Bi-objective Optimization for the Vehicle Routing Problem with Time Windows: Using Route Similarity to Enhance Performance

The Vehicle Routing Problem with Time Windows is a complex combinatorial optimization problem which can be seen as a fusion of two well known sub-problems: the Travelling Salesman Problem and the Bin Packing Problem. Its main objective is to find the lowest-cost set of routes to deliver demand, using identical vehicles with limited capacity, to customers with fixed service time windows. In this paper, we consider the minimization of the number of routes and the total cost simultaneously. Although previous evolutionary studies have considered this problem, none of them has focused on the similarity of solutions in the population. We propose a method to measure route similarity and incorporate it into an evolutionary algorithm to solve the bi-objective VRPTW. We have applied this algorithm to a publicly available set of benchmark instances, resulting in solutions that are competitive or better than others previously published.