# Comprehensive Evaluation of Energy Efficiency Based on TOPSIS for Protocols of Collaborative Wireless Sensor Networks

Authors: Ji’an Li; Jianzhong Zhou; Yongchuan Zhang
Journal: International Journal of Distributed Sensor Networks
 (2015)

---

## Abstract

Comprehensive evaluation of energy efficiency of protocols under certain cost conditions is a relatively new and ill-defined concept for collaborative wireless sensor networks (CWSN). In this paper, multicriteria decision making (MCDM) theory is introduced into comprehensive evaluation of energy efficiency of clustering protocols, which is the predecessor of collaborative protocols. Parameters about energy efficiency of total network, including cost and benefit parameters, are selected to construct a metrics system for the comprehensive evaluation. Technique for order preference by similarity to ideal solution (TOPSIS) without criterion weight is proposed as the method of MCDM, and it can be used to select most efficient scheme among many schemes. The experimental results show that the proposed method is effective and can be used in CWSN protocol selection and deployment of nodes.


---

## Body

## 1. Introduction

Energy efficiency is a major challenge for CWSN [1]. The energy of nodes is strongly limited [2] and battery charging is uneasy. Thus it is of great importance to improve the energy efficiency of CWSN. Energy efficiency of CWSN depends on routing protocols [3] to a large extent, and clustering protocols are original collaborative protocols. We limit our discussion only to the analysis and evaluation of energy efficiency of clustering protocols with certain deployment and energy.Previously, energy efficiency of CWSN clustering protocols was discussed by parameters, respectively, under the same cost condition and mostly by the curves of parameters. Heinzelman et al. presented the advantages of LEACH and LEACH-C by the curve of amount of data over amount of energy dissipation, the curve of amount of data over time, the curve of number of alive nodes over time, and the curve of number of alive nodes over amount of data [4]. The metrics of energy efficiency [5] included energy consumption, average energy, standard deviation of energy, throughput, and energy balance, but these metrics were analyzed, respectively. Network size, message overhead, energy overhead, residual energy, and convergence time were also, respectively, used to discuss the energy efficiency of clustering protocols [6]. Darabkh et al. investigated how the sensor density affected the performance of clustering algorithms [2]. Georgios et al. showed the comparison between SEP protocol and other protocols by parameters such as number of alive nodes and number of throughput [7]. Younis and Fahmy, respectively, selected number of nodes, round when all nodes die, and distance from sink to describe the energy efficiency of HEED protocol [8]. Network lifetime and network size were important parameters for energy efficiency comparison, and every comparison was implemented by parameters, respectively, under the same cost conditions [9, 10].Comprehensive evaluation of energy efficiency of clustering protocols is a novel concept, and it could evaluate energy efficiency of clustering protocols comprehensively. This evaluation is different from analysis based on certain parameters, respectively, under the same cost condition. In this paper, energy efficiency is comprehensive performance concerning parameters such as lifetime, energy consumption, and valid data received by base station for clustering protocols. Also, energy efficiency in this paper is different from the ratio between total energy consumption over the number of packets received by the sink-node [5], ignoring the lifetime of network. Parameters that can easily quantify energy efficiency of clustering routing protocols are selected for comprehensive evaluation. Some physical parameters such as latency, fault tolerance [11], and delay [12] applied in complex protocols are not considered in this paper. The selected parameters could be classified into cost parameters and benefit parameters. Moreover, these parameters may be conflicting criteria.Multicriteria decision making (MCDM) has been widely used in evaluating, selecting, or ranking a finite set of decision schemes characterized by multiple and usually conflicting criteria [13]. Chamodrakas and Martakos [14] introduced fuzzy set representation TOPSIS into access network selection, and the evaluation schemes were access technologies running in one terminal (sensor node). Shi and Zhu put forward a network selection algorithm, intending to select access network technology by multiple attribute decision making (MADM) and group decision making (GDM) [15]. TOPSIS method, one of MADM or MCDM methods, was used to select cluster heads [16], and the schemes were sensor nodes. Comprehensive evaluation of energy efficiency based on MCDM theory for clustering protocols is a fairly new study. Multiple parameters about energy efficiency of clustering protocols are considered as multicriteria in MCDM. One clustering protocol running in network with certain cost parameters is taken as one scheme. We use a novel TOPSIS method without criterion weight to select best efficient scheme. This method is different from the ones based on TOPSIS with criterion weight in [13, 14].Clustering protocols such as LEACH [4], LEACH-C [4], SEP [7], and HEED [8] are original collaborative protocols, whose energy efficiency can be presented easily. There are obvious differences between the four protocols: cluster heads are selected by comparing a generated number with threshold in LEACH, LEACH-C uses a centralized clustering algorithm, then SEP consumes the extra energy of advanced nodes, and cluster head selection for HEED is determined by residual energy of each node and intracluster communication cost. The four protocols are pioneering clustering routing approaches for wireless sensor networks (WSNs). Their basic ideas have inspired many subsequent clustering routing protocols. Therefore, we select them as examples for energy efficiency comprehensive evaluation of clustering protocols in this paper. These clustering protocols will run in all network nodes, not in one sensor node as [14]. Thus, comprehensive evaluation schemes in our research are totally different from access technologies in [14].Comprehensive evaluation of energy efficiency can be used to find which protocol is the best scheme regarding the energy efficiency among many selected clustering protocols under the same cost conditions, under which cost condition among selected conditions one protocol is optimal on energy efficiency, and which scheme is the best among different clustering protocols under different cost conditions. This paper will mainly focus on the above three works.The main contributions of this paper could be summarized as follows:(
1
) a metrics system for the comprehensive evaluation of energy efficiency of clustering routing protocols in CWSN is constructed. These metrics include cost and benefit parameters which would be considered as criteria in MCDM. (
2
) A parameter concerning the fluctuation of clustering protocols is presented. It is the standard deviation of one benefit parameter after repeated simulations for schemes. And it can measure the fluctuation of benefit parameters of clustering protocols under certain conditions. To a certain extent, it can represent the fluctuation of protocols. (
3
) A method based on TOPSIS without criterion weight for the comprehensive evaluation of energy efficiency performance of clustering protocols is proposed.The rest of this paper is organized as follows: a metrics system for comprehensive evaluation is constructed in Section2. Section 3 introduces MCDM theory into comprehensive evaluation and proposes a method based on TOPSIS without criterion weight for the comprehensive evaluation of clustering protocols. Simulations and discussion for the novel comprehensive evaluation of clustering protocols based on TOPSIS without criterion weight are shown in Section 4. And conclusions are drawn in Section 5.


## 2. Metrics System for Evaluation

The sensor nodes are randomly distributed under the conditions described by different cost parameters in this paper. The simulation time is divided into rounds as [4]. The radio energy dissipation model [4] is used in this paper. And the values of parameters about energy dissipation for simulations are listed in Table 1.Table 1
Parameter about radio energy dissipation model.
Parameter
Value
Unit
Initial energy of every node
0.5
J
Control package length
100
bit
Data package length
4000
bit
E
Tx
50
×
10
-
9
J
E
Rx
50
×
10
-
9
J
ε
fs
10
×
10
-
12
J
ε
mp
0.0013
×
10
-
12
J
E
DA
5
×
10
-
9
J
Percentage of nodes becoming into CHs among all nodes
0.05
—The radio energy dissipation model and parameter values in Table1 are also used in Section 4.


### 2.1. A Parameter to Measure Fluctuation of Clustering Protocols

In the applications of the clustering protocols such as LEACH, LEACH-C, SEP, and HEED, massive sensor nodes are deployed in the region randomly, leading to the fluctuation of network. The fluctuation refers to the variation of benefit parameters in repeated experiments. Cluster heads are selected by comparing a randomly generated number with a threshold for LEACH, LEACH-C, SEP, and HEED. The randomness in cluster head selection also aggravates the fluctuation of a protocol in the network.To study the fluctuation of a certain protocol, we simulate LEACH three times under the same conditions. The parameters are set as in Table2.Table 2
Parameters used in 3 repeated simulations of LEACH.
Parameter
Value
Unit
Origin of coordinates
(0, 0)
—
Area of nodes distributed
100
×
100
m2
Coordinate of base station
(50, 350)
—
Total number of all nodes
300
—
Time for simulation
500
Round
Times of simulations repeated
3
—Figure1 shows the curve of number of alive nodes over rounds for LEACH in three simulations under the conditions described in Table 2.Figure 1
Fluctuation of number of alive nodes for LEACH in 3 repeated simulations.The fluctuation of benefit parameters for LEACH protocol under the same cost conditions described in Table2 is presented in Figure 1. Number of alive nodes in several sampling rounds is shown in Table 3. The numbers vary between simulations, especially after the first dead node appears in Figure 1.Table 3
Some of the results in three simulations for fluctuation of number of alive nodes.
Round
Number of alive nodes in 1st simulation
Number of alive nodes in 2nd simulation
Number of alive nodes in 3rd simulation
100
100
100
100
150
67
70
64
200
40
40
42
250
28
26
28
300
15
15
15
350
0
1
1Figure1 and Table 3 show the fluctuation of parameters in three multirounds simulations. The larger the number of simulations is, the more accurately the simulation results present the fluctuation.The standard deviation of benefit parameters (SDP) in multirounds simulations is helpful in describing the fluctuation performance of parameters, and it can describe the fluctuation performance of a protocol running under certain conditions. We choose standard deviation of round at which the first dead node appears (SDRFDN) to represent the fluctuation performance of a protocol under certain conditions. The larger the SDRFDN is, the worse the protocol performs with a heavier fluctuating.In Figure1, the first dead node in the first simulation for LEACH appears at round 105, in the second simulation it appears at round 103, and in the third simulation it appears at round 109. Thus we can calculate that the SDRFDN for the three simulations is 3.0551. This SDRFDN represents the fluctuation performance of LEACH in the three simulations under the cost conditions described as Table 2. The larger the SDRFDN is, the more aggravated the fluctuation is.


