## 5 Conclusions  
Compared to offshore rescue, medium/distant maritime rescue is more challenging. However, most previous works have not fully developed a process for medium/distant maritime rescue, which is essential. The TPM is proposed to determine and optimize the SRP of the amphibious aircraft in medium/distant maritime rescue. To include the influence of the time variation, the TPM comprised the relative motion of the amphibious aircraft and of the PDTs, the change of PDTs' positions, and the changed uncertainty health weight of the PDTs. Based on this, the k-means* and the GA* were used to determine and optimize the SRP of the amphibious aircraft for TPM applications. To evaluate the effectiveness and the applicability of the TPM, a simulation environment based on ABMS was constructed. The amphibious aircraft agent and the PDT agent were built to simulate the SRP of the amphibious aircraft in medium/distant maritime rescue. Finally, considering the practical rescue situation, it took a certain time delay for the rescue base to receive a request for rescue, respond to it, and prepare for the rescue. A capsized ship simulation with 45 PDTs and a 0.5-h time delay was designed to verify the effectiveness of the TPM. Moreover, to verify the applicability of the TPM for different situations, a simulation experiment with 70 PDTs and a 0.5-h time delay was additionally conducted with other parameters equal to those in this study. In addition, to investigate the effect of the time on the effectiveness of the TPM, a TPM with a delay time varying from 1 h to 8 h was simulated for 45 and 70 PDTs, respectively. The simulation results show that the TPM has greatly applicability for different situations. In medium/distant maritime rescue, a delay time of less than 1 h is recommended for the amphibious aircraft to rescue PDTs using TPM. Correspondingly, it should be suggested that the rescue base responds and prepares quickly for rescue in practical situations. The proposed method proves to be available for effective rescue in a medium/distant maritime region. Moreover, the developed simulation environment can serve as a decision-making support tool in evaluating the effectiveness and the rapidity of medium/distant maritime rescue. To the best of our knowledge, the rescue results are unsatisfactory, as the number of PDTs increases because of the limitations on number of the amphibious aircraft and of the lifeboat in this study. Finally, many extensions of this study could be considered in future work. One promising direction is the influence of other parameters on using TPM for medium/distant maritime rescue, such as lifeboat characteristics, the winds, the ocean flow, temperature, and other environment parameters. Moreover, the additional uncertainties of the PDTs could be considered, for example, the age, the weight, and the gender, instead of the correction factor \((\sigma_{i})\), for more accurate rescue results in an actual rescue process. This could not only retrieve more accurate rescue results, but could also enable the association between personal characteristics and simulation results to be observed. Furthermore, a multi-aircraft rescue method should be considered for more complex emergencies using amphibious aircrafts in medium/distant maritime rescue. This also provides a promising direction that allows a more accurate trajectory prediction for PDTs, since the accuracy of the trajectory prediction based on the Monte Carlo experiment decreased with a longer delay time. Conceptualization, L.Y. and Y.X. ; Methodology, L.Y. and Y.X. ; Validation, L.Y. ; Data curation, L.Y. ; Writing--original draft, L.Y. and Y.X. ; Writing--review & editing, L.Y., R.Y., Y.X., Y.T. and H.L. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The authors declare no conflict of interest. * [PERSON] et al. (2021) [PERSON]; [PERSON]; [PERSON]; [PERSON] Optimization Model and Algorithm to Locate Rescue Bases and Allocate Rescue Vessels in Remote Oceans.