# A Variable-Length Chromosome Genetic Algorithm for Time-Based Sensor Network Schedule Optimization

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## Abstract

**:**

## 1. Introduction

## 2. Sensor Network Schedule Optimization Problem

## 3. Overview of Genetic Algorithms

- Selection keeps the best individuals in the population based on their fitness values. The selected individuals survive and remain as they are to the next generation.
- Crossover takes pairs of parent individuals and randomly combines their genes to create children.
- Mutation takes a parent chromosome and introduces random changes to make children.

## 4. Variable-Length Chromosome Genetic Algorithm for Network Scheduling Problem

#### 4.1. Formulation of Variable-Length Chromosome Genetic Algorithm

#### 4.1.1. Chromosome Structure

#### 4.1.2. Crossover Operation

#### 4.1.3. Mutation Operation

- Copy: The child interval is same as the parent interval, like the intervals $\left[{t}_{1}^{i},{t}_{2}^{i}\right]$ and $\left[{t}_{8}^{i},{t}_{9}^{i}\right]$ in the example.
- Insertion: A new interval with inverse mode is inserted in a manner that its start and end times are generated randomly but stay within the boundaries of the parent one, as in the case of the interval $\left[{t}_{2}^{i},{t}_{3}^{i}\right]$ in the example.
- Removal: The parent interval is removed and not inherited by the child node, as in the case of the interval $\left[{t}_{5}^{i},{t}_{6}^{i}\right]$ in the example.
- Shift: The boundaries of the child interval is made by moving those of the parent one backward or forward in the time axis, as in the case of the intervals $\left[{t}_{3}^{i},{t}_{4}^{i}\right]$ and $\left[{t}_{7}^{i},{t}_{8}^{i}\right]$ in the example.

#### 4.2. Energy-Aware Simulation of Sensor Networks

- Node components, whose base interface is node_component. A node component can be of one among five types, i.e., battery, power, sensor, communication, and controller, which are explained below.
- Sensor nodes, whose base interface is basic_node.
- Networks, whose base interface is basic_network.
- Working environments, whose base interface is basic_world.
- Ambient environmental elements, with basic_ambient. An ambient environmental element represents an external physical field, such as temperature, light, humidity, etc., that has impact on the functioning of the sensor network. Examples of possible impacts are energy source for the power components, or measurement values for the sensor components.

- Battery: used to simulate the energy storage behaviors. A library of common battery types, including lead acid, Li-ion, Ni-Cd and Ni-MH, is implemented as part of this platform, using the models given in [35].
- Power: responsible for collecting power from external sources, including ambient energy harvesting as well as wired or wireless sources feeding. Regarding the simulations in this work, a solar energy source is used to charge the batteries using the model given in [36].
- Sensor: used to simulate the sensing mechanism.
- Communication: implementing low- and high-level communication protocols. Note that the communication is for data routing required by other purposes, not for schedule cooperation, as earlier stated in this paper.
- Controller: implementing the functioning and incorporation of the four other components in the node.

## 5. Case Studies and Simulation Results

#### 5.1. Single-Node Case

^{5}and 2.016 × 10

^{5}for the first run and second run, respectively, which are very closed to each other, with 0.26% of difference, showing the reliability of the algorithm’s convergence performance and obtained results. For fixed-length cases with time blocks of 60 min and 30 min, the obtained fitness values are 1.574 × 10

^{6}and 6.283 × 10

^{5}, respectively, due to the low adaptiveness of fixed time blocks. The best resulting schedules from these algorithms are shown in Figure 13, and those with VLC overlap exactly one over the other, with 18 active intervals per day, corresponding to 44% of the time in a day.

#### 5.2. Multiple-Node Case

^{4}when using VLC, and to 8.129 × 10

^{4}when using fixed time blocks. The obtained best network schedules in both cases are shown in Figure 17. Using VLC, the active time coverage in a day for the three nodes individually are 41%, 46%, and 43%, respectively, but their combination makes a coverage of 95% of time in a day. The battery capacity percentage of the nodes when simulated with this schedule is given in Figure 18, and none of them has a final level lower than the initial one, whereas for those of nodes 2 and 3 when using fixed time blocks, the final levels are 25.5% and 2.8% lower than the initial ones, respectively. The cumulated number of measurements is given in Figure 19, which is now smoother than that in the previous scenario. At the end of simulation, the nodes perform 315, 351 and 332 measurements individually, or 998 in total, whereas the total number of measurements when using fixed time blocks is 912, which is 8.6% lower. The results of this case also show that the resultant schedule obtained with VLC is better optimized than the one obtained with fixed time blocks.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 12.**Progress of best fitness value using variable- and fixed-length chromosomes in single-node case.

**Figure 16.**Progress of best fitness value using variable- and fixed-length chromosomes in multiple-node case.

Parameter | Value |
---|---|

Number of nodes (n) | 1 |

Maximal battery capacity | 3500 mAh |

Battery charging rate | 0.8 W |

Background power consumption rate in Sleep mode | 0.05 W |

Average power consumption rate in Active mode | 0.17 W |

Power consumption per measurement | 0.22 Ws |

Power consumption per SMS transmission | 13.27 Ws |

Installation location (latitude, longitude) | 21.004°, 105.846° |

Measurement rate in Active mode | 5 min |

Simulation time (T) | 3 days |

Parameter | Value |
---|---|

Population size | 100 |

Selection rate | 20% |

Mutation rate | 30% |

Crossover rate | 50% |

Rates of mutation operations: Copy, Insertion, Removal, Shift | 90%, 3.33%, 3.33%, 3.33% |

${k}_{\eta}$ | 1 |

${k}_{\tau 1}$ | 1 |

${k}_{\tau 2}$ | 10 |

${k}_{T1}$ | 1 × 10^{8} |

${k}_{T2}$ | 1 × 10^{8} |

${k}_{L1}$ | 1 × 10^{6} |

${k}_{L2}$ | 1 × 10^{6} |

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**MDPI and ACS Style**

Ha, V.-P.; Dao, T.-K.; Pham, N.-Y.; Le, M.-H.
A Variable-Length Chromosome Genetic Algorithm for Time-Based Sensor Network Schedule Optimization. *Sensors* **2021**, *21*, 3990.
https://doi.org/10.3390/s21123990

**AMA Style**

Ha V-P, Dao T-K, Pham N-Y, Le M-H.
A Variable-Length Chromosome Genetic Algorithm for Time-Based Sensor Network Schedule Optimization. *Sensors*. 2021; 21(12):3990.
https://doi.org/10.3390/s21123990

**Chicago/Turabian Style**

Ha, Van-Phuong, Trung-Kien Dao, Ngoc-Yen Pham, and Minh-Hoang Le.
2021. "A Variable-Length Chromosome Genetic Algorithm for Time-Based Sensor Network Schedule Optimization" *Sensors* 21, no. 12: 3990.
https://doi.org/10.3390/s21123990