### 2.2. Metrics System for Comprehensive Evaluation of Clustering Protocols

The comprehensive evaluation intends to select optimal scheme among different protocols with certain initial energy and nodes deployment. Same as the flood risk analysis [17], a system of metrics for comprehensive evaluation will be constructed as in Figure 2. And the parameters in Figure 2 are as follows.Figure 2
A metrics system for comprehensive efficiency performance of clustering protocols.FA is the area of the rectangular field in which sensor nodes are distributed. It is a cost parameter.Density is density of sensor nodes distributed in the field. It is a cost parameter.NN is the number of all nodes distributed in the field at the beginning of network lifetime. It is a cost parameter.Sum is the sum of all nodes’ initial energy. It is a cost parameter.d
center
-
BS is the distance between the center of the area and the base station. It is a cost parameter.t
1 is the time when first invalid node appears or round at which the first dead node appears. It is a benefit parameter associated with lifetime in previous researches.t
2 is the time when all nodes run out of energy. It is a benefit parameter associated with lifetime in previous research.t
1
/
t
2 is the ratio of t
1 and t
2. It is a benefit parameter to compute the performance of lifetime comprehensively.Data means the total bits of effective data received by the base station att
2. It is a benefit parameter.RAT
t
2
-
Sum means the ratio between t
2 and Sum. It is a benefit parameter to describe the balance between lifetime and total energy consumption.RAT
Data
-
Sum means the ratio between Data and Sum. It is a benefit parameter to describe the ability to collect information with certain amount of energy.SDRFDN is the standard deviation of the round at which the first dead node appears (standard deviation oft
1) in repeated simulations of one protocol under the same conditions. It is also a benefit parameter and it is important for comprehensive evaluation. We use it to represent the fluctuation of one protocol running under the same cost conditions in repeated simulations. The cost conditions are described by five cost parameters.We can consider one protocol under certain cost conditions as one scheme or objective for evaluation, and take its corresponding parameters as criteria in MCDM. Therefore, the comprehensive evaluation of clustering protocols’ energy efficiency performance could be MCDM problems.


## 2.1. A Parameter to Measure Fluctuation of Clustering Protocols

In the applications of the clustering protocols such as LEACH, LEACH-C, SEP, and HEED, massive sensor nodes are deployed in the region randomly, leading to the fluctuation of network. The fluctuation refers to the variation of benefit parameters in repeated experiments. Cluster heads are selected by comparing a randomly generated number with a threshold for LEACH, LEACH-C, SEP, and HEED. The randomness in cluster head selection also aggravates the fluctuation of a protocol in the network.To study the fluctuation of a certain protocol, we simulate LEACH three times under the same conditions. The parameters are set as in Table2.Table 2
Parameters used in 3 repeated simulations of LEACH.
Parameter
Value
Unit
Origin of coordinates
(0, 0)
—
Area of nodes distributed
100
×
100
m2
Coordinate of base station
(50, 350)
—
Total number of all nodes
300
—
Time for simulation
500
Round
Times of simulations repeated
3
—Figure1 shows the curve of number of alive nodes over rounds for LEACH in three simulations under the conditions described in Table 2.Figure 1
Fluctuation of number of alive nodes for LEACH in 3 repeated simulations.The fluctuation of benefit parameters for LEACH protocol under the same cost conditions described in Table2 is presented in Figure 1. Number of alive nodes in several sampling rounds is shown in Table 3. The numbers vary between simulations, especially after the first dead node appears in Figure 1.Table 3
Some of the results in three simulations for fluctuation of number of alive nodes.
Round
Number of alive nodes in 1st simulation
Number of alive nodes in 2nd simulation
Number of alive nodes in 3rd simulation
100
100
100
100
150
67
70
64
200
40
40
42
250
28
26
28
300
15
15
15
350
0
1
1Figure1 and Table 3 show the fluctuation of parameters in three multirounds simulations. The larger the number of simulations is, the more accurately the simulation results present the fluctuation.The standard deviation of benefit parameters (SDP) in multirounds simulations is helpful in describing the fluctuation performance of parameters, and it can describe the fluctuation performance of a protocol running under certain conditions. We choose standard deviation of round at which the first dead node appears (SDRFDN) to represent the fluctuation performance of a protocol under certain conditions. The larger the SDRFDN is, the worse the protocol performs with a heavier fluctuating.In Figure1, the first dead node in the first simulation for LEACH appears at round 105, in the second simulation it appears at round 103, and in the third simulation it appears at round 109. Thus we can calculate that the SDRFDN for the three simulations is 3.0551. This SDRFDN represents the fluctuation performance of LEACH in the three simulations under the cost conditions described as Table 2. The larger the SDRFDN is, the more aggravated the fluctuation is.


## 2.2. Metrics System for Comprehensive Evaluation of Clustering Protocols

The comprehensive evaluation intends to select optimal scheme among different protocols with certain initial energy and nodes deployment. Same as the flood risk analysis [17], a system of metrics for comprehensive evaluation will be constructed as in Figure 2. And the parameters in Figure 2 are as follows.Figure 2
A metrics system for comprehensive efficiency performance of clustering protocols.FA is the area of the rectangular field in which sensor nodes are distributed. It is a cost parameter.Density is density of sensor nodes distributed in the field. It is a cost parameter.NN is the number of all nodes distributed in the field at the beginning of network lifetime. It is a cost parameter.Sum is the sum of all nodes’ initial energy. It is a cost parameter.d
center
-
BS is the distance between the center of the area and the base station. It is a cost parameter.t
1 is the time when first invalid node appears or round at which the first dead node appears. It is a benefit parameter associated with lifetime in previous researches.t
2 is the time when all nodes run out of energy. It is a benefit parameter associated with lifetime in previous research.t
1
/
t
2 is the ratio of t
1 and t
2. It is a benefit parameter to compute the performance of lifetime comprehensively.Data means the total bits of effective data received by the base station att
2. It is a benefit parameter.RAT
t
2
-
Sum means the ratio between t
2 and Sum. It is a benefit parameter to describe the balance between lifetime and total energy consumption.RAT
Data
-
Sum means the ratio between Data and Sum. It is a benefit parameter to describe the ability to collect information with certain amount of energy.SDRFDN is the standard deviation of the round at which the first dead node appears (standard deviation oft
1) in repeated simulations of one protocol under the same conditions. It is also a benefit parameter and it is important for comprehensive evaluation. We use it to represent the fluctuation of one protocol running under the same cost conditions in repeated simulations. The cost conditions are described by five cost parameters.We can consider one protocol under certain cost conditions as one scheme or objective for evaluation, and take its corresponding parameters as criteria in MCDM. Therefore, the comprehensive evaluation of clustering protocols’ energy efficiency performance could be MCDM problems.


## 3. Method of Comprehensive Evaluation for Collaborative Protocols

### 3.1. MCDM Methods for Comprehensive Evaluation

Currently, a number of practical MCDM methods are employed for comprehensive evaluation in existing researches. Synthetic scored method, analysis hierarchy process (AHP), gray correlation method, fuzzy evaluation method, and TOPSIS are in the list. Synthetic scored method is based on experts grading method. Indexes are selected and graded by scores. Objectives are selected by accumulative score. This method has very simple procedures but can only be applied to static evaluation. Analytic hierarchy process (AHP) is a structured technique for organizing and analyzing complex decisions. Based on mathematics and psychology, it was developed by Thomas L. Saaty in the 1970s and has been extensively studied and refined since then [17]. The gray relational analysis [18] is based on the degree of difference of development trends between one scheme and the ideal scheme. If the trend of change between the scheme and the ideal scheme is consistent, they have a strong relationship. Otherwise, the relational grade is small. Fuzzy evaluation method is a method of comprehensive evaluation based on fuzzy mathematics. According to fuzzy membership degree theory, a comprehensive evaluation for the objectives restricted by various factors can be made. Technique for order preference by similarity to ideal solution (TOPSIS) was firstly proposed by Hwang and Yong in 1981. It is a common decision making method for finite schemes, contained in multiple criteria decision making (MCDM) [17–19] methods. TOPSIS is widely applied in multiobjective decision problems.Comparing with other methods, TOPSIS is simple and has no special requirements on the data. Therefore, TOPSIS is chosen for comprehensive evaluation of energy efficiency of protocols in CWSN in this paper.


### 3.2. Procedure of Method Based on TOPSIS without Criterion Weight for Evaluation in WSNs

Data processing in TOPSIS without criterion weight employs normalization and direction modification to eliminate the effect of different dimensions and make full use of primary information of data. The processed data could sufficiently reflect the difference on performance of each scheme. TOPSIS has advantages of reality, intuition, and reliability. Moreover, the method has no special requirement on sample data. Therefore, TOPSIS without criterion weight could satisfy the comprehensive evaluation of clustering protocols in CWSN. And the procedure of proposed method is as follows.Step 1 (construct the decision matrix).
Assume that the problem of evaluation is based onm schemes (
S
1
,
S
2
,
…
,
S
m
) and n criteria (
C
1
,
C
2
,
…
C
n
). Each scheme is an object with certain cost conditions. And different objects could be different protocols under the same cost parameters, different cost conditions for one same protocol, or different protocols under different cost conditions. All the ratings are assigned to schemes and presented in the decision matrix A
x
i
j
m
×
n, where x
i
j is the rating of scheme S
i with respect to the criterion C
j [19]:(1)
A
=
S
1
S
2
⋮
S
m
C
1
C
2
⋯
C
n
x
11
x
12
⋯
x
1
n
x
21
x
22
⋯
x
2
n
⋮
⋮
⋱
⋮
x
m
1
x
m
2
⋯
x
m
n
,where S
i represents one scheme which means a running protocol with certain energy and deployment and C
j
(
1
≤
j
≤
12
) means the twelve parameters for evaluation in experiment.Step 2 (direction modification).
The less the cost parameters are, the better the energy efficiency is. Conversely, the larger the benefit parameters are, the better the energy efficiency is. Cost parameters are transformed into benefit parameters, as well as SDRFDN. Consider(2)
x
i
j
′
=
x
i
j
benefit
indicates
1
x
i
j
cost
indicates
i
=
1
,
…
,
m
;
j
=
1
,
…
n
.MatrixB
=
(
x
i
j
′
) can be obtained. A value close to 0 but bigger than 0 is selected as x
i
j, when it is a cost indicator.Step 3.
Normalize the decision matrixB, because dimensions for each parameter are different and difference on magnitude may be huge. Matrix B is normalized to Z
=
z
i
j
m
×
n. This normalization can help with absolving the method from criterion weight. The normalized value z
i
j is calculated as follows:(3)
z
i
j
=
x
i
j
′
∑
i
=
1
m
x
i
j
′
2
i
=
1
,
…
,
m
;
j
=
1
,
…
n
.Step 4.
Determine the positive ideal and negative ideal solutions, respectively, [19]: (4)
Z
+
=
max
⁡
1
≤
i
≤
m
z
i
j
∣
j
=
1,2
,
…
n
=
z
i
+
∣
i
=
1,2
,
…
n
,
(5)
Z
-
=
min
⁡
1
≤
i
≤
m
z
i
j
∣
j
=
1,2
,
…
n
=
z
i
-
∣
i
=
1,2
,
…
n
,where z
i
+ is the positive ideal value for parameter i and z
i
- is the negative ideal value for parameter i.Step 5.
Compute the distances of the existing schemes from the positive ideal and negative ideal solutions as [20]. D
i
+ is the Euclidean distance between the scheme and the positive ideal solution, and D
i
- is the Euclidean distance between the scheme and the negative ideal solution. The two Euclidean distances are calculated, respectively, as follows: (6)
D
i
+
=
∑
j
=
1
n
z
i
j
-
z
i
+
2
i
=
1,2
,
…
,
m
,
(7)
D
i
-
=
∑
j
=
1
n
z
i
j
-
z
i
-
2
i
=
1,2
,
…
,
m
.Step 6.
Calculate the relative closeness to ideal schemes [20]: (8)
Con
i
=
D
-
D
-
+
D
+
,
1
≤
i
≤
m
.Step 7.
Rank the schemes according to relative closeness to the ideal schemes. The bigger theCon
i is, the better the scheme S
i is, among many schemes. In theory, the relative closeness does not represent the real efficiency performance of clustering protocols. However, it turns out that the comprehensive efficiency is better when the relative closeness is closer to 1.


