Constraint Programming Based Algorithm for Solving Large-Scale Vehicle Routing Problems

Abstract

Smart cities management has become currently an interesting topic where recent decision aid making algorithms are essential to solve and optimize their related problems. A popular transportation optimization problem is the Vehicle Routing Problem (VRP) which is high complicated in such a way that it is categorized as a NP-hard problem. VRPs are famous and appear as influential problems that are widely present in many real-world industrial applications. They have become an elemental part of economy, the enhancement of which arises in a significant reduction in costs. The basic version of VRPs, the Capacitated VRP (CVRP) occupies a central position for historical and practical considerations since there are important real-world systems can be satisfactorily modeled as a CVRP. A Constraint Programming (CP) paradigm is used to model and solve the CVRP by applying interval and sequence variables in addition to the use of a transition distance matrix to attain the objective. An empirical study over 52 CVRP classical instances, with a number of nodes that varies from 16 to 200, and 20 CVRP large-scale instances, with a number of nodes that varies from 106 to 459, shows the relative merits of our proposed approach. It shows also that the CP paradigm tackles successfully large-scale problems with a percentage deviation varying from 2% to 10% where several exact and heuristic algorithms fail to tackle them and only a few meta-heuristics can probably solve instances with a such big number of customers.