Background and ObjectiveA method to reduce the absorption of solar radiation and prevent the creation of urban heat islands is to increase shade by vegetation. A shadow creating on buildings, causes houses to cool down, reduces energy consumption and costs, increases the value of houses, and creates a proper visual effect and a sense of well-being and vitality. Although economically, the amount of savings due to shade and cooling of the air for a tree during its lifetime in different climatic regions is different and depends on the type of tree, the amount of shade during the day and in different seasons of the year, but its effect on energy savings and costs are definite. The subject of the present study is strategic planning to increase the shade coverage of trees in urban residential areas. A simple way to create plenty of shade is to plant numerous trees around buildings. However, this method is impractical in many areas that face water shortages due to its high costs. In addition, the presence of additional shadows on the rooftop of the buildings will reduce the ability to be exposed to sunlight and the potential of using solar panels to generate electricity. So the main challenge is using a method that can provide maximum shade coverage on the facade surface and minimum shadow coverage on the rooftop with a few trees in optimal locations. The issue of locating trees with the aim of optimizing shade coverage, i.e. maximizing shade coverage on facades and opening components, and minimizing shadow coverage on the rooftop, is a Non-deterministic Polynomial hard (NP-hard) problem and has no exact solution. Therefore, the 3D Geographic Information System and the Ant Colony Optimization algorithm have been used for this purpose. Previous studies have often examined the effects of tree canopy shade on a single building. But in most cities in Iran, buildings are connected together and form a building block. So, instead of a single building, a building block is examined. In addition, in most previous studies, the effect of shade coverage of a maximum of two trees on the building has been investigated; while in this study, we examine the effect of shade coverage of 15 trees on the building block. None of the studies on optimizing the shade of trees on the facade of the building has used the meta-heuristic optimization methods and its combination with GIS. In this study, a hybrid model of GIS in a three-dimensional environment and ACO is used for maximizing the shade of trees on the facade and opening components of buildings, and minimizing the shade of trees on the rooftop.Materials and Methods Two types of data are required to perform the analysis; The building block properties, for example, dimensions, position, and size of the facade, rooftop, and opening components, and the tree properties (height and position). 3D GIS and ACO algorithms have been used to model tree shade coverage optimization. 3D GIS provides abilities for storing, analyzing, and creating 3D topologies, and ACO is used to summarize real-world conditions in a mathematical problem. GIS and trigonometric rules have been used to store geographical information and spatial topology. After storing the position, composition, and description information of 2D and 3D objects by topological data, Duffie and Beckman relations (2013) is used to extract the position of the shadow. Then, according to Church and Revelle, the Maximal Covering Location Problem (MCLP) is defined. For the following 3 reasons, ACO has been used for three-dimensional optimization; 1) The complex trigonometric rules in calculating the shadow coverage on buildings, 2) There is no deterministic solution for optimization problems because of nonlinear constraints including trigonometric functions, 3) The existence of continuous space around the building block that It is possible to place a tree in any position. The details of the steps are; 1) Define the set of possible locations for the tree based on the height, diameter of the canopy, and around space of the building block, 2) Use a method to place the first tree in all possible places around the building block during hot hours on certain days of the summer and calculate the maximum shade coverage on the building block based on the weight of the building components, 3) Remove the places that may be done in the tree canopy to prevent overlapping of tree canopies, 4) Repeat steps 2 and 3 to place the next trees in the possible places around the building block until the number of trees reaches the desired number of trees to create shade. Considering the infinite possible positions, a simplification step is required to limit the number of available positions. Therefore, the constant space is reduced to possible positions for locating Ni trees with two-meter spacing in the N-S and E-W directions. Further, the possible tree positions in front of the opening components are eliminated to make daylight available, have an outlook from the building, and comment through the doors. The minimum spacing of two meters between the trees and the building is set to prevent unnecessary