Planning the election campaign for leaders of a political party is a complex problem. The party representatives, running mates, and campaign managers have to design an efficient routing and scheduling plan to visit multiple locations while respecting time and budget constraints. Given the limited time of election campaigns in most countries, every minute should be used effectively, and there is very little room for error. In this paper, we formalize this problem as the multiple Roaming Salesman Problem (mRSP), a new variant of the recently introduced Roaming Salesman Problem (RSP), where a predefined number of political representatives visit a set of cities during a planning horizon to maximize collected rewards, subject to budget and time constraints. Cities can be visited more than once and associated rewards are time-dependent (increasing over time) according to the day of the visit and the recency of previous visits. We develop a compact Mixed Integer Linear Programming (MILP) formulation complemented with effective valid inequalities. Since commercial solvers can obtain optimal solutions only for small-sized instances, we develop a Learning-based Granular Variable Neighborhood Search and demonstrate its capability of providing high-quality solutions in short CPU times on real-world instances. The adaptive nature of our algorithm refers to its ability to dynamically adjust the neighborhood structure based on the progress of the search. Our algorithm generates the best-known results for many instances.

中文翻译：

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基于学习的粒度变量邻域搜索，求解具有时间依赖性利润的多周期选举物流问题


规划政党领导人的竞选活动是一个复杂的问题。政党代表、竞选伙伴和竞选经理必须设计有效的路线和日程计划，以访问多个地点，同时尊重时间和预算限制。鉴于大多数国家竞选活动的时间有限，必须有效利用每一分钟，不允许出现任何失误。在本文中，我们将这个问题形式化为多重漫游推销员问题（mRSP），这是最近引入的漫游推销员问题（RSP）的新变体，其中预先确定数量的政治代表在规划范围内访问一组城市以最大化收集奖励，但受预算和时间限制。城市可以被多次访问，相关奖励取决于时间（随着时间的推移而增加），具体取决于访问的日期和之前访问的新近度。我们开发了一个紧凑的混合整数线性规划 (MILP) 公式，并辅以有效的有效不等式。由于商业求解器只能针对小型实例获得最佳解决方案，因此我们开发了一种基于学习的粒度变量邻域搜索，并展示了其在现实世界实例上在短时间内提供高质量解决方案的能力。我们算法的自适应性质是指它能够根据搜索的进度动态调整邻域结构。我们的算法为许多实例生成了最著名的结果。