A Multi-Objective INLP Model of Sustainable Resource Allocation for Long-Range Maritime Search and Rescue

Maritime search and rescue (SAR) operations play a crucial role in reducing fatalities and mitigating human suffering. Compared to short-range maritime SAR, long-range maritime SAR (LRMSAR) is more challenging due to the far distance from the shore, changeful weather, and less available resources. Such an operation put high requirements on decision makers to timely assign multiple resources, such as aircraft and vessels to deal with the emergency. However, most current researches pay attention to assign only one kind of resource, while practically, multiple resources are necessary for LRMSAR. Thus, a method is proposed to provide support for decision makers to allocate multiple resources in dealing with LRMSAR problem; to ensure the sustainable use of resources. First, by analyzing the factors involved in the whole process, we formulated the problem as a multi-objective optimization problem, the objective of which was to maximize both the probability of completing the tasks and the utilities of allocated resources. Based on the theory of search, an integer nonlinear programming (INLP) model was built for different tasks. Second, in order to solve the non-deterministic polynomial-time hardness (NP-hard) model, by constructing a rule base, candidate solutions can be found to improve the calculation efficiency. Furthermore, in order to obtain the optimal scheme, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was applied to the candidate solution sets to approximate Pareto fronts. Finally, an emergency case of Chinese Bohai Sea was used to demonstrate the effectiveness of the proposed model. In the study, 11 resource allocation schemes were obtained to respond to the emergency, and calculation processes of schemes were further analyzed to demonstrate our model's rationality. Results showed that the proposed models provide decision-makers with scientific decision support on different emergency tasks.