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| A two-stage heuristic method for vehicle routing problem with split deliveries and pickups |
| Yong Wang, Xiao-lei Ma, Yun-teng Lao, Hai-yan Yu, Yong Liu |
| School of Management, Chongqing Jiaotong University, Chongqing 400074, China; School of Transportation Science and Engineering, Beihang University, Beijing 100191, China; Department of Civil and Environmental Engineering, University of Washington, Seattle, WA 98195-2700, USA |
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Abstract The vehicle routing problem (VRP) is a well-known combinatorial optimization issue in transportation and logistics network systems. There exist several limitations associated with the traditional VRP. Releasing the restricted conditions of traditional VRP has become a research focus in the past few decades. The vehicle routing problem with split deliveries and pickups (VRPSPDP) is particularly proposed to release the constraints on the visiting times per customer and vehicle capacity, that is, to allow the deliveries and pickups for each customer to be simultaneously split more than once. Few studies have focused on the VRPSPDP problem. In this paper we propose a two-stage heuristic method integrating the initial heuristic algorithm and hybrid heuristic algorithm to study the VRPSPDP problem. To validate the proposed algorithm, Solomon benchmark datasets and extended Solomon benchmark datasets were modified to compare with three other popular algorithms. A total of 18 datasets were used to evaluate the effectiveness of the proposed method. The computational results indicated that the proposed algorithm is superior to these three algorithms for VRPSPDP in terms of total travel cost and average loading rate.
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Received: 03 July 2013
Published: 05 March 2014
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求解集送货可拆分车辆路径问题的两阶段启发式方法
研究目的：集送货可拆分车辆路径问题具有配送和收集需求同时可拆分、客户点需求量可超过单车装载量、客户点被单车访问可超过一次等特点，针对测试该问题的公共数据集寻求有效求解方法，是一项富有挑战性的工作，目前缺乏有效、方便的求解算法。本文探讨求解集送货可拆分车辆路径问题的有效算法。
创新要点：提出两阶段启发式方法，即可行解获取的初始启发式算法和改进初始解的混合启发式算法，为研究车辆路径问题需求拆分和访问次数的松弛提供了有效的求解思路。引用描述该问题实质的逻辑关系模型，结合定义和化简的概念，本文算法为集送货可拆分车辆路径问题的研究，提供了分步计算的实用算法。
方法提亮：组成两阶段启发式方法的各种逻辑关系模型简洁、准确地描述了集送货可拆分车辆路径问题，同时具备可扩展性和可组合性。这些特性的灵活应用，形成本文提出的两阶段优化算法。
重要结论：利用Solomon数据集和可扩展的Solomon数据集进行实验计算，并与禁忌搜索算法（TSA），粒子群算法（PSO）以及并行启发式方法（PHA）比较，结果表明，对于不同规模数据集，本文算法有效节省了总配送成本、提升了平均装载率。
关键词：
集送货可拆分的车辆路径问题（VRPSPDP）,
两阶段启发式方法,
混合启发式算法,
Solomon数据集
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