNP Optimization Results

In this case, the RFID network planning is handled as a multiobjective optimization problem, where each two objective functions are optimized simultaneously. According to thetag coverage-reader interference,tag coverage-load balance,tag coverage-economic efficiency,reader interference-load balance,reader interference-economic efficiency, andload balance-economic efficiencypairs, all obtained Pareto fronts by the MOABC, NSGA-II, and MOPSO algorithms are shown in Figures 5, 6, 7, 8, 9, and 10, respectively. Table 3 shows the best compromise solutions for each objective in the two-dimensional Pareto front.Table 3
The best compromise solutions for each two-objective pair from the Pareto front based on different multiobjective algorithms.
f
1-f
2: tag coverage-reader interference
f
1-f
2: tag coverage-load balance
f
1-f
2: tag coverage-economic efficiency
f
1-f
2: reader interference-load balance
f
1-f
2: reader interference-economic efficiency
f
1-f
2: load balance-economic efficiency
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
X
1
14.6668
14.9591
23.6603
8.0243
14.3741
3.0968
22.1271
12.0735
25.7203
15.0263
16.2267
11.6752
17.2808
11.9258
15.2901
13.5976
14.8326
26.9110
Y
1
14.2470
14.1992
15.3618
8.1933
13.2948
18.8718
16.0752
13.0334
19.2306
15.4210
15.8344
21.2025
15.9344
12.2486
15.7009
11.7350
2.7473
19.0259
X
2
14.4493
14.6396
14.8650
23.8009
14.6396
22.0302
3.0673
16.8770
6.2154
16.9529
15.7222
15.8465
16.1994
12.2200
18.8190
28.2506
17.4607
6.6272
Y
2
14.2839
14.1494
15.4898
13.3678
3.2982
15.4898
12.6043
3.3217
13.6645
15.2430
15.1584
12.4404
17.5005
12.2523
20.9882
18.8189
17.5964
13.0753
X
3
7.5738
14.8056
14.4811
22.4914
22.5116
14.4811
12.2238
23.1667
8.0651
12.5142
15.0240
20.5168
15.3896
16.1644
13.8571
16.4754
12.0461
26.1841
Y
3
14.8167
13.8212
15.5783
18.4790
7.9865
27.6549
12.0984
18.9583
21.8078
12.6226
15.5996
15.8852
11.9416
15.7955
13.2327
2.3578
12.1474
17.4291
X
4
14.1844
21.2353
13.9386
10.8805
6.4234
13.4249
17.0103
21.7660
19.1332
12.2440
14.6418
13.6673
12.2466
13.2044
14.8848
28.1157
8.9226
18.3752
Y
4
14.7374
13.2745
15.3881
0
21.5524
7.1051
1.7632
14.8215
18.6486
13.9441
15.8820
12.5367
12.1589
16.3929
20.4061
16.2639
22.6934
16.9155
X
5
21.8309
16.8342
14.8401
16.7345
25.4174
13.0661
15.6573
7.7429
14.8634
16.8370
15.5021
9.4594
12.2530
16.1182
13.4459
12.1106
6.6118
27.7083
Y
5
15.6692
9.5623
14.8721
2.6244
19.8279
21.5497
2.6164
12.2108
2.9496
16.2388
16.5136
13.8324
12.1940
16.0794
15.4850
3.0829
24.8726
15.9665
X
6
13.7471
17.0190
7.4532
19.4920
24.9699
29.9945
26.0054
24.7067
10.6806
16.3634
15.7880
12.0369
6.9216
9.1411
16.8075
4.8475
6.7352
25.8685
Y
6
22.4647
18.9882
9.1349
29.4010
17.7300
21.6393
16.5819
17.424
16.8855
9.3519
21.7933
12.0127
22.3016
23.9233
9.2303
12.5767
20.9216
17.0771
X
7
21.4122
17.7159
22.2261
12.7520
18.0847
13.4248
10.7506
7.5776
18.4566
28.6247
17.3494
24.9182
2.5598
28.7307
9.0639
26.0313
27.2525
28.2079
Y
7
29.5893
18.7159
9.0002
9.7634
22.5299
18.5291
4.2459
22.2473
29.0428
23.5482
14.6977
10.4249
13.6075
18.0936
12.2212
16.5968
17.2175
16.3333
X
8
23.7329
17.9861
12.7217
1.9005
7.6897
0.6968
7.7477
10.8887
18.7944
11.7648
19.2868
23.6823
9.3788
8.8868
11.5189
10.8501
3.0391
29.5283
Y
8
30.0000
13.7097
1.4773
10.5770
12.3945
27.2645
22.1314
12.2439
12.4288
