A comparison of probabilistic-based optimization approaches for vehicle routing problems

Estimation of distribution algorithms (EDAs) are evolutionary algorithms that use probabilistic modeling to lead a more efficient search for optimal solutions. While EDAs have been applied to several types of optimization problems, they exhibit some limitations to deal with constrained optimization problems. More study and understanding of how can EDAs deal with these problems is required. In this paper we investigate the application of EDAs to a version of the vehicle routing problem in which solutions should satisfy a number of constraints involving the customers, the fleet vehicle, and the items to be delivered. For this problem, we compare two different representations of the solutions, and apply EDAs that use three probabilistic models with different characteristics. Our results show that the combination of an integer representation with tree-based probabilistic model produces the best results and is able to solve vehicle routing problems that contain over thousands of promising paths.