# Internet of Things Energy Consumption Optimization in Buildings: A Step toward Sustainability

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Optimization Model

#### 3.1. Particle Swarm Optimization Algorithm

#### 3.2. Chaotic Particle Swarm Optimization Algorithm

#### 3.3. Fractional Chaotic Particle Swarm Optimization Algorithm

#### 3.4. Interface Node to Send Data Selection

_{ijBS}shows the energy used to send data from the i node through the j interface node to reach the base station. d(s

_{i},s

_{j}) shows the distance from node i to node j and d(s

_{i},BS) represents the distance of node i to the base station. The energy used to send information to the base station is obtained directly from Equation (8).

## 4. Evaluation of the Proposed Method

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- Etx, Erx: the energy used to transmit and receive data in nodes, respectively.
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- Dij: distance between node i and j.
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- Eelec: the available energy in each node.
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- Fij: data transmission rate between two nodes.
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- CS, CR, CB: base station node cost, sensor node cost, and amplifier node cost, respectively.

## 5. Conclusions and Suggestions for Future Work

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- Practical implementation of the proposed method in a smart environment that uses the IoT, such as smart buildings.
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- Using the proposed method for multicast routing, additional research can be conducted in this area, such as how to select routes.
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- Utilizing alternative evolutionary algorithms and evaluating their outcomes to increase the reduction of current overheads and reach more ideal results.
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- Combining the proposed method with other algorithms, such as tree-based algorithms, and presenting it within the IoT domain.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Comparison of (

**a**) energy consumption reduction, and (

**b**) the energy required for data transmission and reception of two normal methods and FCPSO optimization.

T_{p} | P | Cost | |
---|---|---|---|

PSO | O(1) | O(N) | O(N) |

CPSO | O(N/2) | O(N) | O(N^{2}/2) |

FCPSO | O(N^{1−x}) | O(N^{2}) | O(N log N) |

ID | Function | Interval |

F_{1} | $f(x)={\sum}_{i=1}^{n}{x}_{i}^{2}$ | $-\mathrm{\infty}\le {x}_{i}\le \mathrm{\infty}$ $1\le i\le n$ |

F_{2} | $f(x)=\sum _{i=1}^{n}{\left(\left[{x}_{i}+0.5\right]\right)}^{2}$ | $-10\le {x}_{i}\le 10$ |

F_{3} | $f\left(x\right)=An{\sum}_{i=1}^{n}\left[{x}_{i}^{2}-\mathrm{Acos}\left(2\pi {x}_{i}\right)\right]$ | $1\le i\le n$ |

F_{4} | $f(x)={\sum}_{i=1}^{n-1}\left[100{\left({x}_{i+1}-{x}_{i}^{2}\right)}^{2}+{\left({x}_{i}-1\right)}^{2}\right]$ | $-\mathrm{\infty}\le {x}_{i}\le \mathrm{\infty}$ $1\le i\le n$ |

F_{5} | $f(x)=418.9829-{\sum}_{i=1}^{d}{x}_{i}\mathrm{s}\mathrm{i}\mathrm{n}\left(\sqrt{\left|{x}_{i}\right|}\right)$ | $-\mathrm{\infty}\le {x}_{i}\le \mathrm{\infty}$ |

F_{6} | $f(x)=\sum _{i=1}^{n}\left[{x}_{i}^{2}-10\mathrm{c}\mathrm{o}\mathrm{s}\left(2\pi {x}_{i}+10\right)\right]$ | $-5.12\le {x}_{i}\le 5.12$ |

F_{7} | $f(x)=-20\mathrm{e}\mathrm{x}\mathrm{p}\left(-0.2\sqrt{1/n\sum _{i=1}^{n}{x}_{i}^{2}}\right)-\mathrm{e}\mathrm{x}\mathrm{p}\left(1/n\sum _{i=1}^{n}\mathrm{c}\mathrm{o}\mathrm{s}\left(2\pi {x}_{i}\right)\right)+20+e$ | $-5\le x,y\le 5$ |

F_{8} | $f(x)=1/4000\sum _{i=1}^{n}{x}_{i}^{2}-\prod _{i=1}^{n}\mathrm{c}\mathrm{o}\mathrm{s}\left(\frac{{x}_{i}}{\sqrt{i}}\right)+1$ | $-100\le {x}_{i}\le 100$ |

F_{9} | $f\left(x\right)=0.1\left\{{\mathrm{sin}}^{2}\left(3\pi {x}_{i}\right)+\sum _{i=1}^{n}{\left({x}_{i}-1\right)}^{2}\left[1+{\mathrm{sin}}^{2}\left(3\pi {x}_{i}+1\right)\right]+{\left({x}_{n}-1\right)}^{2}\left[1+{\mathrm{sin}}^{2}\left(2\pi {x}_{n}\right)\right]\right\}+\sum _{i=1}^{n}u\left({x}_{i},\mathrm{5,100,4}\right)$ | $-50\le {x}_{i}\le 50$ |

F_{10} | $f(x)=\pi /n\left\{10\mathrm{s}\mathrm{i}\mathrm{n}\left(\pi {y}_{1}\right)+\sum _{i=1}^{n-1}{\left({y}_{i}-1\right)}^{2}\left[1+10{\mathrm{s}\mathrm{i}\mathrm{n}}^{2}\left(\pi {y}_{i+1}\right)\right]+{\left({y}_{n}-1\right)}^{2}\right\}+\sum _{i=1}^{n}u\left({x}_{i},\mathrm{10,100,4}\right)$ ${y}_{i}=1+\left({x}_{i}+1/4\right)u\left({x}_{i},a,k,m\right)=\left\{\right)separators="|">\begin{array}{c}k{\left({x}_{i}-a\right)}^{m},{x}_{i}a,\\ 0-a{x}_{i}a,\\ k{\left(-{x}_{i}-a\right)}^{m},{x}_{i}-a.\end{array}$ | $-50\le {x}_{i}\le 50$ |

