## 3 Simulation Experiments and Analysis
### Background Introduction
Moreover, the activation of sensors for area search tasks incurs additional energy consumption. The baseline energy consumption for the USVs is quantified as 1 unit per 100 m travelled. For each additional sensor carried or activated for detection purposes, an incremental energy expenditure of 0.03 units per 100 m is incurred. \(Energy_{i}^{1}\) and \(Energy_{i}^{2}\) represent the energy loss induced by all USVs travelling to the \(i\)-th mission area and the energy loss of each USV performing the search task, respectively. \(N_{tk}^{i}\) represents the number of USVs carrying the \(k\)-th type of sensor in the \(i\)-th mission area (\(k=1\) for the surface detection sensor, \(k=2\) for the submerged detection sensor, and \(k=3\) for both types of sensors). \(dis_{ij}\) represents the distance between the \(j\)-th USV carrying the \(k\)-th sensor and the \(i\)-th mission area. \(energy_{j}^{1}\) represents the energy loss induced by the USVs during navigation. \(length_{j}\) denotes the path length required by the \(j\)-th USV carrying the \(k\)-th sensor for area detection. \(energy_{j}^{2}\) denotes the energy loss induced by the USVs during area detection (when their sensors are activated). \(Time_{i}\) denotes the total time spent by all USVs travelling to the \(i\)-th mission area and performing the coverage search task. \(Time_{i}^{1}\) denotes the time consumed by all USVs to travel to the \(i\)-th target. \(v_{j}\) denotes the maximum navigational speed of the \(j\)-th USV carrying the \(k\)-th sensor when travelling to the mission area. \(Length_{i}^{1}\) denotes the total length required for surface sounding in the \(i\)-th mission area. \(Length_{i}^{2}\) denotes the total length to be covered for underwater detection in the \(i\)-th mission area. \(v_{j}^{\prime}\) denotes the maximum speed of the \(j\)-th USV when travelling to the mission area. In this paper, the quality of the allocation scheme is assessed using the \(fitness\) level, which has a value between 0 and 1. A higher value of \(fitness\) indicates a better allocation scheme. To better relate the context of this paper to intelligent algorithms, an example of utilizing the RTPK-SFOA is illustrated. In the task scenario, each task assignment scheme is modelled as a two-dimensional array. In the RTPK-SFOA, the position of each sheep represents a task allocation scheme (a feasible solution), and the fitness of each sheep indicates the quality of the corresponding allocation scheme. The extent of the pasture represents the entire solution space. The goat may be a randomly selected sheep after the initialization of the flock. During the iterative process of the algorithm, the shepherd represents the global optimum solution (the feasible solution with the highest fitness value). For the flock, the speeds of the sheep and the goats are related to the dimensions of the feasible solutions. The specific speed values can be determined according to the specific problem, and an appropriate speed can accelerate the convergence of the algorithm. To give the reader a better understanding of the variables used in this paper, the variables that appear in the theory section of the algorithm are described in Figure 1:0