Optimized deployment–monitoring synchronized array method for passive sonobuoys based on an improved NSGA-II algorithm

Unmanned Underwater Vehicles (UUVs) equipped with multiple sensors play an important role in ocean operations; however, navigation failures and communication disruptions may lead to vehicle loss. Passive sonobuoys are widely used for search and recovery of the lost UUV, where the deployment of sonobuoy arrays directly affect detection efficiency and deployment cost. Optimizing passive sonobuoy arrays for deployment–monitoring synchronized searches therefore constitutes a challenging multi-objective optimization problem. To address the premature convergence, limited operator adaptability, and weak population diversity maintenance of the conventional Non-dominated Sorting Genetic Algorithm II (NSGA-II), which hinder its performance in complex multi-objective scenarios, an INSGA-II–based optimization model for deployment–monitoring synchronized searches with passive sonobuoys is constructed. The three-dimensional spatial dispersion characteristics of the lost UUV are first analyzed, and a detection efficiency evaluation model for passive sonobuoy arrays is established. On this basis, a multi-objective optimization framework is constructed to simultaneously maximize detection efficiency while minimizing deployment route length and the number of deployed sonobuoys. The proposed INSGA-II integrates a Logistic map, an adaptive crossover operator, and dynamic crossover and mutation probabilities based on crowding distance to enhance global search capability. Experimental results demonstrate that the proposed method is both feasible and effective. Under a limited sonobuoy deployment constraint, the maximum detection efficiency reaches 0.9088, achieving up to a 13.9% improvement over benchmark algorithms. Moreover, three-dimensional deployment significantly outperforms conventional two-dimensional strategies, with maximum and average improvements of 15.19% and 12.53% in detection efficiency, respectively.