Multilevel refinement strategies for the capacity vehicle routing problem

We discuss the application of the multilevel (ML) refinement technique to the Vehicle Routing Problem (VRP), and compare it to its single-level (SL) counterpart. Multilevel refinement recursively coarsens to create a hierarchy of approximations to the problem and refines at each level. A SL algorithm, which uses a combination of standard VRP heuristics, is developed first to solve instances of the VRP. A ML version, which extends the global view of these heuristics, is then created, using variants of the construction and improvement heuristics at each level. Finally some multilevel enhancements are developed. Experimentation is used to find suitable parameter settings and the final version is tested on two well-known VRP benchmark suites. Results comparing both SL and ML algorithms are presented.