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

• Published in: European journal of operational research Vol. 307; no. 1; pp. 64 - 81
• Main Authors: Benavent, Enrique, Corberán, Ángel, Laganà, Demetrio, Vocaturo, Francesca
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16.05.2023
• Subjects: Feasibility pump; Integer linear programming; Mixed rural postman problem; Multi-Start heuristics; Routing; Integer linear programming; Mixed rural postman problem; Routing; Multi-Start heuristics; Feasibility pump
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2022.09.026

•We focus on the periodic rural postman problem with irregular services.•We propose an algorithm that combines heuristics and mathematical programming.•Multi-start heuristics are used to construct initial solutions.•Some parts of these solutions are recombined through a model-based approach.•The results of an extensive computational study are presented. In this article we address the periodic rural postman problem with irregular services (PRPP–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 PRPP–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.