## 3.1. MCDM Methods for Comprehensive Evaluation

Currently, a number of practical MCDM methods are employed for comprehensive evaluation in existing researches. Synthetic scored method, analysis hierarchy process (AHP), gray correlation method, fuzzy evaluation method, and TOPSIS are in the list. Synthetic scored method is based on experts grading method. Indexes are selected and graded by scores. Objectives are selected by accumulative score. This method has very simple procedures but can only be applied to static evaluation. Analytic hierarchy process (AHP) is a structured technique for organizing and analyzing complex decisions. Based on mathematics and psychology, it was developed by Thomas L. Saaty in the 1970s and has been extensively studied and refined since then [17]. The gray relational analysis [18] is based on the degree of difference of development trends between one scheme and the ideal scheme. If the trend of change between the scheme and the ideal scheme is consistent, they have a strong relationship. Otherwise, the relational grade is small. Fuzzy evaluation method is a method of comprehensive evaluation based on fuzzy mathematics. According to fuzzy membership degree theory, a comprehensive evaluation for the objectives restricted by various factors can be made. Technique for order preference by similarity to ideal solution (TOPSIS) was firstly proposed by Hwang and Yong in 1981. It is a common decision making method for finite schemes, contained in multiple criteria decision making (MCDM) [17–19] methods. TOPSIS is widely applied in multiobjective decision problems.Comparing with other methods, TOPSIS is simple and has no special requirements on the data. Therefore, TOPSIS is chosen for comprehensive evaluation of energy efficiency of protocols in CWSN in this paper.


## 3.2. Procedure of Method Based on TOPSIS without Criterion Weight for Evaluation in WSNs

Data processing in TOPSIS without criterion weight employs normalization and direction modification to eliminate the effect of different dimensions and make full use of primary information of data. The processed data could sufficiently reflect the difference on performance of each scheme. TOPSIS has advantages of reality, intuition, and reliability. Moreover, the method has no special requirement on sample data. Therefore, TOPSIS without criterion weight could satisfy the comprehensive evaluation of clustering protocols in CWSN. And the procedure of proposed method is as follows.Step 1 (construct the decision matrix).
Assume that the problem of evaluation is based onm schemes (
S
1
,
S
2
,
…
,
S
m
) and n criteria (
C
1
,
C
2
,
…
C
n
). Each scheme is an object with certain cost conditions. And different objects could be different protocols under the same cost parameters, different cost conditions for one same protocol, or different protocols under different cost conditions. All the ratings are assigned to schemes and presented in the decision matrix A
x
i
j
m
×
n, where x
i
j is the rating of scheme S
i with respect to the criterion C
j [19]:(1)
A
=
S
1
S
2
⋮
S
m
C
1
C
2
⋯
C
n
x
11
x
12
⋯
x
1
n
x
21
x
22
⋯
x
2
n
⋮
⋮
⋱
⋮
x
m
1
x
m
2
⋯
x
m
n
,where S
i represents one scheme which means a running protocol with certain energy and deployment and C
j
(
1
≤
j
≤
12
) means the twelve parameters for evaluation in experiment.Step 2 (direction modification).
The less the cost parameters are, the better the energy efficiency is. Conversely, the larger the benefit parameters are, the better the energy efficiency is. Cost parameters are transformed into benefit parameters, as well as SDRFDN. Consider(2)
x
i
j
′
=
x
i
j
benefit
indicates
1
x
i
j
cost
indicates
i
=
1
,
…
,
m
;
j
=
1
,
…
n
.MatrixB
=
(
x
i
j
′
) can be obtained. A value close to 0 but bigger than 0 is selected as x
i
j, when it is a cost indicator.Step 3.
Normalize the decision matrixB, because dimensions for each parameter are different and difference on magnitude may be huge. Matrix B is normalized to Z
=
z
i
j
m
×
n. This normalization can help with absolving the method from criterion weight. The normalized value z
i
j is calculated as follows:(3)
z
i
j
=
x
i
j
′
∑
i
=
1
m
x
i
j
′
2
i
=
1
,
…
,
m
;
j
=
1
,
…
n
.Step 4.
Determine the positive ideal and negative ideal solutions, respectively, [19]: (4)
Z
+
=
max
⁡
1
≤
i
≤
m
z
i
j
∣
j
=
1,2
,
…
n
=
z
i
+
∣
i
=
1,2
,
…
n
,
(5)
Z
-
=
min
⁡
1
≤
i
≤
m
z
i
j
∣
j
=
1,2
,
…
n
=
z
i
-
∣
i
=
1,2
,
…
n
,where z
i
+ is the positive ideal value for parameter i and z
i
- is the negative ideal value for parameter i.Step 5.
Compute the distances of the existing schemes from the positive ideal and negative ideal solutions as [20]. D
i
+ is the Euclidean distance between the scheme and the positive ideal solution, and D
i
- is the Euclidean distance between the scheme and the negative ideal solution. The two Euclidean distances are calculated, respectively, as follows: (6)
D
i
+
=
∑
j
=
1
n
z
i
j
-
z
i
+
2
i
=
1,2
,
…
,
m
,
(7)
D
i
-
=
∑
j
=
1
n
z
i
j
-
z
i
-
2
i
=
1,2
,
…
,
m
.Step 6.
Calculate the relative closeness to ideal schemes [20]: (8)
Con
i
=
D
-
D
-
+
D
+
,
1
≤
i
≤
m
.Step 7.
Rank the schemes according to relative closeness to the ideal schemes. The bigger theCon
i is, the better the scheme S
i is, among many schemes. In theory, the relative closeness does not represent the real efficiency performance of clustering protocols. However, it turns out that the comprehensive efficiency is better when the relative closeness is closer to 1.


## 4. Experiment Results

In previous researches, analysis of energy efficiency performance of clustering protocols employs parameters commonly and respectively. In this paper, the analysis in previous work is regarded as traditional analysis. The comparison between comprehensive evaluation and traditional analysis will be made.We assume that the sensors are randomly distributed in the field and are not mobile, and the coordinates of the sink and the dimensions of the sensor field are known. The experiments will be divided into three parts, as mentioned in Section1. The three parts are organized as follows: evaluations for different protocols under the same cost condition are proposed in Section 4.1; evaluations for one protocol under different cost conditions are introduced in Section 4.2; and evaluations for different protocols under different cost conditions are described in Section 4.3.The parameters about radio energy dissipation model in Section4 are the same as Table 1 in Section 2 [4]. The parameters in metrics system proposed in Section 2 are applied in comprehensive evaluation. Regarding the radio energy dissipation model [4], we set the length of rectangular region longer than d
0 so that free space model and multipath model are both used in experiment, and values of other cost parameters are set optionally.We simulate every scheme 100 times by Matlab. The average of 100 values of one parameter in 100 repeated simulations is considered as the result of the parameter. And then the comprehensive evaluation of one scheme could be developed by the method based on TOPSIS in Section3 from these cost and benefit parameters.


### 4.1. Evaluation for Different Clustering Protocols under the Same Cost Conditions

We evaluate the energy efficiency of three protocols LEACH, LEACH-C, and HEED with the same cost parameters to find the most efficient one. Every protocol under certain conditions is simulated 100 times by Matlab. And values of cost parameters are in Table4.Table 4
Same cost conditions for four protocols.
Cost parameter
Full name
Value
Unit
FA
Area of the field nodes distributed in field
100
×
100
m2
Density
Density
0.01
Nodes/m2
NN
Number of nodes distributed in field
100
—
Sum
Sum of all nodes energy in field
50
J
d
center
-
BS
Distance between the center of area and base station
300
mSEP protocol could not be used for this evaluation, because a percentage of the population of sensor nodes is equipped with additional energy resources [7]. It is difficult to equip the cost conditions of SEP same as LEACH, LEACH-C, and HEED.m schemes (objectives) mean three different clustering protocols under the same cost condition, and n criteria include total of twelve parameters of cost and benefit. The values of seven benefit parameters in Figure 2 are from simulations by Matlab.The conditions for simulation could be described as Table4. Value of parameter FA describes the size of the field in which the sensor nodes are distributed. Both its length and width are 100 meters.


