The Open Periodic Vehicle Routing Problem with Time Windows (OPVRPTW) is a practical transportation routing and scheduling problem arising from real-world scenarios. It shares some common features with some classic VRP variants. The problem has a tightly constrained large-scale solution space and requires well balanced diversification and intensification in search. In Variable Depth Neighbourhood Search, large neighbourhood depth prevents the search from trapping into local optima prematurely, while small depth provides thorough exploitation in local areas. Considering the multi-dimensional solution structure and tight constraints in OPVRPTW, a Variable-Depth Adaptive Large Neighbourhood Search (VD-ALNS) algorithm is proposed in this paper. Contributions of four tailored destroy operators and three repair operators at variable depths are investigated. Comparing to existing methods, VD-ALNS makes a good trade-off between exploration and exploitation, and produces promising results on both small and large size benchmark instances
