# Efficient Node Deployment of Large-Scale Heterogeneous Wireless Sensor Networks

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## Abstract

**:**

## 1. Introduction

- (1)
- Describing the deployment problem in the form of 0/1 integer programming,
- (2)
- Considering heterogeneous sensor deployment, including mobile nodes such as robots or UAVs,
- (3)
- Taking into consideration the zone priority to decide a new location of each node,
- (4)
- Considering the nodes’ residual energy when selecting which node to move,
- (5)
- Considering the movement distance and energy to minimize network overall energy consumption.

## 2. Related Work

_{s}, the Euclidean distance is represented by d(s,p) and the deployment point is represented by p.

- (1)
- Area Coverage
- (2)
- Target Coverage
- (3)
- Barrier Coverage

_{1}, t

_{2}, and t

_{3}, whereas all other targets, t

_{4}and t

_{5}, are monitored by two sensor nodes. Additionally, target coverage saves energy and reduces the number of nodes required.

## 3. Problem Description

## 4. Problem Formulation for Optimal Solution

**(1)****Deployment Constraints:**

- (a)
- The constraint in Equation (3) is utilized to ensure that any mobile node s is either in an active or inactive state during any time interval.
- (b)
- The constraint in Equation (4) is used to determine the value of the decision variable ${x}_{si}^{t}$. The sensor node s is set to be active in zone i during time interval t, ${x}_{si}^{t}$ is enforced to 1, If that node is not used in any zone j during the next and previous time intervals.

**(2)****Assignment Constraint:**

**(3)****Mobility Constraints:**

- (a)
- The constraint in Equation (8) is used to ensure that the number of moves made by any node s is less than or equal to the maximum number of moves allowed for that node.
- (b)
- The constraints in Equations (9) and (10) guarantee that the movement of a node s from zone i to zone j does not make zone i empty.

- (a)
- Equations (11) and (12) ensure that the zone j which the node s will move to is not covered by any node, whether stationary or moving node.
- (b)
- The constraints in Equations (13)–(15) handle a special case in which the number of nodes in zone j is 0 but ${\omega}_{j}^{t}<{\omega}_{i}^{t}$.
- (c)
- The constraint in Equation (16) ensures that the number of moves made by a mobile node s during time interval t should be less than or equal to 1.

**(1)****State-Switching Constraints:**

- (a)
- The constraints in Equations (17)–(20) determine the state switching of a sensor node from active to inactive state and vice versa.
- (b)
- For each mobile node, the total number of state switching should be less than or equal to the maximum number of switches allowed for such node as given in Equation (21).

**(2)****Distance Constraints:**

**(3)****Energy Constraints:**

- (a)
- The mobile node s is utilized when its expected residual energy after the movement from zone i to zone j is greater than or equal to the threshold value, and it has the maximum expected residual energy compared to the others at the same time as given in Equations (25)–(28).
- (b)
- The state of the mobile node s is changed from off to on when its residual energy after the state-switching is greater than or equal to the threshold value, as illustrated in Equation (29).

**(4)****Decision Variable Constraint:**

**(5)****Walk-Through Example:**

_{1}, S

_{2}, S

_{3}, and S

_{4,}of four zones Z

_{1}, Z

_{2}, Z

_{3}, and Z

_{4}, which is monitored for two-time intervals t

_{1}and t

_{2}. Table 3 shows the residual energy of each sensor node before and after movement, providing the movement distance and residual energy.

_{1}. Assume that relation between the priority of each zone and the others during the second time interval t

_{2}, is described as ${\omega}_{1}^{{t}_{2}}<{\omega}_{3}^{{t}_{2}}<{\omega}_{2}^{{t}_{2}}<{\omega}_{4}^{{t}_{2}}$.

_{2}, under the parameter combination of Case 1. Aiming to maximize field coverage and minimize movement distance, the deployment patterns of S

_{1}and S

_{2}are exchanged over the entire horizon (t

_{1}and t

_{2}). Now, the residual energy of S

_{1}is zero, which impacts the network lifetime and the proper operation of the WSN. In Case 2, besides the zone priority, the deployment decision is also affected by residual energy to avoid poor-energy nodes. Thus, avoiding poor-energy nodes to improve network lifetime is its second priority. Figure 7b shows the movement operation during the time interval, t

_{2}, under parameter combination of Case 2. The deployment patterns of sensor nodes S

_{3}and S

_{4}are swapped over time periods t

_{1}and t

_{2}for field coverage maximization and energy saving. Now that S

_{4}has no residual energy, depending on it alone to increase energy efficiency will be insufficient.

