## 2 Research Content and Methodology
### Methodology
#### 2.2.2 Complex Area Survey Line Optimization Model  
The CASLOM model is fundamentally an optimized version of the PMOP model, incorporating PMOP's algorithms to achieve efficient and high-precision measurements. It is specifically designed for complex, significant marine areas requiring repeated measurements. The primary aim of the CASLOM model is to develop the most efficient multibeam survey line configurations, optimizing the survey process to adapt effectively to challenging marine environments. Applicable marine conditions: Within a specific real marine area, given that single-beam measurement data were used several years ago, and considering that marine conditions may have changed over the years and single-beam measurement data lack precision, it is necessary to optimize the general multibeam echosounder model. The goal is to achieve the optimal survey line layout so that the stripes formed along the survey lines cover the entire area to be measured as completely as possible, with minimal overlap between adjacent stripes and the shortest possible total length of the survey lines, in order to achieve the most efficient measurement results in practical surveys. We collected single-beam survey data from 8 different sea areas recorded several years ago, each with a sampling area of 5 nautical miles in length (north-south) and 4 nautical miles in width (east-west). The data from the sixth sampling area were selected for demonstration. After data cleaning, the visualized results of the coordinates for this area are shown in Figure 8. Part of the single-beam bathymetric data for this sampling area is presented in Table 1 in Appendix B.1. Using the CASLOM for such marine areas, it is possible to design a set of survey lines that maximize coverage and minimize overlap between lines, addressing the issue of inefficient survey routes. Below are the model's implementation steps. First, determine the optimization objectives. Based on the maritime conditions and the demands of on-site measurement, the following optimization goals have been defined:  
\[\text{Optimize}\left\{ \begin{array}{l}\text{min}(L_{\text{total}})\\ \text{min}(S_{\text{mea}}-S_{\text{mis}})\end{array} \right.\]  
Figure 7: This figure shows the projection of the survey line layout on the XOZ plane when \(\beta=90^{\circ}\) using the MBES system. The survey lines are set as straight lines to maximize the use of the multibeam transducer’s opening angle \(\theta\), thereby achieving the maximum coverage width \(W\). In the diagram, \(D_{x}\) represents the depth measured by each set of survey lines within the rectangular sea area, which helps to optimize the coverage width utilization in deep-sea areas. The survey lines extend parallel along the x-axis, and each line forms a straight line with the normal seabed slope on a plane at an angle \(\alpha\), ensuring continuity and efficiency of coverage. The points \(Q_{i}\) indicate the intersection of the rightmost beam emitted by the survey vessel during the \(i\)-th measurement with the slope. At the same time, \(d_{1},d_{2},\ldots\) represent the distances between different survey lines, and \(d_{1}^{\prime},d_{2}^{\prime},\ldots\) represent the distances between \(Q_{i}\) and \(Q_{i+1}\). By appropriately adjusting these distances, the coverage efficiency can be optimized, and the total length of the survey lines can be reduced. where \(L_{\text{total}}\) is the total length of the survey lines, \(S_{\text{mea}}\) is the area covered by the survey lines, and \(S_{\text{mis}}\) is the area missed in the measurements to enhance economic efficiency and measurement efficiency. The optimization problem is defined as follows:  
\[\text{Optimize}\Bigg{\{} \begin{aligned} &\min(L_{\text{total}})\\ &\min(S_{\text{mea}}-S_{\text{mis}})\end{aligned} \to \max(W(x_{i},y_{i}))\to\text{optimal navigation direction} \tag{4}\]  
Therefore, finding the maximum coverage width at each location within the maritime area is crucial.