**Table 3.**The result of PSO, CPSO and FCPSO algorithms in testbench functions for different orders of derivatives.

Method | The Order of the Fractional Derivative (α) | The Value of the Objective Function | Run time | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

F_{1} | F_{2} | F_{3} | F_{4} | F_{5} | F_{6} | F_{7} | F_{8} | F_{9} | F_{10} | F_{1} | F_{2} | F_{3} | F_{4} | F_{5} | F_{6} | F_{7} | F_{8} | F_{9} | F_{10} | ||

PSO | 0.98371 | 7 × 10^{−5} | 0.983 | 1.2 × 10^{−13} | 4.2 × 10^{−16} | 0.98371 | 7 × 10^{−5} | 0.983 | 2 × 10^{−14} | 3.99958 × 10^{−12} | 0.10098 | 0.09748 | 0.101 | 0.097 | 0.078 | 0.10098 | 0.09748 | 0.101 | 0.097 | 0.078 | |

CPSO | 1.00876 | 0.00088 | 1.009 | 1.8 × 10^{−12} | 3.5 × 10^{−14} | 1.00876 | 0.00088 | 1.009 | 6.4 × 10^{−12} | 1.765 × 10^{−12} | 0.09512 | 0.10276 | 0.095 | 0.102 | 0.12 | 0.09512 | 0.10276 | 0.095 | 0.102 | 0.12 | |

FCPSO | 0.2 | 0.0001802 | 0.00051 | 0.0000102 | 1 × 10^{−12} | 3.75 × 10^{−15} | 0.0001802 | 0.00051 | 1.02 × 10^{−5} | 1.5 × 10^{−12} | 4.10375 × 10^{−12} | 0.08104 | 0.09136 | 0.081 | 0.091 | 0.098 | 0.08104 | 0.09136 | 0.081 | 0.091 | 0.098 |

0.4 | 0.000189 | 0.00049 | 0.000031 | 1 × 10^{−12} | 4.02 × 10^{−15} | 0.000189 | 0.00049 | 3.1 × 10^{−5} | 7.9 × 10^{−12} | 4.90402 × 10^{−12} | 0.12399 | 0.08778 | 0.123 | 0.088 | 0.072 | 0.12399 | 0.08778 | 0.123 | 0.088 | 0.072 | |

0.6 | 0.00033989 | 0.00063 | 1.101 × 10^{−7} | 1 × 10^{−12} | 4.21 × 10^{−15} | 0.00033989 | 0.00063 | 1.10108 × 10^{−7} | 1.9 × 10^{−12} | 3.30421 × 10^{−12} | 0.10525 | 0.18101 | 0.105 | 0.181 | 0.163 | 0.10525 | 0.18101 | 0.105 | 0.181 | 0.163 | |

0.8 | 0.01136 | 0.00026 | 0.0109 | 1 × 10^{−12} | 3 × 10^{−15} | 0.01136 | 0.00026 | 0.0109 | 3.5 × 10^{−12} | 2.903 × 10^{−12} | 0.09274 | 0.09842 | 0.092 | 0.098 | 0.079 | 0.09274 | 0.09842 | 0.092 | 0.098 | 0.079 |

Optimization Algorithms | Mean Error ${\mathit{E}\mathit{R}}_{\mathit{A}}={\frac{\sum _{\mathit{n}=1}^{\mathit{N}}\sqrt{{\left({\mathit{Y}}_{\mathit{n}}-{\mathit{y}}_{\mathit{n}}\right)}^{2}}}{\mathit{N}}}^{\mathit{*}}$ |
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PSO | 0.0829 |

CPSO | 0.0971 |

FCPSO (α = 0.8) | 0.0029 |

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## Share and Cite

**MDPI and ACS Style**

Wang, W.-C.; Dwijendra, N.K.A.; Sayed, B.T.; Alvarez, J.R.N.; Al-Bahrani, M.; Alviz-Meza, A.; Cárdenas-Escrocia, Y.
Internet of Things Energy Consumption Optimization in Buildings: A Step toward Sustainability. *Sustainability* **2023**, *15*, 6475.
https://doi.org/10.3390/su15086475

**AMA Style**

Wang W-C, Dwijendra NKA, Sayed BT, Alvarez JRN, Al-Bahrani M, Alviz-Meza A, Cárdenas-Escrocia Y.
Internet of Things Energy Consumption Optimization in Buildings: A Step toward Sustainability. *Sustainability*. 2023; 15(8):6475.
https://doi.org/10.3390/su15086475

**Chicago/Turabian Style**

Wang, Wen-Cheng, Ngakan Ketut Acwin Dwijendra, Biju Theruvil Sayed, José Ricardo Nuñez Alvarez, Mohammed Al-Bahrani, Aníbal Alviz-Meza, and Yulineth Cárdenas-Escrocia.
2023. "Internet of Things Energy Consumption Optimization in Buildings: A Step toward Sustainability" *Sustainability* 15, no. 8: 6475.
https://doi.org/10.3390/su15086475