An Intelligent Data Analysis of the Structure of NP Problems for Efficient Solution: The Vehicle Routing Case

Abstract

The Vehicle Routing Problem is a combinatorial problem with considerable industrial applications such as in traditional logistics and transportation, or in modern carpooling. The importance of even small contributions to this problem is strongly reflected in a significant cost savings, pollution, waste, etc., given the high impact of the sector in almost any economic transaction. The VRP is often treated as an optimization problem, however, the fitness function converges quickly and the algorithms become stagnant in late steps of the executions, which is a recurrent problem. In this work, we perform an analysis of the structure of solutions to identify potential use of existing ideas from other domains to achieve higher efficiency. In this sense, the feasibility of applying the Partition Crossover –an operator initially designed to tunnel through local optima for the Travelling Salesman Problem– to the Capacitated Vehicle Routing Problem is studied in order to escape local optima. Moreover, an implementation is provided along with an analysis applied to real use-cases, which show a promising rate of local optima tunneling.