Heuristic Approach Based on Lambda-Interchange for VRTPR-Tree on Specific Vehicle Routing Problem with Time Windows

Abstract

We propose VRTPR-Tree and a heuristic approach based on λ-interchange to solve a specific Vehicle Routing Problem with Time Windows (VRPTW). In the problem, delivery demands of customers are given as initial conditions. And, one of the vehicles with different positions visits the customers and transports to their destinations within time limits. For solving this problem, VRTPR-Tree indexes moving vehicles as a tree structure at some point. VRTPR-Tree generates an initial assignment condition for optimizing in a short time. An entry of a node consists of a pointer to a vehicle and a bounding rectangle which implies future positions of the vehicle (in leaf nodes) or pointers to child nodes and a bounding rectangle which encloses bounding rectangles of child nodes (in intermediate nodes). Initially, customers are assigned to a vehicle on the basis of the indexes of VRTPR-Tree, and the delivery orders of the customers are scheduled. Moreover, a heuristic approach based on λ-interchange optimizes the initial solution in the viewpoint of travel cost or customer satisfaction. We performed some experiments on an ideal environment. The experimental results show that our approach produces good results in short assignment and optimization times.