# A Sustainable Location-Allocation Model for Solar-Powered
## 2 Materials and Methods
### Flower Pollination Algorithm (FPA)  
We used image processing to identify the rice field's coordinates. Then, we determined some coordinates on the map for installing some UVUS, and each tool was considered to cover some area of the map. The FPA was used to change the locations of UVUS such that the area uncovered by UVUS was the minimum. Location assignment is part of the real-world problem of warehouse operation, which is considered an optimization problem [19]. FPA shows better performance than other metaheuristic algorithms. Since FPA was found, there are many variants that established this method to solve complex problems in different research domains [20]. FPA performs well on single-objective problem examples but still shows inefficiencies in the number of function evaluations [21]. In 2012, [PERSON] [22] suggested an algorithm that is inspired by flower pollination by bees. There are two types of pollination: local pollination and global pollination. Local pollination occurs when the pollen of a flower fertilizes the buds of its own flower, whereas global pollination involves other flowers. The FPA is based on those modes of pollination, and it is represented in Figure 1. Local or global pollination is determined by the switching probability. This number indicates the probability of a bee switching to another flower to enable global pollination or staying with the same flower to perform local pollination. Let n be the number of initial UVUS in the system; then, \(X_{i}^{t}\), i = 1, 2,..., n represents the axis from the \(i\)-th UVUS coordinate for \(t\)-th iteration(s). The objective of FPA is to determine \(X_{i}^{t+1}\) for every UVUS based on its pollination type, such that they will cover as large an area as possible. Equation (1) is used to set new UVUS coordinates for the local pollination in FPA:  
\[X_{i}^{t+1}=X_{i}^{t}+\epsilon\left(X_{j}^{t}-X_{k}^{t}\right),\text{ where }i \
eq j\
eq k \tag{1}\]  
In Equation (1), the value of \(\epsilon\) is a random number between 0 and 1 to determine the new coordinates of the \(i\)-th UVUS based on the coordinates of two other UVUS--i.e., the \(j\)-th UVUS and the \(k\)-th UVUS. Thus, there must be at least three UVUS to perform this simulation. Equation (2) is used to set new coordinates for an UVUS for global pollination in the FPA:  
\[X_{i}^{t+1}=X_{i}^{t}+(L)\left(X_{i}^{t}-g^{*}\right). \tag{2}\]  
In Equation (2), the value of \(L\) represents the flight distance; it is derived from the Levy distribution function. \(g^{*}\) is the present best solution available amongst the possible populations (case scenarios). \begin{table}
\begin{tabular}{c c c} \hline
**No.** & **Data** & **Description** \\ \hline
1 & The map of the rice field & The outline of the rice field for the domain of the UVUS coordinate \\
2 & The cost of UVUS & The investment cost and production cost of UVUS \\
3 & The specification of UVUS & The height, weight, design, color, voltage, electric current, etc. \\
4 & The area of the rice field & The area of rice field (in m\({}^{2}\)) which UVUS would be installed \\
5 & The range of UVUS & The effective radius of UVUS (in m) to repel pest \\
6 & The user satisfaction & The farmers’ satisfaction toward the technology \\
7 & The rice production rate & The number of rice (in kg) produced in the first 9 months \\
8 & The CSA of the rice & The detailed list of cost to produce 1 kg of the rice \\ \hline \end{tabular}
\end{table} 
Table 2: The data required for the research. Figure 1: The FPA for UVUS location determination. The optimum function in FPA to determine its solution is in (3). \[Z=\sum_{i=1}^{n}\biggl{(}\biggm{|}\frac{d(m_{i},b)}{r}\biggm{|}\biggm{)}+k, \tag{3}\]  
where  
\(Z\): the optimum value. \(n\): the area of rice field, represented by the pixels of the rice field map. \(m_{i}\): the \(m\)-th point in the rice field, \(m\) = 1,2,...,\(n\). \(b\): the nearest UVUS to \(m_{i}\). \(r\): the radius of UVUS tools. \(k\): the number of UVUS tools. \(d(m_{i},b)\): the distance between \(m_{i}\) and \(b\).