A learning-based granular variable neighborhood search for a multi-period election logistics problem with time-dependent profits

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.