#### 4.1.1. Traditional Analyzing

The traditional analyzing of the energy efficiency performance of clustering protocols is based on the curves of respective benefit parameters under the same cost condition.Curves of number of alive nodes over rounds are shown in Figure3. Curves of amount of data received by base station over rounds are shown in Figure 4. Curves of amount of energy consumption over rounds are shown in Figure 5. And curves of amount of data received by base station over amount of energy consumption are shown in Figure 6.Figure 3
Number of alive nodes over time for LEACH, LEACH-C, and HEED.Figure 4
Amount of data received by base station over time for LEACH, LEACH-C, and HEED.Figure 5
Amount of energy consumption over time for LEACH, LEACH-C, and HEED.Figure 6
Amount of data received by base station over amount of energy consumption for LEACH, LEACH-C, and HEED.We can see that LEACH and HEED are better than LEACH-C from the round when first invalid node appears in Figure3. Accordingly, from the round when all nodes die in Figure 3, we can see LEACH is better than LEACH-C and LEACH-C is better than HEED. Another point can be spotted that each curve intersects one another at least once in Figure 3.Figure4 shows the curves of data received by base station over rounds, which also intersect each other. As it is shown in Figure 4, LEACH performs better than HEED, and HEED performs better than LEACH-C.According to curves of amount of energy consumption over rounds in Figure5, amount of energy consumption of LEACH is least, and curves for HEED and LEACH-C intersect each other too. Therefore, it is difficult to find which protocol outperforms others.Figure6 shows the curves of bits of effective data received by base station over energy consumption for three protocols. According to Figure 6, LEACH is better than HEED, and HEED is better than LEACH-C.The conclusion can be presented that protocols’ efficiency evaluation based on respective parameters is unilateral and one-sided, from analysis and comparisons above. Hence, it is with great difficulty to select the most efficient protocol among these protocols under the same conditions because of the conflict among different criteria. It is extremely necessary to put forward the comprehensive evaluation of energy efficiency performance of protocols in network. This evaluation could select the most efficient scheme among many schemes as per multicriteria decision marking theory.


#### 4.1.2. Comprehensive Evaluation Based on Proposed TOPSIS

C
1, C
2, C
3, C
4, and C
5 are cost parameters, and their values are shown in Table 4. And values of the benefit parameters C
6, C
7, C
8, C
9, C
10, C
11, and C
12 are shown in Table 5. Each scheme is one protocol with twelve parameters.Table 5
Values of benefit criteria.
Protocols
t
1 (round)
t
2 (round)
t
1
/
t
2
Data (106 bit)
RAT
t
2
-
Sum
(round/J)
RAT
Data
-
Sum (bit/J)
SDRFDN
LEACH
106
356
0.29775
4.24
7.12
84800
4.382
LEACH-C
70
174
0.4023
1.88
3.48
37665
16.6
HEED
109
147
0.7415
2.95
2.94
59088
9.7528We can see that LEACH performs better than others on some parameters but worse than LEACH-C and HEED on the parametert
1
/
t
2 in Table 5. Hence, we cannot find the optimal scheme from these parameters, respectively, either, same as the analysis of Figure 3. Consequently, we prefer comprehensive evaluation of energy efficiency performance of schemes by TOPSIS method.Calculation procedure is as steps of TOPSIS without criterion weight in Section3.2. Relative closeness for each scheme and the ranking of schemes are presented in Table 6.Table 6
Relative closeness for each scheme and its ranking.
Protocols
Relative closeness
Ranking of relative closeness
LEACH
0.54492
1
LEACH-C
0.39677
3
HEED
0.44171
2In Table6, the relative closeness of LEACH is the biggest and nearest to positive ideal solution. So LEACH is the best among three protocols. LEACH is better than HEED, and LEACH-C is the worst regarding the comprehensive performance of energy efficiency of protocols.We can see from the comparison that the most efficient protocol can be selected out from many protocols under the same cost conditions via comprehensive evaluation method based on TOPSIS without criterion weight, which cannot be achieved via the traditional analyzing. Therefore, the comprehensive evaluation proposed outperforms traditional analysis on protocol selection.


### 4.2. Evaluation for the Same Protocol under Different Cost Conditions

LEACH, LEACH-C, SEP, and HEED protocols are selected as examples for the comprehensive performance evaluation, intending to find the optimal condition for one protocol among different cost conditions. Every protocol under certain conditions is simulated 100 times by Matlab.SEP protocol could be used for this evaluation. And 10% of all nodes are equipped with one time more energy resources than other nodes.m schemes mean m conditions for one clustering protocol, and n criteria include total twelve parameters on cost and benefit.Although the parameterd
center
-
BS affects the performance of the clustering protocol too, it is sufficient to have NN, Density, FA, and Sum changeable for obtaining different cost conditions. The parameter d
center
-
BS is set unchangeable in this evaluation. And the value of d
center
-
BS is 300 m. We select 20 schemes for this evaluation, and the values of cost parameters for schemes are listed in Table 7. The values of seven benefit parameters are from simulations by Matlab.Table 7
Different cost criteria for one protocol.
Schemes
FA(m2)
Density(nodes/m2)
NN
Sum (J)for LEACH, LEACH-C, and HEED protocols
Sum (J)for SEP protocol
d
center
-
BS (m)
Scheme 1
10000
0.002
20
10
11
300
Scheme 2
40000
0.002
80
40
44
300
Scheme 3
90000
0.002
180
90
99
300
Scheme 4
160000
0.002
320
160
176
300
Scheme 5
250000
0.002
500
250
275
300
Scheme 6
10000
0.004
40
20
22
300
Scheme 7
40000
0.004
160
80
88
300
Scheme 8
90000
0.004
360
180
198
300
Scheme 9
160000
0.004
640
320
352
300
Scheme 10
250000
0.004
1000
500
550
300
Scheme 11
10000
0.006
60
30
33
300
Scheme 12
40000
0.006
240
120
132
300
Scheme 13
90000
0.006
540
270
297
300
Scheme 14
160000
0.006
960
480
528
300
Scheme 15
250000
0.006
1500
750
825
300
Scheme 16
10000
0.008
80
40
44
300
Scheme 17
40000
0.008
320
160
176
300
Scheme 18
90000
0.008
720
360
396
300
Scheme 19
160000
0.008
1280
640
704
300
Scheme 20
250000
0.008
2000
1000
1100
300Because the cost conditions are different, the traditional analysis based on respective parameters has difficulty in finding the optimal cost condition, under which the protocol could obtain the best comprehensive performance of energy efficiency. The comprehensive evaluation based on TOPSIS without criterion weight is an effective method to select the most efficient cost condition for one protocol.Different cost conditions are described by the parameters such as NN, Density, FA, and Sum in Section2. And the values of these parameters are listed in Table 7.Relative closeness is calculated by TOPSIS without criterion weight. Under cost conditions described in Table7, the values of benefit parameters, relative closeness, and the ranking of relative closeness are listed in Table 8 for LEACH protocol, in Table 9 for LEACH-C protocol, in Table 10 for SEP protocol, and in Table 11 for HEED protocol.Table 8
The results of simulations and comprehensive evaluation of LEACH protocol under different cost conditions.
Schemes for LEACH
t
1 (round)
t
2 (round)
t
1
/
t
2
Data(107 bit)
RAT
t
2
-
Sum (round/J)
RAT
Data
-
Sum (105 bit/J)
SDRFDN
Relative closeness
Ranking of relative closeness
Scheme 1
119
364
0.32692
1.5716
36.4
15.716
10.01
0.74907
1
Scheme 2
60
546
0.10989
1.7078
13.65
4.2695
5.6497
0.30731
5
Scheme 3
30
597
0.050251
2.0353
6.6333
2.2615
5.3251
0.20065
11
Scheme 4
22
391
0.056266
2.4717
2.4438
1.5448
1.0076
0.16011
14
Scheme 5
3
227
0.013216
3.162
0.908
1.2648
0.79544
0.14484
16
Scheme 6
111
358
0.31006
1.6712
17.9
8.3558
7.3287
0.52289
2
Scheme 7
63
566
0.11131
2.0606
7.075
2.5757
1.2794
0.20969
10
Scheme 8
29
640
0.045312
2.8024
3.5556
1.5569
5.6877
0.14113
17
Scheme 9
22
420
0.052381
3.5731
1.3125
1.1166
0.000001
0.2435
9
Scheme 10
3
239
0.012552
4.2464
0.478
8.4928
0.3266
0.097781
20
Scheme 11
108
358
0.30168
1.7406
11.933
5.8020
5.8769
0.42725
3
Scheme 12
63
573
0.10995
2.4374
4.775
2.0311
0.74155
0.18674
12
Scheme 13
27
654
0.041284
3.5944
2.4222
1.3312
4.3845
0.13733
18
Scheme 14
22
425
0.051765
4.6635
0.88542
9.7157
0.000001
0.24599
7
Scheme 15
3
239
0.012552
5.3122
0.31867
7.0830
0.14071
0.11723
19
Scheme 16
107
356
0.30056
1.8382
8.9
4.5955
4.5856
0.38631
4
Scheme 17
63
577
0.10919
2.7656
3.6063
1.7285
0.72328
0.1796
13
Scheme 18
28
657
0.042618
4.3638
1.825
1.2122
3.8708
0.14654
15
Scheme 19
22
421
0.052257
5.6141
0.65781
8.7720
0.000001
0.2525
6
Scheme 20
2
236
0.0084746
5.967
0.236
5.9670
0.000001
0.24442
8Table 9
The results of simulations and comprehensive evaluation of LEACH-C protocol under different cost conditions.
Schemes for LEACH-C
t
1 (round)
t
2 (round)
t
1
/
t
2
Data(106 bit)
RAT
t
2
-
Sum (round/J)
RAT
Data
-
Sum (bit/J)
SDRFDN
Relative closeness
Ranking of relative closeness
Scheme 1
15
36
0.41667
0.14536
3.6
14536
2.4225
0.54527
1
Scheme 2
32
135
0.23704
1.1384
3.375
28459
10.443
0.27533
8
Scheme 3
32
264
0.12121
4.1012
2.9333
45569
7.4498
0.21925
15
Scheme 4
22
476
0.046218
8.3307
2.975
52067
2.4333
0.21334
16
Scheme 5
3
765
0.0039216
13.691
3.06
54764
1.3536
0.23392
14
Scheme 6
25
58
0.43103
0.37976
2.9
18988
6.1947
0.40962
3
Scheme 7
66
265
0.24906
4.1118
3.3125
51398
14.062
0.27151
10
Scheme 8
36
390
0.092308
12.061
2.1667
67007
8.6156
0.18818
20
Scheme 9
22
629
0.034976
22.963
1.9656
71761
0.9498
0.20944
17
Scheme 10
3
890
0.0033708
36.801
1.78
73603
0.58396
0.25548
13
Scheme 11
38
91
0.41758
0.70992
3.0333
23664
9.2439
0.36559
4
Scheme 12
75
315
0.2381
7.8061
2.625
65051
13.537
0.27404
9
Scheme 13
35
452
0.077434
20.432
1.6741
75673
7.4842
0.19435
19
Scheme 14
22
708
0.031073
38.484
1.475
80174
0.41145
0.26462
12
Scheme 15
3
938
0.0031983
61.888
1.2507
82517
0.23868
0.34578
6
Scheme 16
54
131
0.41221
1.2235
3.275
30588
13.866
0.35739
5
Scheme 17
73
359
0.20334
11.706
2.2437
73165
9.3025
0.26632
11
Scheme 18
34
495
0.068687
29.183
1.375
81064
7.7444
0.20913
18
Scheme 19
22
769
0.028609
55.239
1.2016
86311
0.37322
0.3018
7
Scheme 20
3
989
0.0030334
87.975
0.989
87975
0.14071
0.43495
2Table 10
The results of simulations and comprehensive evaluation of SEP protocol under different cost conditions.
Schemes forSEP
t
1 (round)
t
2 (round)
t
1
/
t
2
Data(107 bit)
RAT
t
2
-
Sum (round/J)
RAT
Data
-
Sum (105 bit/J)
SDRFDN
Relative closeness
Ranking of relative closeness
Scheme 1
69
216
0.31944
0.107
19.636
0.97102
6.0936
0.63529
1
Scheme 2
36
407
0.088452
0.468
9.25
1.06
2.4571
0.28098
9
Scheme 3
21
822
0.025547
1.24
8.303
1.25
3.4031
0.21192
14
Scheme 4
14
1355
0.010332
2.56
7.6989
1.46
0.1
0.21347
13
Scheme 5
3
1926
0.0015576
4.53
7.0036
1.65
1.0565
0.23534
12
Scheme 6
66
216
0.30556
0.210
9.8182
0.95271
4.4518
0.47461
2
Scheme 7
35
429
0.081585
0.950
4.875
1.08
2.0787
0.17895
15
Scheme 8
19
847
0.022432
2.57
4.2778
1.30
3.3302
0.12676
19
Scheme 9
13
1466
0.0088677
5.39
4.1648
1.53
0.000001
0.28333
8
Scheme 10
3
2136
0.0014045
9.44
3.8836
1.72
0.338
0.23571
11
Scheme 11
65
220
0.29545
0.315
6.6667
0.95424
4.8158
0.40896
3
Scheme 12
34
442
0.076923
1.44
3.3485
1.09
2.2082
0.15372
16
Scheme 13
18
875
0.020571
3.88
2.9461
1.31
3.1956
0.11925
20
Scheme 14
13
1537
0.008458
8.13
2.911
1.54
0.000001
0.29124
7
Scheme 15
3
2174
0.0013799
14.0
2.6352
1.69
0.2778
0.26885
10
Scheme 16
63
223
0.28251
0.419
5.0682
0.95117
5.1322
0.37615
4
Scheme 17
34
444
0.076577
1.93
2.5227
1.10
2.235
0.14818
17
Scheme 18
18
896
0.020089
5.22
2.2626
1.32
2.9129
0.13048
18
Scheme 19
13
1595
0.0081505
11.0
2.2656
1.56
0.000001
0.30657
6
Scheme 20
2
2239
0.00089326
18.8
2.0355
1.71
0.000001
0.36477
5Table 11
The results of simulations and comprehensive evaluation of HEED protocol under different cost conditions.
Schemes for HEED
t
1 (round)
t
2 (round)
t
1
/
t
2
Data(105 bit)
RAT
t
2
-
Sum (round/J)
RAT
Data
-
Sum (103 bit/J)
SDRFDN
Relative closeness
Ranking of relative closeness
Scheme 1
73
89
0.82022
0.174
8.9
1.74
6.699
0.61636
1
Scheme 2
29
80
0.3625
0.913
2
2.28
4.5911
0.24491
7
Scheme 3
22
99
0.22222
2.69
1.1
2.99
3.4253
0.18085
12
Scheme 4
16
118
0.13559
6.37
0.7375
3.98
3.2308
0.17318
14
Scheme 5
12
166
0.072289
11.4
0.664
4.56
2.5029
0.19333
11
Scheme 6
90
118
0.76271
0.236
5.9
1.18
10.512
0.47536
2
Scheme 7
26
82
0.31707
2.50
1.025
3.13
3.5997
0.15465
17
Scheme 8
18
91
0.1978
9.84
0.50556
5.46
2.3863
0.14822
18
Scheme 9
12
101
0.11881
20.0
0.31562
6.25
1.76
0.17348
13
Scheme 10
9
152
0.059211
34.4
0.304
6.89
1.3521
0.22642
9
Scheme 11
99
132
0.75
0.358
4.4
1.19
9.4543
0.41694
3
Scheme 12
24
76
0.31579
4.31
0.63333
3.59
3.22
0.13763
20
Scheme 13
17
93
0.1828
16.2
0.34444
5.98
2.23
0.15603
16
Scheme 14
11
100
0.11
32.5
0.20833
6.78
1.60
0.20245
10
Scheme 15
8
126
0.063492
54.4
0.168
7.25
0.704
0.30139
6
Scheme 16
105
139
0.7554
0.353
3.475
0.882
9.2282
0.39055
4
Scheme 17
23
72
0.31944
6.28
0.45
3.93
2.404
0.14132
19
Scheme 18
15
98
0.15306
22.0
0.27222
6.11
1.8289
0.17058
15
Scheme 19
10
96
0.10417
44.7
0.15
6.99
1.38
0.23534
8
Scheme 20
7
118
0.059322
73.3
0.118
7.33
0.448
0.37708
5In Table8, we could find that scheme 1 is the best on parameters such as t
1, t
1
/
t
2, RAT
t
2
-
Sum, and RA
T
Data
-
Sum but not the best on parameters such as t
2, Data, and SDRFDN. Because of the conflict among these parameters, we could not find the best scheme only from these respective parameters. The calculation based on TOPSIS is an effective method to find the best scheme concerning comprehensive efficiency performance of LEACH protocol. From ranking of relative closeness, we can find that scheme 1 ranks 1st and scheme 1 is the best condition for LEACH protocol among 20 schemes. Then scheme 10 ranks the last, so it is the worst.The comprehensive evaluations of other clustering protocols are the same as LEACH protocol.We can find that scheme 1 is the best condition for LEACH-C protocol among 20 schemes, and scheme 8 is the worst from ranking of relative closeness in Table9.We can find from ranking of relative closeness in Table10 that scheme 1 is the best condition for SEP protocol on energy efficiency performance among 20 schemes, and scheme 13 is the worst.We can find from ranking of relative closeness in Table11 that scheme 1 is the best condition for HEED protocol among 20 schemes, and scheme 12 is the worst.The conclusion that the method based on TOPSIS without criterion weight is preferable in selecting the best cost conditions for one protocol’s energy efficiency performance can be gotten from the results of simulations and comprehensive evaluation of LEACH, LEACH-C, SEP, and HEED protocols. Therefore, the proposed algorithm can be used in node deployment.


