Underwater wireless sensor networks have grown considerably in recent years and now contribute substantially to ocean surveillance applications, marine monitoring and target detection. However, the existing deployment solutions struggle to address the deployment of mobile underwater sensor nodes as a stochastic system. The system faces internal and external environment problems that must be addressed for maximum coverage in the deployment region while minimizing energy consumption. In addition, the existing traditional approaches have limitations of improving simultaneously the objective function of network coverage and the dissipated energy in mobility, sensing and redundant coverage. The proposed solution introduced a hybrid adaptive multi-parent crossover genetic algorithm and fuzzy dominance-based decomposition approach by adapting the original non-dominated sorting genetic algorithm II. This study evaluated the solution to substantiate its efficacy, particularly regarding the nodes’ coverage rate, energy consumption and the system’s Pareto optimal metrics and execution time. The results and comparative analysis indicate that the Multi-Objective Optimisation Genetic Algorithm based on Adaptive Multi-Parent Crossover and Fuzzy Dominance (MOGA-AMPazy) is a better solution to the multi-objective sensor node deployment problem, outperforming the non-dominated sorting genetic algorithm II, SPEA2 and MOEA/D algorithms. Moreover, MOGA-AMPazy ensures maximum global convergence and has less computational complexity. Ultimately, the proposed solution enables the decision-maker or mission planners to monitor effectively the region of interest.