## 6 Conclusions and Future Works  
This paper addressed the helicopter rescue routing problem by considering the survivors' limited survival time constraint and modeling it as R-VRPTWLST. An IIG algorithm was proposed to solve this problem. First, a two-dimensional vector encoding method was employed considering the specific features of this problem. Then, a heuristic initialization strategy was designed to generate a high-quality solution. Additionally, three problem-specific search operators were developed to enhance the local search capability of the IIG. Moreover, the SA strategy was used as an acceptance criterion to deal with potential optimal solutions. Finally, the proposed IIG was compared with two efficient heuristic algorithms and four advanced algorithms to evaluate its effectiveness. Compared with two heuristic algorithms, the proposed IIG achieved 39 optimal solutions out of 56 instances. Meanwhile, the average RPI of the IIG was 0.14 and 0.11 times those of the DI and TSH, respectively. Compared with four advanced algorithms, the proposed IIG achieved 42 best average fitness values out of 56 instances. Additionally, the average RPI of the IIG is 0.359, 0.146, 0.151, and 0.074 times those of the IABC, ALNG, VNIG, and SAIG, respectively. These results demonstrate that the proposed IIG outperforms the other algorithms in solving the R-VRPTWLST. The limitations of this study are as follows: (1) the objective function focuses solely on minimizing the total flight distance of helicopters, neglecting other important objectives, such as energy consumption during rescue operations. (2) This study failed to focus on a specific rescue scenario, and some constraints and assumptions are somewhat idealized, such as overlooking a hierarchical and phased manner of rescuing survivors and the multi-trip rescue problem. (3) The proposed IG did not consider the 3D rescue routing problem, neglecting environmental conditions, such as weather, during the execution of the rescue task. Future research could explore the following aspects: (1) the constraints of the rescue problem need to be continuously improved to better align with real-world scenarios. For  
Figure 9: The obtained helicopter routings for the four selected instances. (**a**) Chart for instance rc106; (**b**) chart for instance rc202; (**c**) chart for instance rr105; (**d**) chart for instance rrc104. example, the multi-trip rescue and the limited flight time under constrained resources should be investigated. (2) The assumptions underlying the rescue problem require further refinement to enhance the practical applicability of the R-VRPTWLST. This could include enriching the rescue instance configuration, such as classifying survivors into multiple categories based on the severity of their injuries, prioritizing the transfer of critically injured survivors, and allowing a site to be visited multiple times. Additionally, the differential changes in the survivors' life strength before and after being picked up by two types of helicopters at a rescue site should also be integrated into problem modeling. (3) The multi-objective helicopter rescue problem, which involves balancing various conflicting objectives, such as minimizing rescue time and energy consumption while maximizing flight safety and the quality of rescue tasks, will be investigated in the coming years. At that time, 3D rescue routing problems affected by environmental conditions will also be considered. Future multi-objective optimization algorithms will provide the decision-maker with more diverse schemes to address urgent rescue problems. Conceptualization, X.C. and P.D. ; methodology, X.C. and P.D. ; software, K.Y. and X.W. ; validation, X.C., K.Y. and P.D. ; formal analysis, X.C., K.Y. and P.D. ; data curation, K.Y. and X.W. ; writing--original draft preparation, X.C., K.Y., X.W. and P.D. ; writing--review and editing, X.C., K.Y. and P.D. ; supervision, P.D. ; funding acquisition, P.D. All authors have read and agreed to the published version of the manuscript.