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New heuristic algorithms for the Dubins traveling salesman problem
Journal of Heuristics ( IF 2.7 ) Pub Date : 2020-02-13 , DOI: 10.1007/s10732-020-09440-2
Luitpold Babel

The problem of finding a shortest curvature-constrained closed path through a set of targets in the plane is known as Dubins traveling salesman problem (DTSP). Applications of the DTSP include motion planning for kinematically constrained mobile robots and unmanned fixed-wing aerial vehicles. The difficulty of the DTSP is to simultaneously find an order of the targets and suitable headings (orientation angles) of the vehicle when passing the targets. Since the DTSP is known to be NP-hard there is a need for heuristic algorithms providing good quality solutions in reasonable time. Inspired by standard methods for the TSP we present a collection of such heuristics adapted to the DTSP. The algorithms are based on a technique that optimizes the headings of the targets of an open or closed subtour with given order. This is done by discretizing the headings, constructing an auxiliary network and computing a shortest path in the network. The first algorithm for the DTSP uses the order of the targets obtained from the solution of the Euclidean TSP. A second class of algorithms extends an open subtour by successively adding a new target and closes the tour if all targets have been added. A third class of algorithms starts with a closed subtour consisting of few targets and successively inserts a new target into the tour. The individual algorithms differ by the number of headings to be optimized in each iteration. Extensive simulation results show that the proposed methods are competitive with state-of-the-art methods for the DTSP concerning performance and superior concerning running time, which makes them applicable also to large-scale scenarios.

中文翻译:

杜宾斯旅行商问题的新启发式算法

通过飞机中的一组目标找到最短的曲率约束闭合路径的问题被称为杜宾斯旅行推销员问题(DTSP)。DTSP的应用包括运动受限移动机器人和无人固定翼飞机的运动计划。DTSP的困难在于,在通过目标时,要同时找到目标的顺序和车辆的合适航向(方位角)。由于DTSP已知是NP难解的,因此需要启发式算法在合理的时间内提供高质量的解决方案。受TSP标准方法的启发,我们提出了一系列适用于DTSP的启发式方法。该算法基于一种技术,该技术以给定顺序优化开放或封闭子巡回目标的航向。这是通过离散化标题,构建辅助网络并计算网络中的最短路径来完成的。DTSP的第一种算法使用从欧氏TSP求解中获得的目标顺序。第二类算法通过依次添加新目标来扩展开放子巡视,如果已添加所有目标,则关闭巡视。第三类算法从包含几个目标的闭合子巡视开始,然后将新目标依次插入巡视中。各个算法的不同之处在于每次迭代中要优化的标题数量。大量的仿真结果表明,所提出的方法在性能方面与DTSP的最新方法相比具有竞争优势,并且在运行时间方面具有优越的性能,这使得它们也适用于大规模场景。构建辅助网络并计算网络中的最短路径。DTSP的第一种算法使用从欧氏TSP求解中获得的目标顺序。第二类算法通过依次添加新目标来扩展开放子巡视,如果已添加所有目标,则关闭巡视。第三类算法从包含几个目标的闭合子巡视开始,然后将新目标依次插入巡视中。各个算法的不同之处在于每次迭代中要优化的标题数量。大量的仿真结果表明,所提出的方法在性能方面与DTSP的最新方法相比具有竞争优势,并且在运行时间方面具有优越的性能,这使得它们也适用于大规模场景。构建辅助网络并计算网络中的最短路径。DTSP的第一种算法使用从欧氏TSP求解中获得的目标顺序。第二类算法通过依次添加新目标来扩展开放子巡视,如果已添加所有目标,则关闭巡视。第三类算法从包含几个目标的闭合子巡视开始,然后将新目标依次插入巡视中。各个算法的不同之处在于每次迭代中要优化的标题数量。大量的仿真结果表明,所提出的方法在性能方面与DTSP的最新方法相比具有竞争优势,并且在运行时间方面具有优越的性能,这使得它们也适用于大规模场景。
更新日期:2020-02-13
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