A messy genetic algorithm for the vehicle routing problem with time window constraints

In Vehicle Routing Problems with Time Window Constraints (VRPTW), a set of vehicles with limited capacity, are to be routed from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. To solve the problem, the optimized assignment of vehicles to each customer is needed as to achieve the minimal total cost without violating the capacity and time window constraints. Combinatorial optimization problems of this kind are NP-hard and are best solved to the near optimum by heuristics. This paper describes the authors' research on a rare class of genetic algorithms, known as the Messy Genetic Algorithms (mGA) in solving the VRPTW problem. The mGA has the merit of directly realizing the relational search needed in VRPTW representation, which cannot be easily realized using simple heuristic methods. The mGA was applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances, and yielded 23 solutions better than or equivalent to the best solutions ever published in literature.