# Genetic Algorithms-Based Optimum PV Site Selection Minimizing Visual Disturbance

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}. The study area (Figure 1b) consists of agricultural lands, including vineyards that are critical for the local economy, residences, and urban areas, main roads, and railways. Furthermore, it is surrounded by Natura 2000 areas. Specifically, the Rio Tinto River (Figure 1b), as well as the wider Natura 2000 zone in the northern part of the area, are famous attractions to tourists and scientists because of the special characteristics of their aquatic environment.

## 3. Methodology

#### 3.1. Development of the GIS Database

^{2}) can result in standalone points with very large slope terrain values (representing, for example, a tree). To reduce the effect of these outliers, the average slope of the polygons examined was calculated. If this average value was smaller than 5%, the polygon was considered as a potential area for PV installations in terms of EC5. It is noted that Lidar data were also used to create the DSM model required in the viewshed analysis, including both the ground elevation and the objects’ elevations (buildings, trees etc.).

#### 3.2. Vieswhed Analysis

_{j}. By weighting and aggregating the aforementioned viewshed maps, the disturbance, $DI{S}_{i,pix}$, of an ith, $i=1,\dots ,N$, observer, relevant to a point/pixel, pix, can be quantified according to Equation (1):

_{j}, $j=1,\dots ,M$, corresponds to the weight of the jth viewshed class defined below, whereas ${V}_{j,pix}^{i}$, $i=1,\dots ,N$, $j=1,\dots ,M$, is equal to 1 if the examined point/pixel for the jth viewshed class can be seen by the ith observer, or equal to 0 if the opposite holds true.

_{j}, j = 1,…,M, values are determined. To answer this question, it is necessary to take into consideration two factors. The first one is that the disturbance of an observer decreases in a non-linear way with respect to the distance. The non-linear relationship between an object and an observer has been already indicated in the literature [31,59,60]. The second factor is that the disturbances of all the observers will be aggregated; therefore, the principle of additivity needs to be fulfilled, in a way that the final SDIS map will offer trustworthy results. To fulfil these two requirements, Equation (3) is introduced to calculate c

_{j}, j = 1,…, M:

_{M}is the maximum distance that an observer can see in the case of the M class viewshed (largest maximum distance among all classes), whereas the value of “+1” is used in order to consider the M class as the reference class. For applying Equation (3), the parameter y needs to be defined, having in mind that the smaller the y value is, the more emphasis will be given on objects cited close to an observer. In the present paper, y has been taken as equal to e and, thus, c

_{j}, j = 1,…, M, is finally calculated suing Equation (4) as follows:

_{j}and c

_{j}, j = 1,…, 10, values shown in Table 2. It can be seen that the increase of r

_{j}leads to a nonlinear decrease of c

_{j}. The maximum distance of the 10th class, r

_{10}, is of high importance, since an area located at distance from an observer larger than r

_{10}does not disturb the observer. The intermediate classes support a better discretization of the distances, and, furthermore, they introduce some extra importance to the smaller distances. The reader should have in mind that as the weighted viewshed maps are aggregated (Equation (1)), for a PV placed between 0 m and 100 m from an observer, the $DI{S}_{i,pix}$ will be equal to 28.859 and not equal to 4.912. Figure 4 includes two cumulative viewshed maps for r

_{1}= 100 m and r

_{6}= 1000 m, assuming c

_{1}= c

_{6}=1 in a region around the La Palma Del Condado city. Cumulative weighted viewshed maps, along with the final DSIS map, are cited and discussed in the Results section.

#### 3.3. Optimization Process

_{k}, $k=1,\dots ,K$, has a set of spatial and non-spatial attributes, $A{T}_{k}$, defined as:

_{k}related to EC4 (Table 1), $A{T}_{k,s}$ is the average slope terrain gradient (%) of SP

_{k}related to EC5 (Table 1), $A{T}_{k,SDIS}$ corresponds to the SDIS of SP

_{k}, $A{T}_{k,area}$ is the coverage area (m

^{2}) of $S{P}_{k}$, whereas $A{T}_{k,DG}$ is the distance (m) between the electrical grid station and the most distant point of SP