11.3147
14.2619
19.3590
21.9164
22.6378
0.5988
12.4080
12.6008
15.2288
X
9
0.0394
20.4814
22.5273
0
21.0586
24.5199
28.4301
13.3601
12.1297
29.2736
20.3418
9.8239
27.3754
14.7298
12.8665
7.7341
5.5630
7.9657
Y
9
0.5512
15.7414
7.2266
13.2954
6.2764
10.6532
17.6250
12.0000
14.3425
29.1248
20.5881
8.9728
17.0486
2.5995
14.4691
22.1321
22.9728
21.8465
X
1
0
0.9966
22.9037
3.7019
12.1615
26.1840
19.1473
16.3310
2.8480
2.5991
18.6003
16.1876
4.1920
18.9171
6.5382
26.6609
17.5415
9.6663
13.4027
Y
1
0
25.4693
17.9346
20.9468
23.4485
21.2759
15.3933
18.1338
11.1619
15.7726
2.1852
13.2425
9.9108
18.5032
21.0702
17.8097
17.5877
20.3473
7.7711
P
1
29.6831
25.4623
16.2849
30.0000
22.9925
21.8565
29.1985
7.3709
19.9079
30.0000
20.7485
29.9531
30.0000
28.1238
20.0529
15.7997
21.2355
17.4112
P
2
30.0000
23.9497
22.9714
2.6086
12.4009
16.4076
12.6566
18.7052
19.9648
30.0000
24.2889
28.9745
30.0000
26.9935
21.3541
29.9113
17.1525
8.5656
P
3
29.9923
21.5273
16.2968
30.0000
18.0682
25.2165
1.6545
14.5860
0.7097
29.9835
18.8867
16.2649
30.0000
28.5281
27.7953
29.5788
17.0314
19.7733
P
4
30.0000
24.1162
27.3476
24.5835
25.4954
13.6050
0.0006
9.4255
5.3374
29.9908
21.8553
29.9507
29.9048
28.3914
19.3609
7.3992
22.3946
28.3690
P
5
29.8647
20.9584
27.8525
20.1886
21.6631
29.4136
0
22.4140
15.8294
30.0000
19.6825
20.7239
29.9968
30.0000
18.6862
30.0000
23.1712
7.1341
P
6
29.2786
22.0590
18.9056
29.9921
13.5260
20.3225
29.9308
17.3120
15.2129
29.5915
20.7426
29.8516
30.0000
30.0000
29.9661
30.0000
21.1680
6.6785
P
7
29.9781
28.7987
29.3736
18.0392
11.0446
23.8474
0.0052
17.8124
7.4149
28.1585
24.1357
14.3184
30.0000
29.9349
29.9941
13.0170
16.2818
5.6323
P
8
29.8020
25.3925
25.5862
24.1827
11.9192
12.0720
30.0000
18.6012
5.3309
30.0000
17.9936
29.3191
29.9373
28.4198
30.0000
29.9472
10.7081
10.5206
P
9
29.8250
27.5284
29.9612
7.8134
16.7762
29.8577
0.1760
14.3726
1.7169
30.0000
17.2945
25.0529
29.9955
29.1151
29.7016
29.6526
17.7010
10.4884
P
1
0
29.4446
28.4619
29.5342
30.0000
14.1121
27.6338
29.9470
22.2466
13.1698
30.0000
17.3401
230523
29.9822
30.0000
16.8744
29.9478
11.4670
18.0714
f
1
0.0944
0.1257
0.1816
0.0272
0.1461
0.0262
0.0592
0.0481
0.1704
0.4648
0.5083
0.5471
0.4756
0.4766
0.5256
0
0
0
f
2
0.4998
0.5208
0.5163
0
0
0
0.0244
0.1026
0.0516
0
0.0138
0
0.0971
0.1468
0.2450
0.0124
0.0043
0.0432
WhereX
i and Y
i represent the position of the ith RFID reader in the working area and P
i represents the radiated power of the ith RFID reader.Figure 5
Pareto fronts for tag coverage-reader interference.Figure 6
Pareto fronts for tag coverage-load balance.Figure 7
Pareto fronts for tag coverage-economic efficiency.Figure 8
Pareto fronts for reader interference-load balance.Figure 9
Pareto fronts for reader interference-economic efficiency.Figure 10
Pareto fronts for load balance-economic efficiency.From the results, we can observe that the trade-off among two selected competing objectives is obtained by emphasizing on nondominated solutions and getting a well-distributed set of solutions, respectively. From Figures5–11, it is clear that the MOABC algorithm is able to obtain well-distributed Pareto-optimal fronts. From Table 3, we can see that MOABC gets the best convergence solutions for most of objective pairs.Figure 11
Pareto fronts for tag coverage-reader interference-load balance.


