## 3 IUWSNs Task Allocation Model  
In this part, aiming at the limited computing power and control range of sensors, a task allocation model based on IUWSNs is designed, which introduces the coordinates of monitoring sensor nodes. The model can be simply assumed as \(x\) tasks and \(y\) sensor nodes in IUWSNs. Suppose that \(y\) sensor nodes are arranged in the target area at random to collect \(x\) monitoring information tasks. The aim at this essay is to allocate different tasks to different sensor nodes through task allocation, so as to obtain a relatively large network revenue. Besides, Table 2 records the symbols used in this part. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Proposed Method** & **Year** & **Optimization Strategy** & **Limitations** \\ \hline DPSO-TA & 2021 & An offline discrete Particle swarm optimization algorithm & This algorithm is prone to falling into local optima and unable to obtain global optima. \\ \hline IGA & 2016 & Improved genetic algorithm strategy & Improved genetic algorithms require consideration of many factors, and their implementation is very complex. \\ \hline IACO & 2020 & Improvement by adding operators to ACO & In the event of improper parameter settings, there is a risk of straying away from attaining optimal solutions. \\ \hline SAGA & 2019 & Combining classic SA and GA & The algorithm’s implementation complexity is a challenge, and the specific outcomes are susceptible to the influence of parameters. \\ \hline GABP & 2018 & Combining classic genetic algorithms with neural network algorithms. & This algorithm requires a large amount of computation and requires a large amount of data for training. \\ \hline CEAGA & 2023 & The GA incorporates three operators: chaos, elitist, and adaptive. The Assignment problem of IUWSNs is solved by expanding the solution space and improving the global search ability of the algorithm. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of Algorithms. IUWSNs are networks composed of a large number of distributed sensor nodes used for monitoring, collecting, and transmitting data in the environment. However, energy consumption has always been an important issue in IUWSNs, directly affecting their performance. The energy model in this article is common, as shown in Figure 1.  
\[ET(d,\,G)\,=\, \begin{cases}G\times\left(E_{c}+\phi_{ampx}\times d^{2}\right)&, \quad d\leq d_{0}\\ G\times\left(E_{c}+\phi_{ampy}\times d^{4}\right)&,\quad d>d_{0}\end{cases}  \tag{1}\]  
\[ER(d,\,G)\,=\,E_{c}\times G \tag{2}\]  
Among them, \(ET\) and \(ER\) represent the total energy consumed for transmitting and receiving \(G\)-bit data packets, respectively. \(E_{c}\) represents the dissipated energy per bit of transmission or reception circuit, measured in joules. \(E_{a}\) represents the energy consumed by each bit of power amplifier, and \(d_{0}\) represents the distance boundary. Assuming that the benefits and priorities of task allocation have been assessed and prioritized. In IUWSNs, \(y\) sensor nodes with unique numbers are stochastically arranged in the target sensing area. The urgency evaluation value of the \(j\)th batch of tasks is \(E_{j}\), and the estimated value of the perceived advantage of the \(i\)th sensor unit to the \(j\)th batch of tasks is \(A_{ij}\). Therefore, the benefit value of each sensor unit to the target task is (1), where \(A_{ij}\) represents our benefit to the target. The purpose of goal distribution is to meet the basic principles of goal distribution and pursue the best overall benefits. Therefore, it is assumed that the network revenue value of the task performed by each sensor node is \(r_{j}\). Then, in Equation (2), \(R\) can be used to represent the income of IUWSNs' task allocation, and \(R_{max}\) represents the gain of expanding the network. \[A=1/(ET+ER) \tag{3}\]  
\[r_{ij}=E_{j}\times A_{i,j} \tag{4}\]  
\[R=\sum_{j=1}^{n}r_{i,j} \tag{5}\]  
The solution is coded in decimal system.