AI 中文总结
本文针对旅行商问题，提出递归聚类算法，通过划分城市成簇并结合约束TSP与模拟退火技术进行路由，还给出基于FPGA的实现。该方法能处理更多城市，具有更好扩展性和更高频率，相比之前方法优势明显。
AI 中文摘要
旅行商问题（TSP）因其在各种应用中的关键作用，持续吸引大量研究关注。本文介绍一种递归聚类方法，将城市划分为数量有限的簇，每个簇最多含五个城市及其质心。采用约束TSP和模拟退火技术在每个簇内对城市进行路由，以相邻簇的质心作为路由过程的进出点。该方法因每个簇中城市数量减少，能提供准确且具成本效益的路由解决方案。利用模拟退火建立簇质心之间的连接。基于FPGA的硬件实现证明了路由大量城市的可行性，该方法利用内存存储簇信息，独立于FPGA逻辑硬件，扩展性取决于FPGA内存容量。此外，比较了FPGA执行时使用近似方法的距离计算，因平方欧几里得方法资源利用率低而选用。与先前方法相比，该方法能处理更多城市进行路由，具有更好的扩展性和更高的工作频率。
英文摘要
The Traveling Salesman Problem (TSP) continues to attract significant research interest due to its critical role in various applications. This paper introduces a recursive clustering approach that divides cities into a limited number of clusters, each containing up to five cities and its own centroid. Constrained TSP and simulated annealing techniques are employed to route cities within each cluster, using the centroids of neighboring clusters as entry and exit points for the routing process. This method offers the benefit of producing accurate and cost-effective routing solutions, due to the reduced number of cities in each cluster. The connections between cluster centroids are established using simulated annealing. The FPGA-based proposed hardware implementation demonstrates the feasibility of routing a large number of cities, as the approach leverages memory to store cluster information. Consequently, the method is independent of the FPGA's logic hardware, and its scalability depends on the FPGA's memory capacity. Furthermore, distance calculations using approximate methods for the FPGA execution are compared and the squared Euclidean is chosen due to its low resources' utilization. Compared to previous methods, the proposed approach can handle more cities for routing, offering better scalability and a higher operating frequency.