### 4.3. Evaluation for Different Clustering Routing Protocols under Different Cost Conditions

It is a new study to find which scheme is the best among different clustering protocols under different cost conditions. This study introduces a method based on TOPSIS without criterion weight into comprehensive performance evaluation of different clustering protocols under different cost conditions.SEP protocol could be used for this evaluation too, and 10% of the nodes are equipped with one time more energy resources than other nodes.m schemes include different protocols under respective cost condition, and n criteria include total twelve parameters on cost and benefit. We select 20 schemes for this evaluation. And the values of cost parameters are listed in Table 12. The values of seven benefit parameters are from simulations by Matlab.Table 12
Schemes’ cost conditions setting for evaluation of different protocols under different cost conditions.
Schemes
Clustering protocol running
FA(m2)
Density(nodes/m2)
NN
Sum(J)
d
center
-
BS (m)
Scheme 21
LEACH
10000
0.002
20
10
300
Scheme 22
LEACH
250000
0.002
500
250
300
Scheme 23
LEACH
40000
0.004
160
80
300
Scheme 24
LEACH
90000
0.006
540
270
300
Scheme 25
LEACH
160000
0.008
1280
640
300
Scheme 26
LEACH-C
40000
0.002
80
40
300
Scheme 27
LEACH-C
10000
0.004
40
20
300
Scheme 28
LEACH-C
90000
0.004
360
180
300
Scheme 29
LEACH-C
160000
0.006
960
480
300
Scheme 30
LEACH-C
250000
0.008
2000
1000
300
Scheme 31
SEP
90000
0.002
180
99
300
Scheme 32
SEP
160000
0.004
640
352
300
Scheme 33
SEP
40000
0.006
240
132
300
Scheme 34
SEP
250000
0.006
1500
825
300
Scheme 35
SEP
10000
0.008
80
44
300
Scheme 36
HEED
160000
0.002
320
160
300
Scheme 37
HEED
250000
0.004
1000
500
300
Scheme 38
HEED
10000
0.006
60
30
300
Scheme 39
HEED
40000
0.008
320
160
300
Scheme 40
HEED
90000
0.008
720
360
300Because the cost conditions are different for evaluation of schemes, the traditional analysis could not comprehensively describe the performance of clustering protocols, which means it is incapable to find the optimal scheme among different protocols under different cost conditions. The comprehensive evaluation based on TOPSIS without criterion weight is an effective method to select the best scheme among different clustering protocols running under different cost conditions. The cost conditions of 20 schemes are listed in Table12. Each scheme is one protocol under some variable cost conditions.Relative closeness of these schemes is calculated by the method of TOPSIS without criterion weight. The values of benefit parameters, relative closeness, and the ranking of relative closeness are listed in Table13.Table 13
The results of simulations and comprehensive evaluation of different protocols under different cost conditions.
Schemes
t
1 (round)
t
2 (round)
t
1
/
t
2
Data(106 bit)
RAT
t
2
-
Sum (round/J)
RAT
Data
-
Sum (bit/J)
SDRFDN
Relative closeness
Ranking of relative closeness
Scheme 21
119
364
0.32692
15.7
36.4
1570000
10.01
0.6239
1
Scheme 22
3
227
0.013216
31.6
0.908
126000
0.79544
0.13241
12
Scheme 23
63
566
0.11131
20.6
7.075
258000
1.2794
0.19459
9
Scheme 24
27
654
0.041284
35.9
2.4222
133000
4.3845
0.12614
14
Scheme 25
22
421
0.052257
56.1
0.65781
87720
0.000001
0.27375
6
Scheme 26
32
135
0.23704
1.14
3.375
28459
10.443
0.19217
10
Scheme 27
25
58
0.43103
0.38
2.9
18988
6.1947
0.30449
5
Scheme 28
36
390
0.092308
12.1
2.1667
67007
8.6156
0.10526
18
Scheme 29
22
708
0.031073
38.5
1.475
80174
0.41145
0.12258
16
Scheme 30
3
989
0.0030334
88.0
0.989
87975
0.14071
0.19826
8
Scheme 31
21
822
0.025547
12.4
9.1333
137000
3.4031
0.18488
11
Scheme 32
13
1466
0.0088677
53.9
4.5812
168000
0.000001
0.31356
4
Scheme 33
34
442
0.076923
14.4
3.6833
120000
2.2082
0.11712
17
Scheme 34
3
2174
0.0013799
140.0
2.8987
186000
0.2778
0.32009
3
Scheme 35
63
223
0.28251
4.19
5.575
105000
5.1322
0.26031
7
Scheme 36
16
118
0.13559
0.637
0.7375
3983.3
3.2308
0.12491
15
Scheme 37
9
152
0.059211
3.44
0.304
6888.2
1.3521
0.048565
20
Scheme 38
99
132
0.75
0.03576
4.4
1192
9.4543
0.35293
2
Scheme 39
23
72
0.31944
0.628
0.45
3926
2.404
0.13062
13
Scheme 40
15
98
0.15306
2.20
0.27222
6110.2
1.8289
0.065046
19We could find the best scheme among 20 schemes presented in Table12 by comprehensive evaluation for different clustering protocols under different cost conditions in Table 13. Scheme 21 is the best among 20 schemes, and scheme 37 is the worst. So the method based on TOPSIS without criterion weight is a useful way to find the best scheme among all candidate schemes, which are different clustering protocols under different conditions. Therefore, the proposed algorithm can be used in scheme selection.


