###### Abstract  
Medium/distant maritime rescue is significantly important in the development of maritime business. For typical medium/distant maritime rescue, the range limitation of helicopters and many difficulties between helicopter and ship cooperation lead to unsatisfactory rescue results. Compared to helicopters and ships, amphibious aircrafts could effectively solve the problems faced by helicopters and ships and meet the medium/distant maritime rescue demands with their long cruise range, high speed, high rescue capability and surface landing capability. Therefore, a time-domain planning method (TPM) based on the k-means* clustering algorithm and the genetic algorithm* is proposed in this study for the surface rescue process (SRP) of amphibious aircrafts in medium/distant maritime rescue. To simulate the SRP of amphibious aircrafts, an agent-based simulation environment of medium/distant maritime rescue was constructed based on the Python platform. Finally, a case study was carried out to verify its effectiveness and applicability. The results show that the TPM exhibits satisfactory rescue results for the SRP of the amphibious aircraft and that less than 1 h of delay time is recommended for the amphibious aircraft to rescue the persons in distress by using TPM. * [table]capposition=top  
forest firefighting and maritime rescue [25]. For maritime rescue with amphibious aircrafts, [PERSON] et al. proposed an optimal algorithm for searching routes of amphibious aircrafts, considering their flight characteristics and sea rescue capability [26]. [PERSON] analyzed the factors affecting the siting of amphibious aircrafts [27]. [PERSON] et al. established the amphibious aircraft selection decision model based on the improved fuzzy evaluation method [28]. [PERSON] et al. established a landing search and rescue risk assessment system for amphibious aircrafts. Based on the studied assessment system, they constructed the affiliation function of each index by the assignment method, and determined a fuzzy comprehensive evaluation process [29]. [PERSON] not only used the k-means clustering algorithm, addressing the multi-amphibious aircraft rescue task assignment problem, but also used the ant colony algorithm for multi-aircraft rescue route planning [30]. However, there is no detailed study of the rescue process for amphibious aircrafts. Therefore, it is meaningful and necessary to carry out an in-depth study on the rescue process of amphibious aircrafts, which is the main motivation of this study. For medium/distant maritime rescue, one feasible way is the application of the mathematical methods for optimization. The application of the mathematical methods for optimization has been widely used in various fields, including transportation, military, economy, etc. In terms of maritime rescue, mathematical methods have also been frequently utilized. Firstly, with the development of maritime weather observation technology, the drifting trajectory of the person in distress (PDT) can be obtained through more accurate environmental information by using mathematical methods, which can improve the efficiency and success of maritime rescue [31]. Then, for the maritime rescue process determination and optimization, [PERSON] et al. proposed a method for helicopter search area planning based on a minimum bounding rectangle and k-means clustering [32]. [PERSON] et al. proposed an evaluation framework of helicopter maritime search and rescue which reveals the influence mechanism of uncertainty factors [33]. [PERSON] et al. proposed a new target allocation method based on the improved genetic algorithm called the multi-string genetic algorithm [34]. Moreover, [PERSON] et al. proposed an optimization model of emergency resources allocation, considering multiple restrictions, including accident black spots, the possible locations of rescue bases, different types of emergency resources, and rescue ships [35]. These studies show that mathematical methods have great applications in maritime rescue.