集队定向越野问题

IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
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引用次数: 0

摘要

我们引入了集群定向问题(STOP),它是集群定向问题(SOP)的一个广义变体,其中客户位置被分成多个集群(或小组)。每个群组都与利润相关联,只有访问了该群组中的至少一个客户,才能获得利润。车厂有一支由同质车辆组成的车队,每辆车的行驶时间有限。STOP 的目标是找到一组可行的车辆路线,以获取最大利润。我们首先将该问题表述为混合整数线性规划(MILP),对其进行数学描述。然后,我们开发了一种分支加价格(B&P)算法,以最优方式求解该问题。为了处理大型实例,我们提出了大型邻域搜索 (LNS),它依赖于问题定制的解决方案表示、移除和插入算子。在新生成的实例上进行的多次实验证实了我们方法的性能。值得注意的是,在使用文献中的基准对 SOP 进行测试时,我们的 B&P 方法在 61.9% 的实例中达到了最优。这是首次有如此多的 SOP 实例达到最优解。在求解质量方面,我们的 LNS 优于现有的 SOP 求解算法。在所考虑的 612 个实例中,它改进了 40 个最知名的解决方案。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The set team orienteering problem
We introduce the Set Team Orienteering Problem (STOP), a generalised variant of the Set Orienteering Problem (SOP), in which customer locations are split into multiple clusters (or groups). Each cluster is associated with a profit that can be gained only if at least one customer from the cluster is visited. There is a fleet of homogeneous vehicles at a depot, and each vehicle has a limited travel time. The goal of the STOP is to find a set of feasible vehicle routes to collect the maximum profit. We first formulate the problem as a Mixed Integer Linear Programming (MILP) to mathematically describe it. A branch-and-price (B&P) algorithm is then developed to solve the problem to optimality. To deal with large instances, we propose a Large Neighbourhood Search (LNS), which relies on problem-tailored solution representation, removal, and insertion operators. Multiple experiments on newly generated instances confirm the performance of our approaches. Remarkably, when tested on the SOP using benchmarks available in the literature, our B&P method achieves optimality in 61.9% of these instances. This is the first time such a large number of SOP instances are solved to optimality. Our LNS outperforms existing algorithms proposed to solve the SOP in terms of solution quality. Out of 612 considered instances, it improves 40 best-known solutions.
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来源期刊
European Journal of Operational Research
European Journal of Operational Research 管理科学-运筹学与管理科学
CiteScore
11.90
自引率
9.40%
发文量
786
审稿时长
8.2 months
期刊介绍: The European Journal of Operational Research (EJOR) publishes high quality, original papers that contribute to the methodology of operational research (OR) and to the practice of decision making.
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