This paper introduces a new exact and smooth penalty function to tackle constrained min-max problems. By using this new penalty function and adding just one extra variable, a constrained rain-max problem is transforme...This paper introduces a new exact and smooth penalty function to tackle constrained min-max problems. By using this new penalty function and adding just one extra variable, a constrained rain-max problem is transformed into an unconstrained optimization one. It is proved that, under certain reasonable assumptions and when the penalty parameter is sufficiently large, the minimizer of this unconstrained optimization problem is equivalent to the minimizer of the original constrained one. Numerical results demonstrate that this penalty function method is an effective and promising approach for solving constrained finite min-max problems.展开更多
作为诸多移动机器人应用的基础,完全覆盖旨在为机器人规划出一条访问目标区域所有点且耗时最短的无碰撞路径。此类覆盖应用中,利用多台机器人协同覆盖可以有效缩短覆盖时间并提升系统的鲁棒性,同时也增加了算法设计复杂度和机器人协同...作为诸多移动机器人应用的基础,完全覆盖旨在为机器人规划出一条访问目标区域所有点且耗时最短的无碰撞路径。此类覆盖应用中,利用多台机器人协同覆盖可以有效缩短覆盖时间并提升系统的鲁棒性,同时也增加了算法设计复杂度和机器人协同管理难度。因此,文中研究了已知环境下的多机器人覆盖问题,该问题已被证明是一个NP难题。文中提出了一种启发式的基于多层次图划分的多机器人任务分配方法(Multi-robot Task Assignment Based on Multi-level Graph Partitioning,TAMP),该方法包含一种粗化任务分配算法和一种精细任务分配算法。粗化任务分配算法采用分层粗化的方法,通过图的极大匹配实现了节点融合以降低图的规模,并基于均匀种子的图增长方式获取了一个接近均衡的初始任务分配结果,提高算法效率;精细任务分配算法在粗化任务分配算法的基础上,提出了一种基于边界节点交换的Lazy&Lock策略,用于实现任务细分,提高求解精度。文中在不同规模的随机图和真实世界的治安巡逻场景下进行了仿真验证。仿真结果表明,相比经典的任务分配方法,TAMP方法将可求解的最大计算规模从千级扩大到百万级,小规模图(3000以内)的计算速度加快了20倍,距离最优解偏差均优于经典方法;能够在60 s内解决大规模图(3000~1000000)的任务分配问题,同时将距离最优解偏差控制在0.3%以内。展开更多
基金supported by the Grant of the Academy of Mathematics and System Science of Chinese Academy of Sciences-The Hong Kong Polytechnic University Joint Research Institute (AMSS-PolyU)the Research Grands Council Grant of The Hong Kong Polytechnic University (No. 5365/09E)
文摘This paper introduces a new exact and smooth penalty function to tackle constrained min-max problems. By using this new penalty function and adding just one extra variable, a constrained rain-max problem is transformed into an unconstrained optimization one. It is proved that, under certain reasonable assumptions and when the penalty parameter is sufficiently large, the minimizer of this unconstrained optimization problem is equivalent to the minimizer of the original constrained one. Numerical results demonstrate that this penalty function method is an effective and promising approach for solving constrained finite min-max problems.
文摘作为诸多移动机器人应用的基础,完全覆盖旨在为机器人规划出一条访问目标区域所有点且耗时最短的无碰撞路径。此类覆盖应用中,利用多台机器人协同覆盖可以有效缩短覆盖时间并提升系统的鲁棒性,同时也增加了算法设计复杂度和机器人协同管理难度。因此,文中研究了已知环境下的多机器人覆盖问题,该问题已被证明是一个NP难题。文中提出了一种启发式的基于多层次图划分的多机器人任务分配方法(Multi-robot Task Assignment Based on Multi-level Graph Partitioning,TAMP),该方法包含一种粗化任务分配算法和一种精细任务分配算法。粗化任务分配算法采用分层粗化的方法,通过图的极大匹配实现了节点融合以降低图的规模,并基于均匀种子的图增长方式获取了一个接近均衡的初始任务分配结果,提高算法效率;精细任务分配算法在粗化任务分配算法的基础上,提出了一种基于边界节点交换的Lazy&Lock策略,用于实现任务细分,提高求解精度。文中在不同规模的随机图和真实世界的治安巡逻场景下进行了仿真验证。仿真结果表明,相比经典的任务分配方法,TAMP方法将可求解的最大计算规模从千级扩大到百万级,小规模图(3000以内)的计算速度加快了20倍,距离最优解偏差均优于经典方法;能够在60 s内解决大规模图(3000~1000000)的任务分配问题,同时将距离最优解偏差控制在0.3%以内。
