A multiobjective metaheuristic approach for the integrated vehicle and crew scheduling

Abstract

Article Info AbstractKeywords: mass transit combinatorial optimization evolutionary algorithmsThe integrated vehicle and crew scheduling problem is a hard Combinatorial Optimization problem widely studied over the years. Taking into consideration the range of variables related to the planning process of vehicles and drivers, there are several practical characteristics of the problem that are not reflected in the solutions generated computationally. Among these characteristics, that were not found in the consulted literature, the most important is the existence of multiple objectives. This paper aims at presenting a multiobjective approach for the integrated vehicle and crew scheduling problem based on Genetic Algorithms. A case study in Portimão (Portugal) is presented and discussed. IntroductionIn what concerns buses, urban transportation planning can be divided in several steps, often considered as follows: network design, timetable creation, vehicle scheduling, crew scheduling and crew rostering. Vehicle scheduling and crew scheduling have been a subject of numerous research activities, due to the significant gains that may result from their optimization (Daduna and Paixão, 1995; Wren and Rousseau, 1999).Several researchers have reported the strong interaction between the vehicle scheduling problem and the crew scheduling problem, emphasizing the gains that can be obtained by considering them together (Freling et al., 2003). The integrated problem is usually known as the Vehicle and Crew Scheduling Problem (VCSP).Traditionally, vehicle scheduling and crew scheduling are done separately and in a sequential manner. The Vehicle Scheduling Problem (VSP) is performed in a first stage, being followed by the Crew Scheduling Problem (CSP). Usually, the CSP is more complex than the VSP, and therefore, in general, it is not a suitable strategy to schedule the vehicles without taking into account the requirements for the crews, since these may form the bottleneck of the whole process.In many public transport companies, particularly in developing countries, the costs of crews and drivers are the most significant. Thus, efforts should be focused in minimizing such costs, even when vehicle scheduling is being performed.For the resolution of the VCSP, several approaches have been reported in the literature. Exact optimization methods, based on branch-and-bound, branch-and-cut, column generation, or lagrangian relaxation are presented by Friberg and Haase (1999), Gaffi and Nonato (1999) Approaches based on heuristics and metaheuristics are presented in Ball et al. (1983), Falkner andRyan (1992), Patrikalakis and Xerocostas (1992), Wren and Gualda (1999), Valouxis and Housos (2002), Rodrigues et al. (2006), Laurent and Hao (2007), Steinzen et al. (2007 and Bartodziej et al. (2009). However, the reported heuristic techniques are not easy to generalize and most of them have been developed for very specific problems, with results reported for a small number of instances.Taking into consideration the range of variables related t...

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