shading on the rooftop.Results and Discussion MATLAB environment is used to optimize the shade coverage of trees using the ACO algorithm. For this purpose, properties of the buildings block such as length, width, height, are modeled in a struct in MATLAB. This struct has separate matrices for the north, east, south, and west views of the building block. Another matrix is also used to model the rooftop. Each element of the mentioned matrices is equal to 10× 10 cm from the surface of the building block and has a value of zero. To model the dimensions and location of doors and windows in each facade, another struct includes separate matrices for each facade is used. In these matrices, the amount of elements in the location of doors and windows is one. The characteristics of the sun in the study area are used, including azimuth and altitude of the sun on the studied days in 15-minute intervals from 9 to 15 hours. The shadow is created on building components, by placing the tree in any of the possible locations, and movement of the sun. The elements of the matrices equivalent to the shaded building components change from zero to one. The sum of the values of the matrix elements determines the amount of shadow created by the tree on each component of the building. The sum of the point multiplication of the door/window matrix elements in the facade matrix elements determines the amount of shadow created on the doors/windows. The objective function is defined and the ACO algorithm is used to maximize the shadow coverage of trees on the facade, doors/windows, and minimize the shadow coverage on the rooftop. The results of the ACO show that the optimal shade coverage on the buildings block, which creates the most shade on the facade and doors and windows and the least shade on the roof, depends on the number of trees and the position of the doors and windows in buildings block. In general, as the number of trees increases, the amount of shadow created on the building block components increases.Conclusion The results of the ACO showed that for buildings, in the northern hemisphere, the trees in the north of the buildings have no effect on casting shadows on the components of the building. Due to the fact that in arid and tropical regions there are restrictions on planting trees, finding a suitable position for trees plays an important role in optimizing the shade coverage. Due to the high heat transfer through the doors and windows compared to the facade and rooftop, the higher weight is considered for these components in the objective function. Finding the optimal position of the trees depends a lot on the position of the doors and windows in the building to create the most shadow on these components. For a buildings block with the number and dimensions of buildings assumed in the research and according to the dimensions and position of doors and windows, planting a tree in one of the positions K10, K16, K22, or K28 creates the most optimal shade. These positions are 2 meters from south of the buildings and in the middle of two windows. On average, this tree provides 7.48, 9.22, and 0.85% shade respectively on the facade, doors /windows, and rooftop from 9 to 15 o'clock in four days studied. In the case of planting two trees, two positions from positions K10, K16, K22, or K28 still provide the optimal shade. On average, these two trees provide 13.88%, 18.64%, and 1.69% of shade respectively on the whole facade, doors /windows, and rooftop at 9:00 AM to 3:00 PM. In the case of three trees, positions K8, K18, and K22, in the case of four trees, positions K14, K20, K26, and K32, in the case of five trees, positions K8, K14, K20, K26, and K32 create the optimal shadow. Shading coverage in the case of three trees, is 21.07, 28.54, and 2.54%, respectively on the facade, doors/windows, and rooftop, in the case of four trees, is 24.96, 35.36 and 3.39% respectively on the façade, doors/windows, and rooftop and in the case of five trees is 33.26, 44.70 and 3.95% respectively on the facade, doors/windows, and rooftop. By planting five trees, more than 88% of the south façade and more than 90% of the south façade doors/windows of the building will be covered with shade. However, due to the goal of optimizing the shadow on the building and the greater weight of the doors and windows, the ACO has optimized the position of the trees in such a way that more surfaces of the doors and windows are exposed to the shadows. Due to the fact that in the case of five trees, 90% of the southern facade is in the shade of trees, in the case of six trees, in addition to the southern facade, the eastern and western facades are also considered for planting trees. So that the positions K8, K14, K20, and K30 are chosen in the distance of 2 meters from the south and the position of H2 is chosen in the distance f 2 meters from the west, and the position of H36 is chosen in the distance of 2 meters from the east. On average, these trees provide 33.95%, 42.29%, and 3.64% shade respectively on the facade, doors/windows, and rooftop.
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