A branch‐and‐cut algorithm for the pickup‐and‐delivery traveling salesman problem with handling costs

IF 1.6 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE Networks Pub Date : 2022-10-01 DOI:10.1002/net.22096

D. Krishnan, Tieming Liu

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Abstract

In the Pickup‐and‐Delivery Traveling Salesman Problem with Handling Costs (PDTSPH), a single vehicle has to satisfy multiple customer requests, each defined by a pickup location and a delivery location. Cargo handling is performed at the rear end of the vehicle, in a Last‐In‐First‐Out (LIFO) order for PDTSPH. However, additional handling operations are permitted with a penalty if other loads that block the access to the delivery have to be unloaded and reloaded. The objective of PDTSPH is to minimize the total transportation and handling cost. In this paper, we present a new Mixed Integer Programming (MIP) model and a branch‐and‐cut algorithm to solve PDTSPH. We also present new integral separation procedures to effectively handle the exponential number of constraints in our MIP model. A family of inequalities are introduced to enhance the scalability of our implementation. The performance of our approach is compared with a compact formulation from the literature (Veenstra et al. [21]) in instances ranging from 9 to 21 customer requests. Computational results show our algorithm outperforming the compact formulation in 69% of instances with an average runtime improvement of 57%.

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带处理成本的接送旅行推销员问题的分支割算法

在具有处理成本的接送旅行推销员问题（PDTSPH）中，一辆车必须满足多个客户请求，每个请求由接送地点和交付地点定义。货物搬运在车辆后端执行，按照PDTSPH的后进先出（LIFO）订单。但是，如果必须卸载和重新装载阻碍运输的其他装载物，则允许进行额外的搬运操作，并进行处罚。PDTSPH的目标是将总运输和处理成本降至最低。在本文中，我们提出了一种新的混合整数规划（MIP）模型和一种分支和切割算法来求解PDTSPH。我们还提出了新的积分分离程序，以有效地处理MIP模型中的指数约束。引入了一系列不平等，以增强我们实施的可扩展性。在9至21个客户请求的情况下，将我们的方法的性能与文献中的紧凑配方（Veenstra等人[21]）进行了比较。计算结果表明，我们的算法在69%的实例中优于紧凑公式，平均运行时间提高了57%。

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来源期刊

Networks 工程技术-计算机：硬件

CiteScore

4.40

自引率

9.50%

发文量

审稿时长

12 months

期刊介绍： Network problems are pervasive in our modern technological society, as witnessed by our reliance on physical networks that provide power, communication, and transportation. As well, a number of processes can be modeled using logical networks, as in the scheduling of interdependent tasks, the dating of archaeological artifacts, or the compilation of subroutines comprising a large computer program. Networks provide a common framework for posing and studying problems that often have wider applicability than their originating context. The goal of this journal is to provide a central forum for the distribution of timely information about network problems, their design and mathematical analysis, as well as efficient algorithms for carrying out optimization on networks. The nonstandard modeling of diverse processes using networks and network concepts is also of interest. Consequently, the disciplines that are useful in studying networks are varied, including applied mathematics, operations research, computer science, discrete mathematics, and economics. Networks publishes material on the analytic modeling of problems using networks, the mathematical analysis of network problems, the design of computationally eﬃcient network algorithms, and innovative case studies of successful network applications. We do not typically publish works that fall in the realm of pure graph theory (without signiﬁcant algorithmic and modeling contributions) or papers that deal with engineering aspects of network design. Since the audience for this journal is then necessarily broad, articles that impact multiple application areas or that creatively use new or existing methodologies are especially appropriate. We seek to publish original, well-written research papers that make a substantive contribution to the knowledge base. In addition, tutorial and survey articles are welcomed. All manuscripts are carefully refereed.