_{2}, under the parameter combination of Case 3. Aiming to maximize field coverage and energy efficiency, the deployment patterns of sensor nodes S

_{2}and S

_{3}are exchanged during the time intervals t

_{1}and t

_{2}. Here, the residual energy on S

_{2}and S

_{3}are 2 J and 5 J, respectively. Thus, it is possible to observe that considering the expected residual energy after the movement, the movement distance and zone priority into deployment decision turn into much better energy efficiency than the other cases.

## 5. Ant Colony Optimization Based Solution

_{i}, i = 0, 1, …, |P|, will select deployment point p

_{j}, j = 1, 2, …, |P|, to visit next is given by:

_{i}and d

_{j}at the time t, ${\eta}_{k}(t)$, and ${\psi}_{j}(t)$ are the heuristic information; α, β, and γ are the weight factors that control the pheromone value and the heuristic information parameters respectively.

**A.****Pheromone calculation**

**B.****Calculation of the heuristic information**

## 6. Performance Evaluation

**A.****Performance Criteria**

- (1)
- Network Lifetime [26] is the period from the start of network operations to the first failed node due to battery depletion.
- (2)
- Coverage Ratio is very essential in our deployment method. That is reasonable since our main goal is to increase network coverage. The coverage ratio is defined as the number of zones covered with at least one sensor node. In this context, the highest priority zones should be covered as much as possible.

_{i}is the zone’s i priority, and n is the number of covered zones.

**B.****Methodology**

_{dac}is the required power for data acquisition, and D

_{so}is the duration of a single operation. In this work, we have adopted the same values in [8]. NB = 1 KB, D

_{so}= 0.135 µs, and P

_{dac}= 300 mW.

**C.****Results and Discussion**

- (1)
- Network Lifetime Evaluation

- (2)
- Coverage Ratio Evaluation

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 7.**The movement operation during the time interval, t

_{2}under various parameter combinations (

**a**) Case 1, (

**b**) Case 2, and (

**c**) Case 3.

Paper ID | Parameters | |||
---|---|---|---|---|

Residual Energy | Movement Consumed Energy | Movement Distance | Areas (Zones) Priority | |

[6] | √ | × | × | √ |

[13] | × | × | √ | √ |

Proposed Algorithm | √ | √ | √ | √ |

Given Parameters | |
---|---|

Notation | Description |

S | The set of all mobile nodes. |

A | The set of all zones in the monitored field. |

T | The time horizon. |

TN | The set of all stationary and mobile nodes in the monitored field. |

${\omega}_{i}^{t}$ | The time-varying weight function for each zone $i\in A$, where $t\in T$. |

${M}_{s}$ | The maximum number of moves allowed for such node s, $s\in S$. |

${P}_{s}$ | The maximum number of switches allowed for such node s, $s\in S$. |

${d}_{sij}^{t}$ | Is the Euclidean distance between the location of node s on zone i and its new location on zone j(center of zone j), where $i,j\in A$, $s\in S$ and $t\in T$. |

${E}_{sij}^{t}$ | The energy required for the movement of node s from zone i to zone j at time interval t, where $i,j\in A$, $s\in S$ and $t\in T$. |

$E{S}_{s}$ | The energy required for changing the state of node s from off to on $s\in S$. |

$R{E}_{s}^{t}$ | Is the residual energy of node s at time interval t, where $s\in S$ and $t\in T$. |

Indicator Parameter | |

${\delta}_{si}^{t}$ | 1 if node s is on zone i at time t and 0 otherwise. |

Decision Variables | |

${x}_{si}^{t}$ | 1 if node s exists in active state on zone i at time interval t, and 0 otherwise, $\forall s\in S,\forall i\in A,\forall t\in T$. |

${y}_{si}^{t}$ | 1 if node s exists in inactive state on zone i at time interval t, and 0 otherwise, $\forall s\in S,\forall i\in A,\forall t\in T$. |

