Exact methods for mono-objective and Bi-Objective Multi-Vehicle Covering Tour Problems

The Multi-vehicle Covering Tour Problem and the Bi-Objective Multi-vehicle Covering Tour Problem have been studied for more than thirty years. Both problems have several practical applications in industry. In this paper, we propose an effective exact method for the Multi-vehicle Covering Tour Problem based on column generation techniques. The effectiveness of the exact method is owed to tailored dominance rules and completion bounds. To validate our approach, we conducted extensive computational experiments on instances from literature. The comparison with state-of-the-art methods shows the effectiveness of the proposed method. In particular, seven open instances are closed to optimality for the first time, and the best lower bounds of the six open instances are improved. The exact method for the Multi-vehicle Covering Tour Problem is also embedded in a ϵ-constraint exact method to solve its bi-objective counterpart. Computational results show that the lower bound set provided by this bi-objective exact method is stronger than those provided by the state-of-the-art method from the literature.