A Genetic Algorithm for Rich Vehicle Routing Problems Optimization Bochra Rabbouch 1 , Foued Saadaoui 2 , Rafaa Mraihi 3 1 Universit´ e de Tunis, Institut Sup´ erieur de Gestion de Tunis, Avenue de la Libert´ e, Cit´ e Bouchoucha, Le Bardo Tunis 2000, TUNISIA 2 Saudi Electronic University, Prince Saud Bin Mohammed Bin Muqrin Road Ar Rabi District, P.O. Box 93499, Riyadh 11673, SAUDI ARABIA 3 Universit´ e de Manouba, Ecole Sup´ erieure de Commerce de Tunis, Campus Universitaire de La Manouba, Tunis 2010, TUNISIA Abstract. The purpose of this paper is to study a rich vehicle routing problem (VRP), involving the number and capacity limitation of vehi- cles, time constraints including ready and due dates of each customer, heterogenous vehicle fleet and different warehouses for vehicles. A genetic algorithm (GA) is proposed to tackle this highly constrained problem. It is noticeable that, no GA-type method has been previously proposed for a multi-depot heterogenous limited fleet VRP with time windows. The proposed algorithm is tested on benchmark instances, showing good computational results, and thus proving to be promising in addressing other complex case of VRPs. Keywords: Rich Vehicle Routing Problem, Combinatorial Optimiza- tion, Genetic Algorithm, MDHVRPTW, VRPLIB. 1 Introduction The vehicle routing problem (VRP) is one of the most challenging combinatorial optimization problems, which continues to draw the attention of both academia and professionals in many fields, especially in transportation and logistics, biol- ogy, finance, etc. The role of a VRP is to find an optimal set of routes, over a single period, for a fleet of vehicles starting and ending at a central depot, to serve each customer exactly once. The objectives of VRP are, for the most part, to minimize the travel and the vehicle costs (respectively the time spent during the transportation system, the total travel distance, the number of vehicles used, the fuel consumption) or to maximize the profits. In this paper, we consider a model of a practical VRP, which can be de- fined as follows: Given a limited fleet of vehicles with heterogeneous capacities, parked in multiple central depots. The vehicles must serve several customers geographically scattered with different demands, while respecting capacity and time constraints, and must define several routes with a minimum transportation distance. All itineraries start and end at the same depot and each customer is served only once by just one vehicle with a compatible capacity. In the current