_{k}. Furthermore, $A{T}_{k,set}$ represents the set (category) where an SP

_{k}belongs, and can take the labelled values of “A”, “B” or “C” according to Table 3. Set A includes the optimum solutions; namely, all SPs that minimize the DSIS indicator, satisfy none of the exclusion criteria, and are consistent with the two siting preferences. Set C includes $SPs$ that satisfy any of the EC1, EC2, or EC3 exclusion criteria, while, at the same time, correspond to pure non-agricultural areas (EC4). Finally, in set B, SPs that do not belong to either A or B sets are included. Specifically, set B contains SPs that satisfy only EC5 and/or EC4 (i.e., they correspond to vineyards). Accordingly, in this set, areas that are not eligible for PV installations only due to economic reasons are classified. Furthermore, it contains SPs that although do not satisfy any of the exclusion criteria, they do not correspond to solutions that lead to minimum DSIS values and/or are consistent with the two siting preferences.

_{k}, $k=1,\dots ,K$, to one of the A, B, or C sets. This problem has many similarities with graph theory and matching problems [61], as the SPs will be matched to a set according to their attributes. The aforementioned matching and classification are implemented in two successive stages. In the first stage, SPs that satisfy EC1–EC4 are determined by deploying the relevant data and the thematic maps of the GIS database, and by performing the required spatial intersections using a relevant R package. If, for example, an SP

_{k}intersects with the 150 m buffer of an environmentally protected area (EC1), then AT

_{k,set}= “C”. Similarly, for EC4, if AT

_{k,use}≠ “agricultural”, then AT

_{k,set}= “C”. The intersections are performed in each GAs iteration following an approach that will be presented later in this section. The aforementioned SPs are classified to the C set and are subtracted from the OR superset. Each $S{P}_{k}$∉$C$ is taken into account in the second stage, where the GAs algorithm determines the elements (SPs) of the A set according to Table 3. Thus, the objective function of the present optimization problem is defined as follows:

_{max}denotes the maximum allowable distance from the grid station for installing PVs, whereas in Equation (10), Area

_{min}corresponds to the minimum allowable total coverage area of PV installations. By setting different values for DG

_{min}and Area

_{min}based on relevant preferences, different optimum solutions can be obtained. Having solved the optimization problem described by Equations (6)–(10) and, thus, having determined the SPs that belong to the A set, the remaining SPs are classified to set B.

_{k,use}attribute (Equation (7)), the land use data included in the GIS database are used. Similarly, by deploying the slope terrain raster map of the GIS database, the $A{T}_{k,s}$ attribute (Equation (8)) is quantified and is taken as equal to the average value of the raster pixels that fall inside an SP. As for the $A{T}_{k,SDIS}$ attribute (Equation (6)), the final SDIS raster produced from the viewshed analysis is “clipped” using the spatial features of an SP as a “mask”. The masked $SDI{S}_{pix}$ (Equation (2)) values are then summed up to quantify $A{T}_{k,SDIS}$.

_{k,set}= “A” could have been considered. This approach, however, would result to extensively sparse optimum solutions within the examined region, which, in turn, would be difficult to be realized in terms of regional planning. For this reason, another approach is deployed in the present paper, facilitating the formation of compact regions with $S{P}_{k}\in A$. Specifically, a chromosome is represented by two distinctive triangles, which intersect with and include a number of SPs (Figure 5). At each iteration, the GAs algorithm initially finds the SPs of the triangles that belong to the C set and excludes them from further analysis. For the remaining SPs of the two triangles, Equations (6)–(10) are then applied, and the SPs satisfying those equations (i.e., SPs∈A) correspond to a potential optimum solution.

^{10}= 1024 and 2

^{11}= 2048, any of the X, Y coordinates require 11 bits to be represented in a binary form. Accordingly, 22 bits are required to create a point, 66 to create one triangle, and 132 to create two triangles. The latter 132 bits correspond to a chromosome (i.e., a possible solution to the optimization problem containing SPs that belong to the A set). Three-hundred generations of a population of 125 chromosomes each have been used. The mutation and the crossover probability have been set to 35% and 85%, respectively, determining which of the chromosomes will survive to the next generation. Elitism has been also deployed, letting the best five chromosomes survive always to the next generation. Penalties with successively decreasing values are assigned in the algorithm in a sequential manner as follows: (i) for points or triangle areas that fall outside of the examined region, as well as for triangles that intersect with each other (penalties with the largest values); (ii) for limitations resulting from the exclusion criteria of Table 1 related to set C (penalties with intermediate values); and, finally, (iii) for limitations resulting from the constraints described by Equations (7)–(10) (penalties with the smaller values). In this way, the algorithm efficiently promotes the chromosomes that fulfill as many requirements as possible.