${m}_{sij}^{t}$ | 1 if node s is moved from zone i to zone j at time interval t, and 0 otherwise, $\forall s\in S,\forall i,j\in A,\forall t\in T$. |

$o{n}_{si}^{t}$ | 1 if node s is turned to active state at time interval t on zone i, and 0 otherwise, $\forall s\in S,\forall i\in A,\forall t\in T$. |

$of{f}_{si}^{t}$ | 1 if node s is deactivated at time interval t on zone i, and 0 otherwise, $\forall s\in S,\forall i\in A,\forall t\in T$. |

${g}_{i}$ | 1 if the number of all nodes on zone i is greater than one node at time interval t, and 0 otherwise, where $i\in A$ and $t\in T$. |

${N}_{j}$ | 1 if the number of all nodes on zone j is greater than zero at time interval t, and 0 otherwise, where $j\in A$ and $t\in T$. |

${Z}_{n}$ | 1 if the difference the distance of n and s is less than zero and 0 otherwise, where $n,s\in S$. |

${e}_{\upsilon}$ | 1 if the difference between the residual energy of s at time interval t is less than that of node υ and 0 otherwise, where $\upsilon ,s\in S$, and $t\in T$. |

$s{p}_{ij}$ | 1 if the number of nodes on zone i is greater than one node at time t, and the weight of zone j is less than that of zone i, and 0 otherwise, $i,j\in A$. |

Sensor Nodes | Residual Energy | Movement Distance | Movement Required Energy | Residual Energy after Movement | |||
---|---|---|---|---|---|---|---|

Z_{3} | Z_{4} | Z_{3} | Z_{4} | Z_{3} | Z_{4} | ||

S_{1} | 10 J | 10 m | 40 m | 10 J | 40 J | 0 J | Not enough |

S_{2} | 7 J | 30 m | 5 m | 30 J | 5 J | Not enough | 2 J |

S_{3} | 15 J | 10 m | 30 m | 15 J | 30 J | 5 J | Not enough |

S_{4} | 20 J | 25 m | 20 m | 25 J | 20 J | Not enough | 0 J |

Combination | Parameters | |||
---|---|---|---|---|

Zone Priority | Residual Energy | Movement Distance | Movement Consumed Energy | |

Case 1 | √ | × | √ | × |

Case 2 | √ | √ | × | × |

Case 3 | √ | √ | √ | √ |

Parameters | Values |
---|---|

Network size | 300 m × 300 m |

Number of sink nodes | 1 |

Maximum number of retransmission | 4 |

Packet size | 50 byte |

Data rate | 19.2 Kbps |

Frequency | 868 MHz |

Transmission power | 0 dBm |

Maximum transmission range | 200 m |

Path loss exponent | 3 |

Shadow fading variance | 4 |

Noise power | −141 dBm |

Reference distance | 1 m |

λ | 15 |

Strategies | Deployment |
---|---|

Strategy 1 | Random Distribution |

Strategy 2 | At Line along the middle of the network |

Strategy 3 | At the Network Corners |

Strategy 4 | Uniform Distribution |

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**MDPI and ACS Style**

Elfouly, F.H.; Ramadan, R.A.; Khedr, A.Y.; Yadav, K.; Azar, A.T.; Abdelhamed, M.A.
Efficient Node Deployment of Large-Scale Heterogeneous Wireless Sensor Networks. *Appl. Sci.* **2021**, *11*, 10924.
https://doi.org/10.3390/app112210924

**AMA Style**

Elfouly FH, Ramadan RA, Khedr AY, Yadav K, Azar AT, Abdelhamed MA.
Efficient Node Deployment of Large-Scale Heterogeneous Wireless Sensor Networks. *Applied Sciences*. 2021; 11(22):10924.
https://doi.org/10.3390/app112210924

**Chicago/Turabian Style**

Elfouly, Fatma H., Rabie A. Ramadan, Ahmed Y. Khedr, Kusum Yadav, Ahmad Taher Azar, and Mohamed A. Abdelhamed.
2021. "Efficient Node Deployment of Large-Scale Heterogeneous Wireless Sensor Networks" *Applied Sciences* 11, no. 22: 10924.
https://doi.org/10.3390/app112210924