## 6 Conclusions  
This paper introduces an SGP vertex extraction filtering algorithm designed to optimize the SGP in obstacle grid maps into the TSP. This algorithm can find a shorter and smoother route than intelligent path planning algorithms within a short time frame. In scenarios involving large-scale maps and high obstacle densities, the performance of SGPVEFA is particularly outstanding.  
From the ablation experiments in Section 5.2 of the paper, it is evident that SGPVEFA spends very little time optimizing an SGP into a TSP, with most of its time dedicated to solving the SGP problem. The algorithm's complexity is determined by the number of points in the given SGP and the distribution of obstacles, rather than the map's dimensions. Therefore, increasing the map size does not degrade the algorithm's efficiency, but it does slow down the search for SGPs. However, due to the low coupling degree of SGPVEFA, when dealing with larger problem scales, we can integrate it with heuristic algorithms. First, we used heuristic algorithms to solve SGPs, and then applied this algorithm to solve TSPs.  
However, due to the complexity of two-dimensional obstacle grid maps, this paper has not yet provided rigorous proof that this method can solve the TSP. Additionally, SGPVEFA has certain limitations. For example, SGPVEFA requires pre-acquiring the SGP of the obstacle grid map, whereas some heuristic algorithms do not require this step, which may limit its applicability. Moreover, it can only solve problems with obstacle grid maps, and in real-world scenarios, the problem needs to be modeled into a similar situation, which is not an easy task. Furthermore, SGPVEFA is a static algorithm, and obstacles and feasible paths can change over time, necessitating the integration of dynamic response mechanisms. Additionally, the problems we encounter are not limited to two-dimensional planes; for instance, in drone path planning, future research could explore extending SGPVEFA to three-dimensional space. In recent years, many new heuristic techniques have been developed to optimize complex nonlinear problems, such as the Beetle Antennae Olfactory Recurrent Neural Network [27] and BAS-ADAM [28]. We will attempt to compare or integrate these new technologies in our future research.  
Conceptualization, Y.Z.; methodology, Y.Z.; software, J.C.; validation, Y.Z. and J.C.; formal analysis, Y.Z.; investigation, J.C.; resources, J.C.; data curation, J.C.; writing--original draft preparation, J.C.; writing--review and editing, Y.Z.; visualization, J.C.; supervision, Y.Z.; project administration, Y.Z.; funding acquisition, Y.Z. All authors have read and agreed to the published version of the manuscript.  
This study was funded by National Natural Science Foundation of China (Grant No.: 62402200).  
Not applicable.  
The benchmark data set used in Section 5.3 of this paper is from the following link. [[https://www.movingai.com/benchmarks/street/index.html](https://www.movingai.com/benchmarks/street/index.html)]([https://www.movingai.com/benchmarks/street/index.html](https://www.movingai.com/benchmarks/street/index.html)). Accessed on 20 June 2025. The rest of the data are randomly generated.  
**Conflicts of Interest:** This study does not have any conflicts of interest with any organization or individual.