ABSTRACT This paper formalises path planning problem for a group of heterogeneous Dubins vehicles performing tasks in a remote fashion and develops a memetic algorithm-based method to effectively produce the paths. In the setting, the vehicles are initially located at multiple depots in a two-dimensional space and the objective of planning is to minimise a weighted sum of the total tour cost of the group and the largest individual tour cost amongst the vehicles. While the presented formulation takes the form of a mixed-integer linear programme (MILP) for which off-the-shelf solvers are available, the MILP solver easily loses the tractability as the number of tasks and agents grow. Therefore, a memetic algorithm tailored to the presented formulation is proposed. The algorithm features a sophisticated encoding scheme to efficiently select the order of performing tasks. In addition, a path refinement technique that optimises detailed tours with the sequence of visits fixed is proposed to finally obtain further optimised trajectories. Comparative numerical experiments show the validity and efficiency of the proposed methods compared with the previous methods in the literature.

中文翻译：

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多辆 Dubins 车辆执行远程任务的基于模因算法的路径生成

摘要 本文为一组以远程方式执行任务的异构 Dubins 车辆的路径规划问题形式化，并开发了一种基于模因算法的方法来有效地生成路径。在设置中，车辆最初位于二维空间中的多个站点，规划的目标是最小化团队总旅行成本和车辆中最大的个人旅行成本的加权和。虽然所提出的公式采用混合整数线性程序 (MILP) 的形式，可以使用现成的求解器，但随着任务和代理数量的增加，MILP 求解器很容易失去易处理性。因此，提出了一种适合于所提出的公式的模因算法。该算法具有复杂的编码方案，可以有效地选择执行任务的顺序。此外，提出了一种路径细化技术，该技术在固定访问顺序的情况下优化详细旅行，以最终获得进一步优化的轨迹。对比数值实验表明，与文献中的先前方法相比，所提出方法的有效性和效率。