Multi-Period Travelling Politician Problem: A Hybrid Metaheuristic Solution Method

TL;DR

This paper introduces a hybrid metaheuristic approach to solve the Multi-period Travelling Politician Problem, optimizing campaign routes over multiple days with flexible depots, and demonstrates its effectiveness on real-world instances.

Contribution

It develops a novel hybrid multi-start Iterated Local Search with Variable Neighbourhood Descent for this complex routing problem, outperforming existing methods.

Findings

Achieved 7 optimal solutions and 17 new best solutions on test instances.

Outperformed a recent two-phase matheuristic in solution quality.

Provided practical insights for campaign planning through scenario analysis.

Abstract

This paper studies the Multi-period Travelling Politician Problem whose objective is to maximise the net benefit accrued by a party leader during a fixed campaign period. The problem is also characterised by flexible depots since the daily tours realised by the party leader may not start and end at the same city. A hybrid multi-start Iterated Local Search method complemented with a Variable Neighbourhood Descent is developed to solve the problem heuristically. Two constructive procedures are devised to generate initial feasible solutions. The proposed method is tested on 45 problem instances involving 81 cities and 12 towns in Turkey. Computational results show that the hybrid metaheuristic approach outperforms a recently proposed two-phase matheuristic by producing 7 optimal solutions and 17 new best solutions. In addition, interesting practical insights are provided using scenario analysis that could assist campaign planners in their strategic decisions.