A two-phase hybrid algorithm for the periodic rural postman problem with irregular services on mixed graphs.

In this article we address the periodic rural postman problem with irregular services ( P RP P -IS), where some arcs and/or edges of a mixed graph must be traversed (to be serviced) a certain number of times in some subsets of days of a given time horizon. The goal is to define a set of minimum cost tours, one for each day or period of the time horizon, that satisfy the service requirements. For this problem we propose a two-phase algorithm that combines heuristics and mathematical programming. In the first phase, two different procedures are used to construct feasible solutions: a multi-start heuristic based on feasibility pump and a multi-start constructive heuristic. From these solutions, some fragments (parts of tours associated with the different days) are extracted. The second phase determines a solution for the P RP P -IS by combining the fragments by means of a mathematical model. We show the effectiveness of this solution approach through an extensive experimental phase on different sets of instances. (c) 2022 Elsevier B.V. All rights reserved.