_{max}and Area

_{min}values. More specifically, 10 different DG

_{max}values have been taken into account, varying from 2.5 km to 7.0 km, with a step of 0.5 km. Regarding Area

_{min}, 10 different values of this quantity have been also considered, from 0.5 km

^{2}(≈0.8% of the overall region) to 5.0 km

^{2}(8% of the overall region), with a step of 0.5 km

^{2}. To perform all the required computations, the computer cluster, Aristotelis of Aristotle University of Thessaloniki, has been used, deploying 125 CPUs simultaneously, one for every chromosome of each generation. The corresponding results are, finally, used as a basis to create a relevant web-GIS application, which is presented in the next section. This application is realized by using the R packages, “shiny” [63], “leaflet” [64], “tmap” [65], and “plotly” [66].

## 4. Results and Discussion

^{2}and belong to set C. Most of these areas correspond to environmentally protected areas, followed by minor roads and non-agricultural areas.

_{10}= 5000 m and c

_{10}= 1), whereas in Figure 7b, the finally produced SDIS map, where all viewshed classes of Table 2 are taken into account, is presented. In Figure 7a, the symbol SDIS

_{10}has been used in the legend to denote results that have been obtained for all N observers (Equation (1)), but for $DI{S}_{i,pix}={c}_{10}{V}_{10,pix}^{i}$, $i=1,\dots ,N$ in Equation (2). The results of Figure 7a indicate large SDIS

_{10}values in the high elevation areas, since those areas correspond to the most visible ones from a large distance. However, it can be seen that the SDIS map (Figure 7b) offers better results in terms of disturbance, since it accounts for the largest effect of the nearest objects on the visibility in an efficient manner. Accordingly, large SDIS values are bounded in areas located close to the roads and the residencies.

_{max}and Area

_{min}combinations are summarized in Table 4. In this table, values ≥ 2.5 correspond to penalty values and denote DG

_{max}and Area

_{min}combinations without any possible solutions (i.e., A = {}). The results of Table 4 indicate that for a given DG

_{max}value, the increase of the minimum allowable total coverage area for PV installations (Area

_{min}) generally leads to larger SDIS values. This is attributed to the fact that by increasing Area

_{min}, larger areas suitable for installing PVs can be allocated, leading to a larger social disturbance. The opposite holds true for DG

_{max}, since for a given Area

_{min}, the increase of DG

_{max}reduces the space suitable for PV installations, and, thus, it leads, in general, to smaller SDIS values. The effect of the DG

_{max}and Area

_{min}siting preferences on the optimization results is also shown schematically in Figure 8, where the minimum SDIS values of Table 4 for the 67 non-empty solution sets are plotted. It is also interesting to note that empty solution sets are mainly obtained for numerous Area

_{min}values, when DG

_{max}≤ 3.5 km. For example, for DG

_{max}= 2.5 km, only one optimum solution has been obtained in the case of the smallest examined Area

_{min}(equal to 0.5 km

^{2}). This, in turn, illustrates that for small DG

_{max}values, extensive areas for PV installations cannot be found in the region.

_{max}= 7.0 km and Area

_{min}= 0.5 km

^{2}(smallest examined low bound of PV locations’ total coverage area), whereas in Figure 10, the A set entities corresponding to the aforementioned DG

_{max}, but to Area

_{min}= 5.0 km

^{2}(largest examined low bound of PV locations’ total coverage area), are presented.

_{min}= 0.5 km

^{2}(Figure 9), optimum locations are bounded in the north-eastern region of the study area. Some of these locations also correspond to optimum solutions when Area

_{min}= 5.0 km

^{2}(Figure 10). However, for this Area

_{min}value, a larger number of optimum areas are obtained, which are also distributed in the form of compact regions within the whole examined study area. Although only two triangles are deployed in the GAs algorithm to identify optimum spatial entities (see Section 3.3), the results of Figure 10 clearly indicate that distinguishable compact regions of optimum locations for PV installations can be realized. This is attributed to the ability of the algorithm to create large-size triangles, which, at the end of the iterative optimization process, will include only spatial entities belonging to set A.

