Advancing Multispectral Image-Derived Physics-Based Bathymetry: Multi-Objective Evolutionary Computation for Shallow Water Depth Retrieval

Satellite derived bathymetry (SDB) has become a cost effective and efficient way to monitor coral reefs on a large scale. Physics-based SDB methods retrieve bathymetry by minimizing a cost function that measures the difference between the observed spectra and radiative transfer model (RTM) simulations. Most existing physics-based SDB methods adopt a single cost function, typically focus on matching spectral amplitude, and ignore other complementary spectral discriminators such as spectral shape. This limitation can compromise retrieval accuracy when spectral amplitude exhibits significant variability due to noise, varying illumination conditions, or benthic endmember variability. To address this problem, this research formulates physics-based SDB as a constrained multi-objective optimization problem (CMOP). The decomposition-based constrained multi-objective differential evolution (DCMODE) algorithm is proposed to simultaneously optimize two cost functions, namely the root-mean-square error (RMSE) and the spectral angle distance (SAD). In DCMODE, evenly distributed weight vectors are produced to guide the optimization under different trade-off preferences. The constrained penalty boundary intersection (CPBI) is introduced as a quantitative criterion for evaluating solutions based on convergence, diversity, and feasibility. Bathymetry results from Landsat-8 OLI images in four study areas in the Xisha Islands indicate that DCMODE achieves higher accuracy than single-objective optimization methods, decreasing the RMSE by 0.03∼0.12 m and the mean absolute error (MAE) by 0.16∼0.19 m. This research demonstrates that multi-objective optimization, as embodied in the DCMODE algorithm, provides a promising framework for enhancing the robustness of physics-based SDB methods. The code and data are publicly available on https://github.com/leic-sysu/RTM-DCMODE.