非均匀速度车辆路径问题的改进近似算法
Improved Approximations for Vehicle Routing with Nonuniform Speeds
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中文总结 AI 辅助
针对非均匀速度车辆路径问题，研究异构旅行商问题及带容量约束的异构车辆路径问题的不同版本，提出改进的近似算法以最小化车辆最大完成时间。
中文摘要 AI 辅助
我们研究在完全无向图上的非均匀速度车辆路径问题，该图的顶点集包含一个配送中心和一组客户，且距离满足三角不等式。每辆车有指定的速度，若速度为$s$的车辆行驶总长度为$L$，则其完成时间为$L/s$。在异构旅行商问题（HetTSP）中，每辆车执行一条从配送中心出发并返回配送中心的路线，且这些路线共同访问所有客户，目标是最小化车辆中的最大完成时间。我们为HetTSP提供了一个$6$近似算法，改进了之前针对任意固定$\delta>0$的$90(1+\delta)$近似算法。我们还考虑了异构带容量约束车辆路径问题（HetCVRP）的两个版本：每个客户有一个需求，车辆具有相同的容量；车辆可执行多条路线，每条路线从配送中心出发并返回，且在连续路线之间于配送中心重新装载，每条路线上交付的总需求不得超过车辆容量。在HetCVRP的拆分交付版本中，客户的需求可在多次访问中拆分，可能由不同车辆完成，我们为该问题提供了一个$\frac92+2\sqrt3<7.965$近似算法。在HetCVRP的非拆分交付版本中，每个客户的全部需求必须在一次访问中交付，我们提供了一个$\frac{11}{2}+3\sqrt2<9.743$近似算法，改进了之前针对任意固定$\delta>0$的$450(1+\delta)$近似算法。
英文摘要
We study vehicle routing with vehicles of different speeds on a complete undirected graph whose vertex set consists of a depot and a set of clients, where the distances satisfy the triangle inequality. Each vehicle has a specified speed, and if the total length traveled by a vehicle of speed $s$ is $L$, its completion time is $L/s$. In the heterogeneous traveling salesman problem (HetTSP), each vehicle executes one tour starting and ending at the depot, and the tours collectively visit all clients. The objective is to minimize the maximum completion time among the vehicles. We give a $6$-approximation algorithm for HetTSP, improving the previous $90(1+δ)$-approximation for any fixed $δ>0$. We also consider two versions of the heterogeneous capacitated vehicle routing problem (HetCVRP). Each client has a demand, and the vehicles have identical capacities. A vehicle may execute several tours, each starting and ending at the depot, and reload at the depot between consecutive tours; the total demand delivered on each tour cannot exceed the vehicle capacity. In the split-delivery version of HetCVRP, the demand of a client may be divided among multiple visits, possibly by different vehicles. We give a $\frac92+2\sqrt3<7.965$-approximation algorithm for this problem. In the unsplit-delivery version of HetCVRP, the entire demand of each client must be delivered in a single visit. We give a $\frac{11}{2}+3\sqrt2<9.743$-approximation algorithm, improving the previous $450(1+δ)$-approximation for any fixed $δ>0$.
发表机构
- School of Mathematics and Statistics, Yunnan University（云南大学数学与统计学院）
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