Interactive Heuristic for Practical Vehicle Routing Problem with Solution Shape Constraints

The vehicle routing problem (VRP) with solution shape constraints is defined, and an interactive heuristic is proposed for its solution. A set of tours with desirable shapes–-that is, that are visually attractive–-possesses two characteristics. Each tour of a visually attractive set of tours is compact, and tours within the set do not cross one another. The visual attractiveness of tours is of great importance in practical routing applications and plays a central role in whether tours are adopted in actual freight transportation operations in many industries, including courier operations of large package delivery companies. Numerical experiments were conducted on real-world data to assess the proposed heuristic. Results of the experiments show that the heuristic, coupled with effective shape measures, is able to provide solutions with significantly improved layout while maintaining satisfactory results in terms of conventional VRP measures (e.g., required fleet size and total cost).