I. Introduction
Discrete optimization is a part of mathematical optimization which handles discrete quantities. There are various practical implementations on discrete optimization problems, such as the Travelling Salesman Problem (TSP), Vehicle Routing Problem (VRP), Knapsack Problem (KP) and Graph Coloring Problem (GCP). VRP (Dantzig and Ramser, 1959) is the generalization of Travelling Salesman Problems with numerous real-world applications, based on combinatorial optimization and integer programming. The traveling paths for a fleet of vehicles are subject to routing and scheduling, so that global minimization in terms of distance, time windows, capacity limits, labor expense, pick-up and delivery can be reached under a set of constraints. In fact, there is an ultimate goal to minimize the total expense across many fields of transportation, distribution, exploration and exploitation. Thus VRP becomes an interesting and challenging research field. Exact algorithms and heuristic algorithms can both be applied for VRP problem solving [1].