# Particle Swarm Optimization for Outdoor Lighting Design

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## Abstract

**:**

## 1. Introduction

## 2. Outdoor Lighting

#### 2.1. Energy Efficiency Classification

- Functional street lighting: It encompasses lighting installations for motorways, dual carriageways, urban streets and roads.
- Ambient street lighting: It is generally placed on low supports in urban areas for lighting pedestrian and commercial areas, pavements, parks and gardens, historic centers and roads with low speeds limits.

_{0}symbol. This magnitude is a ratio of the minimum illuminance level to the average illuminance level. An overall uniformity value of 0.4, or 40%, is recommended to ensure that lighting installations do not create dark patches next to lighter patches. This effect makes it difficult for our eyes to adjust quickly enough to see if it is safe to proceed along any route. Furthermore, low uniformity ratios, such as frequent changes of contrasting high- and low-lit road segments, may cause enormous eye discomfort, leading to stress and tiredness which may often have a negative impact on road safety [18]. In other words, uniformity is what distinguishes a good quality road lighting installation from a poor one [19]. Thus, a good lighting system is one that is designed to distribute an appropriate amount of light evenly with uniformity values of 0.40 using lamps with a rating of at least 60 on the color rendering index (CRI) [20].

#### 2.2. Lighting Systems

_{0}). Both equations will be used in the algorithm to search for the configuration with the highest energy efficiency with an overall uniformity at least of 0.4, as is set in the regulations.

## 3. Particle Swarm Optimization for Outdoor Lighting Optimization

- 1.
- First of all, the algorithm has to initialize the population with random positions, as in Equation (3), and velocities, as in Equation (4), in the search space.$${x}_{i}=\left(x,{x}_{i2},\dots ,{x}_{id},\dots ,{x}_{in}\right)$$$${v}_{i}=\left({v}_{i1},{v}_{i2},\dots ,{v}_{id},\dots ,{v}_{in}\right)$$
- 2.
- Analyze value of each particle according to a fitness function, selecting the particle with the best solution as the leader.
- 3.
- Update the velocity of each particle according to the following Equation (5):$${v}_{k+1}^{i}\left(t\right)=w*{v}_{k}^{i}+{\phi}_{1}\left({p}_{k}^{i}-{x}_{k}^{i}\right)+{\phi}_{2}\left({p}_{g}-{x}_{k}^{i}\right)$$

- 4.
- Update the position of each particle according to Equation (6):$${x}_{k+1}^{i}={x}_{k}^{i}+{v}_{k+1}^{i}$$
- 5.
- Evaluate the quality of each particle according to a fitness function, which is also the objective function, in our case the function which calculates the energy efficiency of the outdoor lighting installation.
- 6.
- Check the quality of the particle result. In case the quality of the solution is better than the best particle result, it will be updated with the value of the current particle.
- 7.
- In case one of the solutions reached by any of the particles is better than the current leader, the leader of the swarm is updated.
- 8.
- Check if the maximum number of iterations has been reached or if the best solution fits the fitness value. In case the maximum number of iterations is not reached, the algorithm will go to the third step again.

## 4. Experiments and Discussion

- Number of particles in swarm = {20, 30, 40, 50, 60, 70, 80, 100, 120}.
- Number of iterations = {1–60}.
- Inertia weight (ω) = {0.1, 0.3, 0.5, 0.7, 0.8, 0.9, 1.1, 1.3, 1.5, 1.7}.

#### 4.1. Experiment 1

#### 4.2. Experiment 2

#### 4.3. Algorithm Validation

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

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Inertia Weight (ω) | Maximum Energy Efficiency Index (${\mathit{I}}_{\mathit{\epsilon}}$) | Do the Particles Converge? |
---|---|---|

0.1 | 0.85 | Yes |

0.3 | 1.32 | Yes |

0.5 | 1.66 | Yes |

0.7 | 1.71 | Yes |

0.9 | 1.69 | Yes |

1.1 | 1.69 | No |

1.3 | 1.68 | No |

1.5 | 1.67 | No |

1.7 | 1.64 | No |

Particle Swarm Size | ${\mathit{I}}_{\mathit{\epsilon}}$ Maximum Value (Mean) | Convergence Iteration | Memory Used (Bytes) |
---|---|---|---|

20 | 1.904 | 35–40 | 127,192 |

30 | 1.954 | 30–35 | 147,856 |

40 | 2.017 | 30–35 | 168,552 |

50 | 2.030 | 20–25 | 189,216 |

60 | 2.083 | 20–25 | 209,912 |

70 | 2.083 | 15–20 | 230,576 |

80 | 2.083 | 15–20 | 251,272 |

100 | 2.084 | 15–20 | 292,632 |

120 | 2.084 | 10–15 | 333,992 |

Spacing between Luminaires | ${\mathit{I}}_{\mathit{\epsilon}}$ (DIALux) | ${\mathit{I}}_{\mathit{\epsilon}}$ (algorithm) | Deviation |
---|---|---|---|

17 | 0.763 | 0.747 | −2.09% |

27 | 0.821 | 0.799 | −2.67% |

30 | 0.820 | 0.814 | −1.21% |

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**MDPI and ACS Style**

Castillo-Martinez, A.; Ramon Almagro, J.; Gutierrez-Escolar, A.; Del Corte, A.; Castillo-Sequera, J.L.; Gómez-Pulido, J.M.; Gutiérrez-Martínez, J.-M.
Particle Swarm Optimization for Outdoor Lighting Design. *Energies* **2017**, *10*, 141.
https://doi.org/10.3390/en10010141

**AMA Style**

Castillo-Martinez A, Ramon Almagro J, Gutierrez-Escolar A, Del Corte A, Castillo-Sequera JL, Gómez-Pulido JM, Gutiérrez-Martínez J-M.
Particle Swarm Optimization for Outdoor Lighting Design. *Energies*. 2017; 10(1):141.
https://doi.org/10.3390/en10010141

**Chicago/Turabian Style**

Castillo-Martinez, Ana, Jose Ramon Almagro, Alberto Gutierrez-Escolar, Antonio Del Corte, José Luis Castillo-Sequera, José Manuel Gómez-Pulido, and José-María Gutiérrez-Martínez.
2017. "Particle Swarm Optimization for Outdoor Lighting Design" *Energies* 10, no. 1: 141.
https://doi.org/10.3390/en10010141