A math-hyper-heuristic approach for large-scale vehicle routing problems with time windows

Vehicle routing is known as the most challenging but an important problem in the transportation and logistics filed. The task is to optimise a set of vehicle routes to serve a group of customers with minimal delivery cost while respecting the problem constraints such as arriving within given time windows. This study presented a math-hyper-heuristic approach to tackle this problem more effectively and more efficiently. The proposed approach consists of two phases: a math phase and a hyper-heuristic phase. In the math phase, the problem is decomposed into sub-problems which are solved independently using the column generation algorithm. The solutions for these sub-problems are combined and then improved by the hyper-heuristic phase. Benchmark instances of large-scale vehicle routing problems with time windows were used for evaluation. The results show the effectiveness of the math phase. More importantly the proposed method achieved better solutions in comparison with two state of the art methods on all instances. The computational cost of the proposed method is also lower than that of other methods.