Analysis of the Degree of Difficulty in Solving Vehicle Routing Problem with Time Windows

Vehicle routing problem with time windows (VRPTW) is a well-known NP-complete problem in operational research and computer science. In the literature, a great amount of research has been focused on various genetic algorithms (GAs) to solve VRPTW. However, little attention is made to measure to what degree a particular instance of VRPTW is difficult when GA is used. In this paper, fitness distance correlation (FDC) analysis is adopted to predict the problem difficulty of a given instance of VRPTW, being able to guide the design of well-suited GAs. Solomon's R1 instances are used as test instances and the FDC results shows all the instances are classified as deceptive and misleading problems where fitness increases with distances decreasing.