Solving Vehicle Routing Problems Using Constraint Programming and Lagrangean Relaxation in a Metaheuristics Framework

This paper presents a methodology based on the Variable Neighbourhood Search metaheuristic, applied to the Capacitated Vehicle Routing Problem. The presented approach uses Constraint Programming and Lagrangean Relaxation methods in order to improve algorithm’s efficiency. The complete problem is decomposed into two separated subproblems, to which the mentioned techniques are applied to obtain a complete solution. With this decomposition, the methodology provides a quick initial feasible solution which is rapidly improved by metaheuristics’ iterative process. Constraint Programming and Lagrangean Relaxation are also embedded within this structure to ensure constraints satisfaction and to reduce the calculation burden. By means of the proposed methodology, promising results have been obtained. Remarkable results presented in this paper include a new best-known solution for a rarely solved 200-customers test instance, as well as a better alternative solution for another benchmark problem.