arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 2106.01648math.OC
收藏

带AND型优先约束的多行程单车路径问题的分解算法

Decomposition Algorithm for the Multi-Trip Single Vehicle Routing Problem with AND-type Precedence Constraints

Mina Roohnavazfar, Seyed Hamid Reza Pasandideh

摘要:

本文讨论了一种新的变种的多行程单车辆路径问题的节点是通过与型优先约束相互关联。该问题的目的是确定一个行程序列访问所有的节点尊重每个优先约束内和之间的路线,使总的旅行费用最小化。我们的动机来自路由问题,其中一个节点可能有一组前辈(不只是一个单一的拨号乘车或皮卡和交付问题中提出的)导致一组成对的关系,指定哪些客户需要访问之前,其他的。我们开发了三个混合整数规划(MIP)模型,制定的问题。模型进行实验比较,以确定最好的一个。此外,基于逻辑的Benders分解(LBBD)算法的基础上开发的解决方案,允许分解成一个分配主问题和独立的排序子问题的原始问题。设计了一种新的有效的最优割,以实现更快的收敛。通过与文献中最近提出的切割性能进行比较,实验研究。我们进一步放松算法,找到次最优解,并证明其效率。进行了大量的计算实验,以评估所提出的算法的解决方案的质量和CPU时间。

英文摘要:

This paper addresses a new variant of the multi-trip single vehicle routing problem where the nodes are related to each other through AND-type precedence constraints. The problem aims at determining a sequence of trips to visit all the nodes respecting every precedence constraint within and among the routes so to minimize the total traveling cost. Our motivation comes from routing problems where a node may have a set of predecessors (not just single one proposed in the dial-a-ride or pickup and delivery problems) resulting in a set of pairwise relations that specify which customers need to be visited before which other ones. We develop three Mixed Integer Programming (MIP) models to formulate the problem. The models are experimentally compared to determine the best one. Moreover, a solution approach based on the Logic-Based Benders Decomposition (LBBD) algorithm is developed which allows to decompose the original problem into an assignment master problem and independent sequencing subproblems. A new valid optimality cut is devised to achieve faster convergence. The cut performance is experimentally investigated by comparing with a recently proposed one in the literature. We further relax the algorithm to find the sub-optimal solution and demonstrate its efficiency. Extensive computational experiments are conducted to assess the proposed algorithms in terms of solution quality and CPU time.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