## 3 Simulation Experiments and Analysis
### Background Introduction  
This paper establishes a framework for conducting autonomous search missions involving USVs in detection scenarios. Each autonomous search mission comprises underwater and surface coverage-based search tasks. Each USV is equipped with either a surface detection sensor (exclusively for surface detection), an underwater detection sensor (exclusively for underwater detection), or both sensors (for both surface and underwater detection) and initiates its journey from a starting point, carrying its respective sensors to the designated mission area for search coverage. The mission is considered complete once all USVs have fulfilled their individual search tasks. This detection scheme is described further in the document. In Figure 1, the operational area of the USVs is confined to a rectangular zone measuring 5000 m by 22,000 m. The red squares represent USVs equipped with surface detection sensors, the blue triangles indicate USVs with underwater detection sensors, and the black dots denote USVs carrying both types of sensors. The black rectangular area at the top represents the mission area, with each USV allocated to a maximum of one mission area for conducting detection tasks. The capabilities of the USVs within the scenario vary, specifically in terms of their maximum sailing speeds (5 m/s to 10 m/s), the types of sensors carried, and their maximum coverage detection speeds (1.4 m/s to 2 m/s). The sensors onboard the USVs are capable of detecting information within a 100 m radius of their location. At this point, a set of USVs denoted as \(U=\{u_{1},u_{2},\ldots,u_{N_{u}}\}\) is present, where \(N_{u}\) represents the number of USVs; \(TASK=\{task_{1},task_{2},\ldots,task_{N_{t}}\}\), where \(N_{t}\) denotes the number of target areas. Once the task allocation process for the USVs is completed, they commence their respective missions. While navigating to their task areas and initiating their sensors to conduct searches over the designated regions, the USVs experience energy losses. The ultimate objective of the USV task allocation process is to ensure minimal energy depletion for all USVs while efficiently completing the area search tasks. To assess the quality of the allocation results, this paper introduces a fitness function. \[fitness=1-\left(w_{1}*\frac{Energy}{Energy_{max}}+w_{2}*\frac{Time}{Time_{ max}}\right). \tag{20}\]  
_Energy_ and _Time_ are terms used to the quantify energy loss and temporal expenditure, respectively, within the context of the allocation scheme. The weighting coefficients \(w_{1}\) and \(w_{2}\) represent the relative importance levels assigned to energy conservation and exped  
Figure 1: Task scenario. completion during the task allocation process, respectively. It is stipulated that \(w_{1}+w_{2}=1\). With the aim of minimizing the total time spent, this study sets \(w_{1}\) to 0.1 and \(w_{2}\) to 0.9. The subsequent sections detail the computational methodologies for determining \(Energy\) and \(Time\). \[Energy=\sum_{i=1}^{Nt}Energy_{i}. \tag{21}\]  
\[Energy_{i}=Energy_{i}^{1}+Energy_{i}^{2}. \tag{22}\]  
\[Energy_{i}^{1}=\sum_{k=1}^{3}\sum_{j=1}^{N_{R}^{i}}dis_{ij}*energy_{j}^{1}. \tag{23}\]  
\[Energy_{i}^{2}=\sum_{k=1}^{3}\sum_{j=1}^{N_{R}^{i}}length_{j}*energy_{j}^{2}. \tag{24}\]  
\[Time=max_{i=1}^{Nt}\{Time_{i}\}. \tag{25}\]  
\[Time_{i}=Time_{i}^{1}+Time_{i}^{2}. \tag{26}\]  
\[Time_{i}^{1}=max_{k=1}^{3}max_{j=1}^{N_{R}^{i}}\frac{dis_{ij}}{v_{j}}. \tag{27}\]  
\[Time_{i}^{2}=max\left\{\frac{Length_{i}^{1}}{\left(\sum_{j=1}^{N_{R}^{i}}v_{j} ^{\prime}+\sum_{j=1}^{N_{R}^{i}}v_{j}^{\prime}\right)},\frac{Length_{i}^{2}}{ \left(\sum_{j=1}^{N_{R}^{i}}v_{j}^{\prime}+\sum_{j=1}^{N_{R}^{i}}v_{j}^{ \prime}\right)}\right\}. \tag{28}\]  
In this context, \(Energy_{i}\) denotes the energy expended by all USVs as they navigate to and execute area search operations within the \(i\)-th task region. The energy consumed during navigation increases with the number of sensors equipped on each USV.