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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.

Multi-period travelling politician problem: A hybrid metaheuristic solution method