Construct, Merge, Solve and Adapt Applied to a Bus Driver Scheduling Problem with Complex Break Constraints

Bus Driver Scheduling (BDS) is a combinatorial optimization problem that consists in assigning atomic driving duties (legs) belonging to predetermined routes to bus drivers. We consider the highly-constrained, real-world version of the problem proposed by Kletzander and Musliu (2020), with complex break rules specified by a collective agreement and public regulation. We propose a Construct, Merge, Solve and Adapt (CMSA) algorithm, which is a recent metaheuristic proposed by Blum et al. (2016) based on the idea of problem instance reduction. At each iteration of the algorithm, sub-instances of the original instance are solved by an exact solver. These sub-instances are obtained by merging the components of the solutions generated by a probabilistic greedy algorithm. We compare our method with the state-of-the-art approaches on the benchmark instances. The results show that CMSA compares favourably with other metaheuristics on most instances and with exact techniques on large ones.