_{max}and Area

_{min}combinations. The user can: (a) set, via bars, his/her preferences regarding the values of DG

_{max}and Area

_{min}; (b) visualize all the results (optimum areas, as well as spatial entities belonging to B and C sets); and (c) download a matrix that contains all spatial information (e.g., official IDs) related to the areas of set A.

## 5. Conclusions

_{max}(maximum allowable PV locations—grid station distance) and Area

_{min}(minimum allowable total coverage area of PV installations). The main conclusions of the present investigation can be summarized as follows:

- The map of the proposed SDIS indicator can be easily created by both researchers and practitioners with low computational cost, and it accounts for the larger effect of the nearest objects on the visibility in an efficient manner. Accordingly, it can offer more realistic results than traditional viewsheds for assessing the visual effect of PV installations to the public.
- For a given DG
_{max}value, the increase of Area_{min}facilitates the allocation of larger optimally suitable areas for installing PVs; thus, the aforementioned increase leads generally to larger SDIS values. The opposite holds true for DG_{max}, since, from a physical point of view, the increase of DG_{max}for a given Area_{min}value reduces the space suitable for PV installations.For the examined study area, the GAs-driven optimization process has led to empty optimum solution sets for numerous Area_{min}values, especially when DG_{max}≤ 3.5 km, demonstrating that for small DG_{max}values, extensive areas for PV installations cannot be found in the region. - The developed GAs-driven optimization process offers the ability to determine distinguishable, but compact, regions of optimum locations for PV installations within the examined region, facilitating relevant regional planning decisions. The consideration of the SDIS indicator in the objective function can contribute to the mitigation of potential social oppositions and negative impacts on land activities, since optimum areas correspond to those that will have the minimum visual impact to the community.
- The developed web-GIS application presents a flexible and easy-to-use tool that enables the visualization of PV plants’ optimum locations in the study area for different bounds of the PV locations—grid station in-between distance and of the PV locations’ total coverage area. Accordingly, it facilitates policy-makers to choose the set of solutions that better fulfils their preferences/strategies related to the above factors. The flexibility of the tool can also contribute to the reduction of bureaucracy, as well as to the further boost of the local solar energy market in an environmentally friendly and socially accepted manner.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

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**Figure 1.**(

**a**) Location of the study area in the wider area of Andalusia, Spain; (

**b**) boundaries of the study area.

**Figure 3.**Locations of the observers on the major and minor roads and on the railway in a region around the La Palma Del Condado city along with the developed DSM.

**Figure 4.**Cumulative (not weighted) viewshed maps in a region around the La Palma Del Condado city for two different maximum visibility distances: (

**a**) 100 m; (

**b**) 1000 m (white areas correspond to the most visible areas).

**Figure 5.**One of the two triangles of a chromosome, intersecting with and including a number of SPs (red blocks). X

_{i}, Y

_{i}, i = 1,2,3, are the spatial coordinates of the triangle’s vertices in the deployed X − Y grid. Red lines correspond to minor roads, the pink line represents the railway, and the background is the SDIS raster.

**Figure 8.**Minimum values of the objective function for the examined DG

_{max}and Area

_{min}combinations that lead to non-empty solution sets (values of the SDSIS indicator have to be multiplied by 10

^{9}).

**Figure 9.**Set A optimum solutions for DG

_{max}= 7.0 km and Area

_{min}= 0.5 km

^{2}(values of the SDIS map have to be multiplied by 10

^{9}).

**Figure 10.**Set A optimum solutions for DG

_{max}= 7.0 km and Area

_{min}= 5.0 km

^{2}(values of the SDIS map have to be multiplied by 10

^{9}).

**Figure 11.**A view of the web-GIS application for selecting optimum locations for PV installation in La Palma del Condado municipality.