## 4.1. Evaluation for Different Clustering Protocols under the Same Cost Conditions

We evaluate the energy efficiency of three protocols LEACH, LEACH-C, and HEED with the same cost parameters to find the most efficient one. Every protocol under certain conditions is simulated 100 times by Matlab. And values of cost parameters are in Table4.Table 4
Same cost conditions for four protocols.
Cost parameter
Full name
Value
Unit
FA
Area of the field nodes distributed in field
100
×
100
m2
Density
Density
0.01
Nodes/m2
NN
Number of nodes distributed in field
100
—
Sum
Sum of all nodes energy in field
50
J
d
center
-
BS
Distance between the center of area and base station
300
mSEP protocol could not be used for this evaluation, because a percentage of the population of sensor nodes is equipped with additional energy resources [7]. It is difficult to equip the cost conditions of SEP same as LEACH, LEACH-C, and HEED.m schemes (objectives) mean three different clustering protocols under the same cost condition, and n criteria include total of twelve parameters of cost and benefit. The values of seven benefit parameters in Figure 2 are from simulations by Matlab.The conditions for simulation could be described as Table4. Value of parameter FA describes the size of the field in which the sensor nodes are distributed. Both its length and width are 100 meters.


### 4.1.1. Traditional Analyzing

The traditional analyzing of the energy efficiency performance of clustering protocols is based on the curves of respective benefit parameters under the same cost condition.Curves of number of alive nodes over rounds are shown in Figure3. Curves of amount of data received by base station over rounds are shown in Figure 4. Curves of amount of energy consumption over rounds are shown in Figure 5. And curves of amount of data received by base station over amount of energy consumption are shown in Figure 6.Figure 3
Number of alive nodes over time for LEACH, LEACH-C, and HEED.Figure 4
Amount of data received by base station over time for LEACH, LEACH-C, and HEED.Figure 5
Amount of energy consumption over time for LEACH, LEACH-C, and HEED.Figure 6
Amount of data received by base station over amount of energy consumption for LEACH, LEACH-C, and HEED.We can see that LEACH and HEED are better than LEACH-C from the round when first invalid node appears in Figure3. Accordingly, from the round when all nodes die in Figure 3, we can see LEACH is better than LEACH-C and LEACH-C is better than HEED. Another point can be spotted that each curve intersects one another at least once in Figure 3.Figure4 shows the curves of data received by base station over rounds, which also intersect each other. As it is shown in Figure 4, LEACH performs better than HEED, and HEED performs better than LEACH-C.According to curves of amount of energy consumption over rounds in Figure5, amount of energy consumption of LEACH is least, and curves for HEED and LEACH-C intersect each other too. Therefore, it is difficult to find which protocol outperforms others.Figure6 shows the curves of bits of effective data received by base station over energy consumption for three protocols. According to Figure 6, LEACH is better than HEED, and HEED is better than LEACH-C.The conclusion can be presented that protocols’ efficiency evaluation based on respective parameters is unilateral and one-sided, from analysis and comparisons above. Hence, it is with great difficulty to select the most efficient protocol among these protocols under the same conditions because of the conflict among different criteria. It is extremely necessary to put forward the comprehensive evaluation of energy efficiency performance of protocols in network. This evaluation could select the most efficient scheme among many schemes as per multicriteria decision marking theory.


### 4.1.2. Comprehensive Evaluation Based on Proposed TOPSIS

C
1, C
2, C
3, C
4, and C
5 are cost parameters, and their values are shown in Table 4. And values of the benefit parameters C
6, C
7, C
8, C
9, C
10, C
11, and C
12 are shown in Table 5. Each scheme is one protocol with twelve parameters.Table 5
Values of benefit criteria.
Protocols
t
1 (round)
t
2 (round)
t
1
/
t
2
Data (106 bit)
RAT
t
2
-
Sum
(round/J)
RAT
Data
-
Sum (bit/J)
SDRFDN
LEACH
106
356
0.29775
4.24
7.12
84800
4.382
LEACH-C
70
174
0.4023
1.88
3.48
37665
16.6
HEED
109
147
0.7415
2.95
2.94
59088
9.7528We can see that LEACH performs better than others on some parameters but worse than LEACH-C and HEED on the parametert
1
/
t
2 in Table 5. Hence, we cannot find the optimal scheme from these parameters, respectively, either, same as the analysis of Figure 3. Consequently, we prefer comprehensive evaluation of energy efficiency performance of schemes by TOPSIS method.Calculation procedure is as steps of TOPSIS without criterion weight in Section3.2. Relative closeness for each scheme and the ranking of schemes are presented in Table 6.Table 6
Relative closeness for each scheme and its ranking.
Protocols
Relative closeness
Ranking of relative closeness
LEACH
0.54492
1
LEACH-C
0.39677
3
HEED
0.44171
2In Table6, the relative closeness of LEACH is the biggest and nearest to positive ideal solution. So LEACH is the best among three protocols. LEACH is better than HEED, and LEACH-C is the worst regarding the comprehensive performance of energy efficiency of protocols.We can see from the comparison that the most efficient protocol can be selected out from many protocols under the same cost conditions via comprehensive evaluation method based on TOPSIS without criterion weight, which cannot be achieved via the traditional analyzing. Therefore, the comprehensive evaluation proposed outperforms traditional analysis on protocol selection.


## 4.1.1. Traditional Analyzing

The traditional analyzing of the energy efficiency performance of clustering protocols is based on the curves of respective benefit parameters under the same cost condition.Curves of number of alive nodes over rounds are shown in Figure3. Curves of amount of data received by base station over rounds are shown in Figure 4. Curves of amount of energy consumption over rounds are shown in Figure 5. And curves of amount of data received by base station over amount of energy consumption are shown in Figure 6.Figure 3
Number of alive nodes over time for LEACH, LEACH-C, and HEED.Figure 4
Amount of data received by base station over time for LEACH, LEACH-C, and HEED.Figure 5
Amount of energy consumption over time for LEACH, LEACH-C, and HEED.Figure 6
Amount of data received by base station over amount of energy consumption for LEACH, LEACH-C, and HEED.We can see that LEACH and HEED are better than LEACH-C from the round when first invalid node appears in Figure3. Accordingly, from the round when all nodes die in Figure 3, we can see LEACH is better than LEACH-C and LEACH-C is better than HEED. Another point can be spotted that each curve intersects one another at least once in Figure 3.Figure4 shows the curves of data received by base station over rounds, which also intersect each other. As it is shown in Figure 4, LEACH performs better than HEED, and HEED performs better than LEACH-C.According to curves of amount of energy consumption over rounds in Figure5, amount of energy consumption of LEACH is least, and curves for HEED and LEACH-C intersect each other too. Therefore, it is difficult to find which protocol outperforms others.Figure6 shows the curves of bits of effective data received by base station over energy consumption for three protocols. According to Figure 6, LEACH is better than HEED, and HEED is better than LEACH-C.The conclusion can be presented that protocols’ efficiency evaluation based on respective parameters is unilateral and one-sided, from analysis and comparisons above. Hence, it is with great difficulty to select the most efficient protocol among these protocols under the same conditions because of the conflict among different criteria. It is extremely necessary to put forward the comprehensive evaluation of energy efficiency performance of protocols in network. This evaluation could select the most efficient scheme among many schemes as per multicriteria decision marking theory.


## 4.1.2. Comprehensive Evaluation Based on Proposed TOPSIS

C
1, C
2, C
3, C
4, and C
5 are cost parameters, and their values are shown in Table 4. And values of the benefit parameters C
6, C
7, C
8, C
9, C
10, C
11, and C
12 are shown in Table 5. Each scheme is one protocol with twelve parameters.Table 5
Values of benefit criteria.
Protocols
t
1 (round)
t
2 (round)
t
1
/
t
2
Data (106 bit)
RAT
t
2
-
Sum
(round/J)
RAT
Data
-
Sum (bit/J)
SDRFDN
LEACH
106
356
0.29775
4.24
7.12
84800
4.382
LEACH-C
70
174
0.4023
1.88
3.48
37665
16.6
HEED
109
147
0.7415
2.95
2.94
59088
9.7528We can see that LEACH performs better than others on some parameters but worse than LEACH-C and HEED on the parametert
1
/
t
2 in Table 5. Hence, we cannot find the optimal scheme from these parameters, respectively, either, same as the analysis of Figure 3. Consequently, we prefer comprehensive evaluation of energy efficiency performance of schemes by TOPSIS method.Calculation procedure is as steps of TOPSIS without criterion weight in Section3.2. Relative closeness for each scheme and the ranking of schemes are presented in Table 6.Table 6
Relative closeness for each scheme and its ranking.
Protocols
Relative closeness
Ranking of relative closeness
LEACH
0.54492
1
LEACH-C
0.39677
3
HEED
0.44171
2In Table6, the relative closeness of LEACH is the biggest and nearest to positive ideal solution. So LEACH is the best among three protocols. LEACH is better than HEED, and LEACH-C is the worst regarding the comprehensive performance of energy efficiency of protocols.We can see from the comparison that the most efficient protocol can be selected out from many protocols under the same cost conditions via comprehensive evaluation method based on TOPSIS without criterion weight, which cannot be achieved via the traditional analyzing. Therefore, the comprehensive evaluation proposed outperforms traditional analysis on protocol selection.


