Hybrid approach to solve a crew scheduling problem: an exact column generation algorithm improved by metaheuristics

This paper shows a successful hybrid approach to improve a column generation algorithm. The objective is to construct daily duties to bus drivers, in order to cover a set of trips. Due to a large number of variables, the problem is decomposed in a master and a subproblem. The subproblem iteratively generates duties to the master problem, so the main task is to solve the subproblem. An exact ILP model may do this, but it is generally time consuming. We propose a heuristic based in the linear relaxation of this model to quickly generate many duties, and the ILP is called only when the heuristic fails, to obtain and prove optimality. We also use two metaheuristics to solve the subproblem: GRASP and genetic algorithm. All three heuristics improved the column generation algorithm and a hybrid approach using two of them turns out to be even faster for some instances.