ID | Criterion | Incompatibility Zones | Spatial Data Source |
---|---|---|---|

EC1 | Distance from environmentally protected areas (Natura 2000 areas) | ≤150 m | [47] |

EC2 | Distance from major roads | ≤100 m | La Palma Del Condado municipality (personal communication) |

EC3 | Distance from railway network | ≤50 m | |

EC4 | Land use | Non-agricultural areas and vineyards | |

EC5 | Slope of terrain | ≥5% | [48] |

j | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

r_{j} (m) | 100 | 200 | 300 | 400 | 500 | 1000 | 1500 | 2000 | 3500 | 5000 |

c_{j} | 4.912 | 4.219 | 3.813 | 3.526 | 3.303 | 2.609 | 2.204 | 1.916 | 1.357 | 1.000 |

No. | Feature | Set A | Set B | Set C | |
---|---|---|---|---|---|

1 | EC1 satisfaction | No | No | No | Yes |

2 | EC2 satisfaction | ||||

3 | EC3 satisfaction | ||||

4 | EC4 satisfaction | Yes (vineyards) | Partial (only non-agricultural areas are included) | ||

5 | EC5 satisfaction | Yes | Not examined | ||

6 | Minimum SDIS indicator | Yes | No | Not examined | Not examined |

7 | Distance from grid station smaller than a predefined upper bound | ||||

8 | PV locations’ total coverage area larger than a predefined low bound |

**Table 4.**Minimum values of the objective function for the examined DG

_{max}and Area

_{min}combinations. Results with values < 2.5 should be multiplied by 10

^{9}.

Area_{min} Values (km^{2}) | DG_{max} Values (km) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

2.5 | 3.0 | 3.5 | 4.0 | 4.5 | 5.0 | 5.5 | 6.0 | 6.5 | 7.0 | |

0.5 | 0.022 | 0.025 | 0.024 | 0.009 | 25.000 | 0.011 | 0.010 | 0.009 | 0.006 | 0.006 |

1.0 | 5.000 | 0.048 | 0.044 | 0.033 | 0.028 | 0.020 | 0.029 | 0.019 | 0.018 | 0.017 |

1.5 | 7.500 | 7.500 | 0.070 | 0.051 | 0.042 | 0.045 | 0.037 | 0.039 | 0.028 | 0.025 |

2.0 | 10.000 | 10.000 | 0.101 | 0.091 | 0.067 | 0.065 | 60.000 | 0.052 | 0.038 | 0.034 |

2.5 | 12.500 | 12.500 | 0.128 | 0.094 | 0.089 | 0.097 | 0.100 | 0.081 | 0.064 | 0.048 |

3.0 | 15.000 | 15.000 | 15.000 | 0.140 | 0.120 | 0.104 | 0.122 | 0.096 | 0.082 | 0.077 |

3.5 | 17.500 | 17.500 | 17.500 | 0.163 | 0.147 | 0.139 | 0.159 | 0.125 | 0.101 | 0.071 |

4.0 | 20.000 | 20.000 | 20.000 | 0.168 | 0.170 | 0.165 | 20.000 | 0.157 | 0.118 | 0.093 |

4.5 | 45.000 | 22.500 | 22.500 | 22.500 | 0.229 | 22.500 | 22.500 | 22.500 | 0.148 | 0.109 |

5.0 | 50.000 | 150.000 | 25.000 | 25.000 | 25.000 | 25.000 | 25.000 | 0.204 | 0.178 | 0.124 |

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## Share and Cite

**MDPI and ACS Style**

Nagkoulis, N.; Loukogeorgaki, E.; Ghislanzoni, M.
Genetic Algorithms-Based Optimum PV Site Selection Minimizing Visual Disturbance. *Sustainability* **2022**, *14*, 12602.
https://doi.org/10.3390/su141912602

**AMA Style**

Nagkoulis N, Loukogeorgaki E, Ghislanzoni M.
Genetic Algorithms-Based Optimum PV Site Selection Minimizing Visual Disturbance. *Sustainability*. 2022; 14(19):12602.
https://doi.org/10.3390/su141912602

**Chicago/Turabian Style**

Nagkoulis, Nikolaos, Eva Loukogeorgaki, and Michela Ghislanzoni.
2022. "Genetic Algorithms-Based Optimum PV Site Selection Minimizing Visual Disturbance" *Sustainability* 14, no. 19: 12602.
https://doi.org/10.3390/su141912602