Multi-objective optimization of resource allocation and patrol routing for a maritime patrol and rescue system considering spatial risk distribution

Timely and effective search and rescue (SAR) services are crucial for ensuring maritime safety. Proactive patrol operations provide an effective means of improving the response capability and resource utilization efficiency of maritime patrol and rescue systems. However, existing maritime rescue systems mainly rely on fixed rescue bases and cannot fully account for spatial variations in maritime risk during resource allocation. To address this issue, this study proposes a multi-objective optimization approach for a maritime patrol and rescue system considering spatial risk distribution. Historical maritime accident data and AIS data are integrated, and a convolutional neural network–multilayer perceptron (CNN–MLP) model is developed to estimate the risk index of each service subarea. Based on this, a multi-objective optimization model is formulated for maritime patrol and rescue operations, integrating patrol-point location, SAR ship task allocation, and patrol routing into a unified framework. Considering the large continuous search space for patrol-point locations, the varying number of decision variables, and the complex combinatorial optimization characteristics, a hybrid optimization algorithm combining fuzzy C-means clustering and simulated annealing-based variable neighborhood search (FCM-SA-VNS) is proposed. Numerical experiments are conducted in the South China Sea, and different-scale instances are used to compare the proposed algorithm with NSGA-II and MOPSO. The results demonstrate that FCM-SA-VNS consistently generates superior Pareto non-dominated solutions with better convergence and diversity across different-scale test instances. Sensitivity analysis further investigates the variations of system configurations under different operational constraints and service requirements, providing guidance for parameter setting in maritime patrol and rescue systems. The proposed approach can provide decision support for offshore SAR resource deployment and patrol planning.