## 4.2. Evaluation for the Same Protocol under Different Cost Conditions

LEACH, LEACH-C, SEP, and HEED protocols are selected as examples for the comprehensive performance evaluation, intending to find the optimal condition for one protocol among different cost conditions. Every protocol under certain conditions is simulated 100 times by Matlab.SEP protocol could be used for this evaluation. And 10% of all nodes are equipped with one time more energy resources than other nodes.m schemes mean m conditions for one clustering protocol, and n criteria include total twelve parameters on cost and benefit.Although the parameterd
center
-
BS affects the performance of the clustering protocol too, it is sufficient to have NN, Density, FA, and Sum changeable for obtaining different cost conditions. The parameter d
center
-
BS is set unchangeable in this evaluation. And the value of d
center
-
BS is 300 m. We select 20 schemes for this evaluation, and the values of cost parameters for schemes are listed in Table 7. The values of seven benefit parameters are from simulations by Matlab.Table 7
Different cost criteria for one protocol.
Schemes
FA(m2)
Density(nodes/m2)
NN
Sum (J)for LEACH, LEACH-C, and HEED protocols
Sum (J)for SEP protocol
d
center
-
BS (m)
Scheme 1
10000
0.002
20
10
11
300
Scheme 2
40000
0.002
80
40
44
300
Scheme 3
90000
0.002
180
90
99
300
Scheme 4
160000
0.002
320
160
176
300
Scheme 5
250000
0.002
500
250
275
300
Scheme 6
10000
0.004
40
20
22
300
Scheme 7
40000
0.004
160
80
88
300
Scheme 8
90000
0.004
360
180
198
300
Scheme 9
160000
0.004
640
320
352
300
Scheme 10
250000
0.004
1000
500
550
300
Scheme 11
10000
0.006
60
30
33
300
Scheme 12
40000
0.006
240
120
132
300
Scheme 13
90000
0.006
540
270
297
300
Scheme 14
160000
0.006
960
480
528
300
Scheme 15
250000
0.006
1500
750
825
300
Scheme 16
10000
0.008
80
40
44
300
Scheme 17
40000
0.008
320
160
176
300
Scheme 18
90000
0.008
720
360
396
300
Scheme 19
160000
0.008
1280
640
704
300
Scheme 20
250000
0.008
2000
1000
1100
300Because the cost conditions are different, the traditional analysis based on respective parameters has difficulty in finding the optimal cost condition, under which the protocol could obtain the best comprehensive performance of energy efficiency. The comprehensive evaluation based on TOPSIS without criterion weight is an effective method to select the most efficient cost condition for one protocol.Different cost conditions are described by the parameters such as NN, Density, FA, and Sum in Section2. And the values of these parameters are listed in Table 7.Relative closeness is calculated by TOPSIS without criterion weight. Under cost conditions described in Table7, the values of benefit parameters, relative closeness, and the ranking of relative closeness are listed in Table 8 for LEACH protocol, in Table 9 for LEACH-C protocol, in Table 10 for SEP protocol, and in Table 11 for HEED protocol.Table 8
The results of simulations and comprehensive evaluation of LEACH protocol under different cost conditions.
Schemes for LEACH
t
1 (round)
t
2 (round)
t
1
/
t
2
Data(107 bit)
RAT
t
2
-
Sum (round/J)
RAT
Data
-
Sum (105 bit/J)
SDRFDN
Relative closeness
Ranking of relative closeness
Scheme 1
119
364
0.32692
1.5716
36.4
15.716
10.01
0.74907
1
Scheme 2
60
546
0.10989
1.7078
13.65
4.2695
5.6497
0.30731
5
Scheme 3
30
597
0.050251
2.0353
6.6333
2.2615
5.3251
0.20065
11
Scheme 4
22
391
0.056266
2.4717
2.4438
1.5448
1.0076
0.16011
14
Scheme 5
3
227
0.013216
3.162
0.908
1.2648
0.79544
0.14484
16
Scheme 6
111
358
0.31006
1.6712
17.9
8.3558
7.3287
0.52289
2
Scheme 7
63
566
0.11131
2.0606
7.075
2.5757
1.2794
0.20969
10
Scheme 8
29
640
0.045312
2.8024
3.5556
1.5569
5.6877
0.14113
17
Scheme 9
22
420
0.052381
3.5731
1.3125
1.1166
0.000001
0.2435
9
Scheme 10
3
239
0.012552
4.2464
0.478
8.4928
0.3266
0.097781
20
Scheme 11
108
358
0.30168
1.7406
11.933
5.8020
5.8769
0.42725
3
Scheme 12
63
573
0.10995
2.4374
4.775
2.0311
0.74155
0.18674
12
Scheme 13
27
654
0.041284
3.5944
2.4222
1.3312
4.3845
0.13733
18
Scheme 14
22
425
0.051765
4.6635
0.88542
9.7157
0.000001
0.24599
7
Scheme 15
3
239
0.012552
5.3122
0.31867
7.0830
0.14071
0.11723
19
Scheme 16
107
356
0.30056
1.8382
8.9
4.5955
4.5856
0.38631
4
Scheme 17
63
577
0.10919
2.7656
3.6063
1.7285
0.72328
0.1796
13
Scheme 18
28
657
0.042618
4.3638
1.825
1.2122
3.8708
0.14654
15
Scheme 19
22
421
0.052257
5.6141
0.65781
8.7720
0.000001
0.2525
6
Scheme 20
2
236
0.0084746
5.967
0.236
5.9670
0.000001
0.24442
8Table 9
The results of simulations and comprehensive evaluation of LEACH-C protocol under different cost conditions.
Schemes for LEACH-C
t
1 (round)
t
2 (round)
t
1
/
t
2
Data(106 bit)
RAT
t
2
-
Sum (round/J)
RAT
Data
-
Sum (bit/J)
SDRFDN
Relative closeness
Ranking of relative closeness
Scheme 1
15
36
0.41667
0.14536
3.6
14536
2.4225
0.54527
1
Scheme 2
32
135
0.23704
1.1384
3.375
28459
10.443
0.27533
8
Scheme 3
32
264
0.12121
4.1012
2.9333
45569
7.4498
0.21925
15
Scheme 4
22
476
0.046218
8.3307
2.975
52067
2.4333
0.21334
16
Scheme 5
3
765
0.0039216
13.691
3.06
54764
1.3536
0.23392
14
Scheme 6
25
58
0.43103
0.37976
2.9
18988
6.1947
0.40962
3
Scheme 7
66
265
0.24906
4.1118
3.3125
51398
14.062
0.27151
10
Scheme 8
36
390
0.092308
12.061
2.1667
67007
8.6156
0.18818
20
Scheme 9
22
629
0.034976
22.963
1.9656
71761
0.9498
0.20944
17
Scheme 10
3
890
0.0033708
36.801
1.78
73603
0.58396
0.25548
13
Scheme 11
38
91
0.41758
0.70992
3.0333
23664
9.2439
0.36559
4
Scheme 12
75
315
0.2381
7.8061
2.625
65051
13.537
0.27404
9
Scheme 13
35
452
0.077434
20.432
1.6741
75673
7.4842
0.19435
19
Scheme 14
22
708
0.031073
38.484
1.475
80174
0.41145
0.26462
12
Scheme 15
3
938
0.0031983
61.888
1.2507
82517
0.23868
0.34578
6
Scheme 16
54
131
0.41221
1.2235
3.275
30588
13.866
0.35739
5
Scheme 17
73
359
0.20334
11.706
2.2437
73165
9.3025
0.26632
11
Scheme 18
34
495
0.068687
29.183
1.375
81064
7.7444
0.20913
18
Scheme 19
22
769
0.028609
55.239
1.2016
86311
0.37322
0.3018
7
Scheme 20
3
989
0.0030334
87.975
0.989
87975
0.14071
0.43495
2Table 10
The results of simulations and comprehensive evaluation of SEP protocol under different cost conditions.
Schemes forSEP
t
1 (round)
t
2 (round)
t
1
/
t
2
Data(107 bit)
RAT
t
2
-
Sum (round/J)
RAT
Data
-
Sum (105 bit/J)
SDRFDN
Relative closeness
Ranking of relative closeness
Scheme 1
69
216
0.31944
0.107
19.636
0.97102
6.0936
0.63529
1
Scheme 2
36
407
0.088452
0.468
9.25
1.06
2.4571
0.28098
9
Scheme 3
21
822
0.025547
1.24
8.303
1.25
3.4031
0.21192
14
Scheme 4
14
1355
0.010332
2.56
7.6989
1.46
0.1
0.21347
13
Scheme 5
3
1926
0.0015576
4.53
7.0036
1.65
1.0565
0.23534
12
Scheme 6
66
216
0.30556
0.210
9.8182
0.95271
4.4518
0.47461
2
Scheme 7
35
429
0.081585
0.950
4.875
1.08
2.0787
0.17895
15
Scheme 8
19
847
0.022432
2.57
4.2778
1.30
3.3302
0.12676
19
Scheme 9
13
1466
0.0088677
5.39
4.1648
1.53
0.000001
0.28333
8
Scheme 10
3
2136
0.0014045
9.44
3.8836
1.72
0.338
0.23571
11
Scheme 11
65
220
0.29545
0.315
6.6667
0.95424
4.8158
0.40896
3
Scheme 12
34
442
0.076923
1.44
3.3485
1.09
2.2082
0.15372
16
Scheme 13
18
875
0.020571
3.88
2.9461
1.31
3.1956
0.11925
20
Scheme 14
13
1537
0.008458
8.13
2.911
1.54
0.000001
0.29124
7
Scheme 15
3
2174
0.0013799
14.0
2.6352
1.69
0.2778
0.26885
10
Scheme 16
63
223
0.28251
0.419
5.0682
0.95117
5.1322
0.37615
4
Scheme 17
34
444
0.076577
1.93
2.5227
1.10
2.235
0.14818
17
Scheme 18
18
896
0.020089
5.22
2.2626
1.32
2.9129
0.13048
18
Scheme 19
13
1595
0.0081505
11.0
2.2656
1.56
0.000001
0.30657
6
Scheme 20
2
2239
0.00089326
18.8
2.0355
1.71
0.000001
0.36477
5Table 11
The results of simulations and comprehensive evaluation of HEED protocol under different cost conditions.
Schemes for HEED
t
1 (round)
t
2 (round)
t
1
/
t
2
Data(105 bit)
RAT
t
2
-
Sum (round/J)
RAT
Data
-
Sum (103 bit/J)
SDRFDN
Relative closeness
Ranking of relative closeness
Scheme 1
73
89
0.82022
0.174
8.9
1.74
6.699
0.61636
1
Scheme 2
29
80
0.3625
0.913
2
2.28
4.5911
0.24491
7
Scheme 3
22
99
0.22222
2.69
1.1
2.99
3.4253
0.18085
12
Scheme 4
16
118
0.13559
6.37
0.7375
3.98
3.2308
0.17318
14
Scheme 5
12
166
0.072289
11.4
0.664
4.56
2.5029
0.19333
11
Scheme 6
90
118
0.76271
0.236
5.9
1.18
10.512
0.47536
2
Scheme 7
26
82
0.31707
2.50
1.025
3.13
3.5997
0.15465
17
Scheme 8
18
91
0.1978
9.84
0.50556
5.46
2.3863
0.14822
18
Scheme 9
12
101
0.11881
20.0
0.31562
6.25
1.76
0.17348
13
Scheme 10
9
152
0.059211
34.4
0.304
6.89
1.3521
0.22642
9
Scheme 11
99
132
0.75
0.358
4.4
1.19
9.4543
0.41694
3
Scheme 12
24
76
0.31579
4.31
0.63333
3.59
3.22
0.13763
20
Scheme 13
17
93
0.1828
16.2
0.34444
5.98
2.23
0.15603
16
Scheme 14
11
100
0.11
32.5
0.20833
6.78
1.60
0.20245
10
Scheme 15
8
126
0.063492
54.4
0.168
7.25
0.704
0.30139
6
Scheme 16
105
139
0.7554
0.353
3.475
0.882
9.2282
0.39055
4
Scheme 17
23
72
0.31944
6.28
0.45
3.93
2.404
0.14132
19
Scheme 18
15
98
0.15306
22.0
0.27222
6.11
1.8289
0.17058
15
Scheme 19
10
96
0.10417
44.7
0.15
6.99
1.38
0.23534
8
Scheme 20
7
118
0.059322
73.3
0.118
7.33
0.448
0.37708
5In Table8, we could find that scheme 1 is the best on parameters such as t
1, t
1
/
t
2, RAT
t
2
-
Sum, and RA
T
Data
-
Sum but not the best on parameters such as t
2, Data, and SDRFDN. Because of the conflict among these parameters, we could not find the best scheme only from these respective parameters. The calculation based on TOPSIS is an effective method to find the best scheme concerning comprehensive efficiency performance of LEACH protocol. From ranking of relative closeness, we can find that scheme 1 ranks 1st and scheme 1 is the best condition for LEACH protocol among 20 schemes. Then scheme 10 ranks the last, so it is the worst.The comprehensive evaluations of other clustering protocols are the same as LEACH protocol.We can find that scheme 1 is the best condition for LEACH-C protocol among 20 schemes, and scheme 8 is the worst from ranking of relative closeness in Table9.We can find from ranking of relative closeness in Table10 that scheme 1 is the best condition for SEP protocol on energy efficiency performance among 20 schemes, and scheme 13 is the worst.We can find from ranking of relative closeness in Table11 that scheme 1 is the best condition for HEED protocol among 20 schemes, and scheme 12 is the worst.The conclusion that the method based on TOPSIS without criterion weight is preferable in selecting the best cost conditions for one protocol’s energy efficiency performance can be gotten from the results of simulations and comprehensive evaluation of LEACH, LEACH-C, SEP, and HEED protocols. Therefore, the proposed algorithm can be used in node deployment.


