Bi-objective evolutionary heuristics for bus driver rostering

Document Type

Journal Article

Publication Date


Subject Area

mode - bus


bus driver rostering, bi-objective problems, evolutionary algorithms


The Bus Driver Rostering Problem (BRP) refers to the assignment of drivers to the daily crew duties that cover a set of schedules for buses of a company during a planning period of a given duration, e.g., a month. An assignment such as this, denoted as roster, must comply with legal and institutional rules, namely Labour Law, labour agreements and the company’s regulations. This paper presents a new bi-objective model for the BRP, assuming a non-cyclic rostering context. One such model is appropriate to deal with the specific and diverse requirements of individual drivers, e.g. absences. Two evolutionary heuristics, differing as to the strategies adopted to approach the Pareto frontier, are described for the BRP. The first one, following a utopian strategy, extends elitism to include an infeasible (utopic) and two potential lexicographic individuals in the population, and the second one is an adapted version of the well known SPEA2 (Strength Pareto Evolutionary Algorithm). The heuristics’ empirical performance was studied through computational tests on BRP instances generated from the solution of integrated vehicle-crew scheduling problems, along with the rules of a public transit company operating in Portugal. This research shows that both methodologies are adequate to tackle these instances. However, the second one is, in general, the more favourable. In reasonable computation times they provide the company’s planning department with several rosters that satisfy all the constraints, an achievement which is very difficult to obtain manually. In addition, among these rosters they identify the potentially efficient ones with respect to the BRP model’s two objectives, one concerning the interests of administration, the other the interests of the workers. Both heuristics have advantages and drawbacks. This suggests that they should be used complementarily. On the other hand, the heuristics can, with little effort, be adapted to a wide variety of rostering rules.