An efficient ant colony system for Vehicle Routing Problems with Time Windows

This paper presents an efficient algorithm based on a meta‐heuristic Multiple Ant Colony System (MACS) for solving Vehicle Routing Problems with Time Windows (VRPTW). This study aims to determine the minimum cost routes for a fleet of vehicles of the same capacity to meet the demand of a set of customers within a specified time interval called a time window. The methodology, known as MACS‐VRPTW, uses two ant colonies to minimise the number of vehicles and total time required to serve all customers. The algorithm was implemented in the Java environment, and six standard problems used as benchmarks in the literature were tested.