## 4.4. Three-Objective MORNP Optimization Results

In this case, three competing objectives are optimized simultaneously by the MOEA and MOSI algorithms. According to the three-objective combination set, namely,tag coverage-reader interference-load balance,tag coverage-reader interference-economic efficiency,tag coverage-load balance-economic efficiency, andreader interference-load balance-economic efficiency, all obtained Pareto fronts by the MOABC, NSGA-II, and MOPSO algorithms are shown in Figures 11, 12, 13, and 14, respectively. Table 4 shows the best compromise Pareto-optimal solutions for each objective in the three-dimensional Pareto front, respectively.Table 4
The best compromise solutions for each three-objective combination from the Pareto front based on different multiobjective algorithms.
f
1-f
2-f
3: tag coverage-reader interference-load balance
f
1-f
2-f
3: tag coverage-reader interference-economic efficiency
f
1-f
2-f
3: tag coverage-load balance-economic efficiency
f
1-f
2-f
3: reader interference-load balance-economic efficiency
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
MOABC
MOPSO
NSGA-II
X
1
30.0000
15.6458
20.3190
14.4420
11.8283
8.4442
26.8131
17.8148
17.5537
25.8946
22.6339
27.2339
Y
1
16.9790
14.3781
12.5002
0
18.3440
20.7029
16.5430
14.6978
17.6758
16.4923
16.1318
13.4871
X
2
11.6783
16.2336
18.2667
7.0450
17.0533
23.4947
12.0077
13.8891
7.9142
29.9279
14.4756
3.6646
Y
2
6.8240
10.2314
12.2365
24.7556
15.0016
17.5124
11.8382
7.9821
22.1609
18.4677
17.6092
19.5012
X
3
25.4676
18.2227
24.0731
26.9491
7.3295
7.7721
28.9775
16.5915
4.3063
17.5268
14.9108
21.3461
Y
3
14.1602
6.5977
19.6585
18.6439
16.4109
21.3357
18.2038
15.0106
5.9032
17.6167
14.0875
14.3025
X
4
5.9639
11.0810
14.0721
17.3119
16.4662
22.9025
8.1405
13.4403
12.2387
28.0962
13.8269
15.3770
Y
4
13.4280
23.6013
13.4354
18.3675
17.3788
16.5265
21.7743
23.5938
12.0325
16.4211
14.1824
25.2919
X
5
15.2744
14.6464
15.1293
12.4728
17.1886
8.2734
2.8157
22.4016
25.1392
12.6584
14.6806
12.7989
Y
5
17.3405
10.8091
6.9810
11.0377
17.4837
17.5023
11.3618
14.1959
12.8338
11.7092
15.0255
22.7917
X
6
20.2859
14.0696
13.3128
6.9209
17.6499
28.3456
27.2172
3.7468
14.6130
14.7326
13.2400
27.0443
Y
6
11.6031
9.2959
19.4163
20.6577
16.9948
18.6085
16.6506
12.6232
2.5993
2.6127
17.7407
19.0955
X
7
28.1739
21.6110
22.2639
4.3360
10.6829
25.4949
28.7175
14.7962
26.1424
29.9136
13.6599
12.9675
Y
7
29.6683
11.5423
9.9485
13.6199
16.8479
13.6055
16.1278
2.1734
15.7406
15.3185
6.6932
12.9054
X
8
20.9052
16.7326
10.6803
2.3055
15.4599
5.3180
17.7040
28.6417
26.2886
3.0762
15.0238
25.6991
Y
8
13.2269
11.8862
8.8565
10.7391
6.5395
27.2699
17.7577
18.8571
17.2283
12.6195
13.8859
13.8272
X
9
2.5844
17.4557
5.6418
9.9599
25.5618
12.3296
15.5689
9.0791
2.5127
7.9611
14.8855
23.1240
Y
9
30.0000
9.2592
29.6541
19.3121
16.3300
21.1540
2.6437
21.8757
13.5274
22.2376
15.1088
5.5600
X
1
0
6.9912
9.7717
26.9739
18.6074
12.3257
24.2924
3.5366
26.2076
27.2014
27.3023
12.2537
13.2477
Y
1
0
22.8135
12.3124
14.5397
15.6450
11.8818
10.9631
13.8447
16.4889
16.0260
18.4885
11.5432
6.3683
P
1
28.5994
10.2497
24.3570
29.3637
19.6143
9.7765
0
10.7962
5.3177
0
16.9192
9.1608
P
2
29.9048
14.8504
20.5618
28.9276
17.3447
11.2273
29.8120
12.8104
4.5570
29.4346
16.1668
8.1942
P
3
29.3810
15.5604
5.5342
28.4916
17.7065
22.6933
0.1976
18.7327
21.5341
20.5107
20.0453
19.8892
P
4
29.7105
18.3519
29.8482
29.9584
18.1298
0
30.0000
0
23.8859
0.2752
18.0065
10.7492
P
5
29.9965
12.0862
27.3747
30.0000
16.6680
6.0234
3.5911
0
29.4297
3.2871
21.4912
0
P
6
0
16.6213
7.2695
28.5306
19.4510
4.3180
0
7.3890
16.9454
27.9123
17.7692
20.0606
P
7
0
20.5853
0
29.1589
16.6647
22.7788
8.9367
17.8957
20.7766
0
12.4918
12.6108
P
8
30.0000
23.1314
12.8241
27.0217
21.8865
15.0980
26.6633
22.7678
25.9616
6.2084
17.1475
17.9766
P
9
0
15.1540
28.5495
30.0000
20.8408
28.6249
7.7588
20.7964
10.3521
28.7588
13.4188
28.7101
P
1
0
29.8938
16.5469
20.3087
29.1991
20.2684
16.3864
30.0000
14.7074
0.1723
29.5780
18.0411
23.8331
f
1
0.4300
0.2413
0.0400
0.2827
0.3225
0.1291
0.0281
0.0926
0.4132
0.3735
0.3489
0.0803
f
2
0.4583
0.5458
06788
0.6043
0.5522
0.7583
0
0
0.0698
0.3212
0.5562
0.6562
f
3
0
0
0
0.0627
0.2661
