Optimization model for multibeam sounding line deployment based on genetic algorithm

Abstract

Multibeam sounding technology is a cutting-edge method used for measuring underwater topography, widely applied across various fields. The actual seafloor terrain often exhibits significant fluctuations, leading to challenges such as insufficient coverage in shallow areas and excessive overlap in deep-water zones, resulting in inefficient operations. Rational selection of line spacing helps improve measurement efficiency and ensures data integrity. In this paper, taking the 2023 National College Student Mathematical Modeling Competition Problem B as a background, we conduct a thorough analysis of the variation patterns of the coverage width of multibeam sounding strips with respect to various parameters. We establish models for ocean depth and coverage width, determining how the strip coverage width changes with distance and the angle between survey lines in different scenarios. Finally, employing genetic algorithms and differential methods, we identify decision variables, objective functions, and constraints to formulate a nonlinear programming model. Through iterative searches, we obtain an optimal sounding line deployment plan that maximizes coverage of the target sea area while keeping the overlap rate below 20%. The calculated missed measurement error is approximately 32.774%, and the overlap rate is around 10.477%, indicating a high level of model accuracy.