## 4.3. Evaluation for Different Clustering Routing Protocols under Different Cost Conditions

It is a new study to find which scheme is the best among different clustering protocols under different cost conditions. This study introduces a method based on TOPSIS without criterion weight into comprehensive performance evaluation of different clustering protocols under different cost conditions.SEP protocol could be used for this evaluation too, and 10% of the nodes are equipped with one time more energy resources than other nodes.m schemes include different protocols under respective cost condition, and n criteria include total twelve parameters on cost and benefit. We select 20 schemes for this evaluation. And the values of cost parameters are listed in Table 12. The values of seven benefit parameters are from simulations by Matlab.Table 12
Schemes’ cost conditions setting for evaluation of different protocols under different cost conditions.
Schemes
Clustering protocol running
FA(m2)
Density(nodes/m2)
NN
Sum(J)
d
center
-
BS (m)
Scheme 21
LEACH
10000
0.002
20
10
300
Scheme 22
LEACH
250000
0.002
500
250
300
Scheme 23
LEACH
40000
0.004
160
80
300
Scheme 24
LEACH
90000
0.006
540
270
300
Scheme 25
LEACH
160000
0.008
1280
640
300
Scheme 26
LEACH-C
40000
0.002
80
40
300
Scheme 27
LEACH-C
10000
0.004
40
20
300
Scheme 28
LEACH-C
90000
0.004
360
180
300
Scheme 29
LEACH-C
160000
0.006
960
480
300
Scheme 30
LEACH-C
250000
0.008
2000
1000
300
Scheme 31
SEP
90000
0.002
180
99
300
Scheme 32
SEP
160000
0.004
640
352
300
Scheme 33
SEP
40000
0.006
240
132
300
Scheme 34
SEP
250000
0.006
1500
825
300
Scheme 35
SEP
10000
0.008
80
44
300
Scheme 36
HEED
160000
0.002
320
160
300
Scheme 37
HEED
250000
0.004
1000
500
300
Scheme 38
HEED
10000
0.006
60
30
300
Scheme 39
HEED
40000
0.008
320
160
300
Scheme 40
HEED
90000
0.008
720
360
300Because the cost conditions are different for evaluation of schemes, the traditional analysis could not comprehensively describe the performance of clustering protocols, which means it is incapable to find the optimal scheme among different protocols under different cost conditions. The comprehensive evaluation based on TOPSIS without criterion weight is an effective method to select the best scheme among different clustering protocols running under different cost conditions. The cost conditions of 20 schemes are listed in Table12. Each scheme is one protocol under some variable cost conditions.Relative closeness of these schemes is calculated by the method of TOPSIS without criterion weight. The values of benefit parameters, relative closeness, and the ranking of relative closeness are listed in Table13.Table 13
The results of simulations and comprehensive evaluation of different protocols under different cost conditions.
Schemes
t
1 (round)
t
2 (round)
t
1
/
t
2
Data(106 bit)
RAT
t
2
-
Sum (round/J)
RAT
Data
-
Sum (bit/J)
SDRFDN
Relative closeness
Ranking of relative closeness
Scheme 21
119
364
0.32692
15.7
36.4
1570000
10.01
0.6239
1
Scheme 22
3
227
0.013216
31.6
0.908
126000
0.79544
0.13241
12
Scheme 23
63
566
0.11131
20.6
7.075
258000
1.2794
0.19459
9
Scheme 24
27
654
0.041284
35.9
2.4222
133000
4.3845
0.12614
14
Scheme 25
22
421
0.052257
56.1
0.65781
87720
0.000001
0.27375
6
Scheme 26
32
135
0.23704
1.14
3.375
28459
10.443
0.19217
10
Scheme 27
25
58
0.43103
0.38
2.9
18988
6.1947
0.30449
5
Scheme 28
36
390
0.092308
12.1
2.1667
67007
8.6156
0.10526
18
Scheme 29
22
708
0.031073
38.5
1.475
80174
0.41145
0.12258
16
Scheme 30
3
989
0.0030334
88.0
0.989
87975
0.14071
0.19826
8
Scheme 31
21
822
0.025547
12.4
9.1333
137000
3.4031
0.18488
11
Scheme 32
13
1466
0.0088677
53.9
4.5812
168000
0.000001
0.31356
4
Scheme 33
34
442
0.076923
14.4
3.6833
120000
2.2082
0.11712
17
Scheme 34
3
2174
0.0013799
140.0
2.8987
186000
0.2778
0.32009
3
Scheme 35
63
223
0.28251
4.19
5.575
105000
5.1322
0.26031
7
Scheme 36
16
118
0.13559
0.637
0.7375
3983.3
3.2308
0.12491
15
Scheme 37
9
152
0.059211
3.44
0.304
6888.2
1.3521
0.048565
20
Scheme 38
99
132
0.75
0.03576
4.4
1192
9.4543
0.35293
2
Scheme 39
23
72
0.31944
0.628
0.45
3926
2.404
0.13062
13
Scheme 40
15
98
0.15306
2.20
0.27222
6110.2
1.8289
0.065046
19We could find the best scheme among 20 schemes presented in Table12 by comprehensive evaluation for different clustering protocols under different cost conditions in Table 13. Scheme 21 is the best among 20 schemes, and scheme 37 is the worst. So the method based on TOPSIS without criterion weight is a useful way to find the best scheme among all candidate schemes, which are different clustering protocols under different conditions. Therefore, the proposed algorithm can be used in scheme selection.


## 5. Conclusions

Energy limitation is a focal point for CWSN applications. Protocols have significant affection on energy efficiency of CWSN. This paper proposes a new concept of comprehensive evaluation for energy efficiency of protocols and introduces an approach based on TOPSIS without criterion weight into this comprehensive evaluation. Original collaborative protocols LEACH, LEACH-C, SEP, and HEED are selected to comprehensively evaluate the energy efficiency under certain cost conditions. Simulation results show that this approach based on TOPSIS without criterion weight is effective and can be taken into full use in three kinds of applications:(
1
) selecting the most efficient protocol in terms of energy efficiency performance among different clustering protocols under the same cost condition, (
2
) selecting the best condition meaning node deployment, under which a protocol could obtain the best comprehensive energy efficiency performance, and (
3
) selecting the best scheme among different protocols under different cost conditions. Therefore, the proposed approach can guide the deployment of CWSN nodes and be used in the selection of collaborative protocols. In the future work, we are to further consider some latest collaborative protocols with complex parameters in comprehensive evaluation of protocols.



---

*Source: 640736-2015-04-05.xml*