0.4006
0.0287
0.1211
0.0019
0.0082
0.3079
0.3542Figure 12
Pareto fronts for tag coverage-reader interference-economic efficiency.Figure 13
Pareto fronts for tag coverage-load balance-economic efficiency.Figure 14
Pareto fronts for reader interference-load balance-economic efficiency.It is clear that each RNP objective cannot be further improved without degrading the other related optimized objectives. Figures11–14 clearly show the relationships among all presented objective functions. Between the obtained Pareto-optimal solutions, it is necessary to choose one of them as a best compromise for implementation.Figures15(a)–15(l) show the reader locations and radiated power contours for the four three-objective MORNP instances, in which the best results obtained by MOABC, MOPSO, and NSGA-II are compared in a visible way. A contour in the figures represents the points with the same radiated power (which equals the value assigned to that contour). It can be seen in Figure 15 that the power peaks in the working area are the points where the readers are placed. Then, the signal strength decreases with respect to the distance to the readers. The figures clearly show that all the MO algorithms try to (1) generate an optimal reader network layout with high tag coverage rate; (2) maintain sufficient distances between RFID readers to reduce interference; (3) provide a satisfactory economic efficiency by increasing the best-server areas; and (4) configure the network in a load balance scheme so that each reader in the network serves the optimal amount of tags according to its capacity.Reader distribution and radiated power contour obtained by MOABC, MOPSO, and NSGA-II: (a)–(c) for tag coverage-reader interference-load balance; (d)–(f) for tag coverage-reader interference-economic efficiency; (g)–(h) for tag coverage-load balance-economic efficiency; (j)–(l) for reader interference-load balance-economic efficiency.
(a)
MOABC
(b)
MOPSO
(c)
NSGA-II
(d)
MOABC
(e)
MOPSO
(f)
NSGA-II
(g)
MOABC
(h)
MOPSO
(i)
NSGA-II
(j)
MOABC
(k)
MOPSO
(l)
NSGA-IIIt can once again be proved that the MOABC algorithm is giving better performance for four three-objective MORNP cases, while the other two algorithms sometimes have redundant readers and cannot provide full coverage. All the results confirm that the MOEA and MOSI methods are impressive tools for solving the multiobjective RFID network planning problem where multiple Pareto-optimal solutions can be obtained in a single run.


## 5. Conclusion

In this paper, we have compared three state-of-the-arts evolutionary and swarm intelligence based multiobjective algorithms, namely, MOABC, NSGA-II, and MOPSO, to solve the multiobjective RFID network planning (MORNP). This work differs from previous approaches to RFID network planning, because our new MORNP model focuses on use of multiobjective algorithms to find all the Pareto optimal solutions and to achieve the optimal planning solutions by simultaneously optimizing four conflicting objectives, instead of transforming multiobjective functions into a single objective function in the previous works on RNP. By applying multiobjective approaches for solving MORNP, a new framework was established that could handle different objectives and would enable the planner to find the optimal RFID network plan based on multiobjective EAs and SI.To summarize, some of the contributions of this work are the formulation presented and applied to solve the MORNP and the comparison made among MOABC, NSGA-II, and MOPSO, where we analyze the behavior of each of them in two- and three-objective MORNP totally composed of 10 instances of different nature. As we have seen, MOABC is the algorithm that best results have obtained in most instances.Evaluating new algorithms for this MORNP problem is a matter of future work. In particular, we have planned comparisons with other known multiobjective evolutionary and swarm-based algorithms that have received a lot of attention in the literature. Furthermore, we will also investigate the application of parallel or distributed techniques for solving the MORNP.



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*Source: 961412-2014-04-01.xml*