IFAC PapersOnLine 50-1 (2017) 14656–14661 ScienceDirect Available online at www.sciencedirect.com 2405-8963 © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2017.08.1906 © 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. A hybrid genetic algorithm to solve a multi-objective Pickup and Delivery Problem Z. Al Chami * H. Manier * M.-A. Manier * C. Fitouri *,**,*** Keywords: Transportation, Urban logistics, Genetic Algorithm, Metaheuristic approach, selective PDPTW. 1. INTRODUCTION The Pickup and Delivery Problem (PDP) aims at routing a fleet of vehicles on a given transportation network to serve a set of nodes with known demand under specified constraints. In an urban context, this problem is often more critical because of the applied policies in many cities such as reg- ulation of parking, hours of operations and street access. In this context, additional constraints such as time win- dows and vehicle capacity may be taken into consideration. For example, only small vehicles may be allowed to access the city center in order to provide the pickup or the deliv- ery operations. Moreover, freight transportation increases congestion and noise so the public authorities may allow such transportation in limited hours per day. In the considered problem, each vehicle has a limited capacity. The vehicles start their routes from the depot, serve nodes in the network and return to the depot at the end of their routes. The present quantity in every vehicle after visiting a node must not exceed its maximal capacity. Each node represents a pickup location or a delivery one. A time window is also associated for each node and the vehicle visiting this node cannot arrive after the end of its time window. If the vehicle arrives earlier than the beginning of the designated time window interval, it must wait until the service time begins. In our problem, we have included the paired demands aspect which means that every vehicle has to connect an origin (supplier) to its destination (customer). The supplier may be the depot or any other pickup location and the customer may be also the depot or any other delivery location. In this paper, we study a new variant of the classic PDP which is the Selective PDP with Time Windows and Paired Demands (SPDPTWPD). This variant is a generalization of the standard PDP where in addition of the Time Windows constraints, the visit of all nodes is not obligatory. Additionally, each tour must satisfy the precedence constraints to ensure that a customer should not be visited before his supplier. The remaining of this paper is organized as follows: in section 2 we provide a brief literature review. After that, section 3 formally defines our new variant. Section 4 is dedicated to explain our hybrid genetic algorithm. Experimental results are given in section 5. Finally, section 6 concludes this paper and gives directions for further research. 2. LITERATURE REVIEW The PDP is a variant of VRP (Vehicle Routing Problem) which is a popular combinatorial optimization problem. It consists in finding an optimal set of routes for a fleet of vehicles in order to serve a specified collection of clients. A taxonomic review of the VRP literature published between 2009 and June 2015 has recently been presented by (Braekers et al., 2016). * Univ. Bourgogne Franche-Comt´ e, UTBM, OPERA, F-90010 Belfort, France (e-mail: zaher.al-chami@utbm.fr, herve.manier@utbm.fr, marie-ange.manier@utbm.fr). ** Univ. Bourgogne Franche-Comt´ e, FEMTO-ST institute, ENSMM, CNRS, 25000, Besan¸ con, France (e-mail: fitouricyrine@yahoo.fr) *** Universit´ e de Tunis, ENSIT, LR13ES03 SIME, 1008, Montfleury, Tunisia Abstract: The Pickup and Delivery Problem, known as PDP, is one of the most combinatorial optimization problems studied in the literature. In this type of problems, loads must be transported by a fleet of vehicles from pickup sites to delivery sites. A set of constraints must be respected in relation with the capacity of the vehicles, the opening and closing times of each site. This paper presents the first metaheuristic method to solve a new variant of the PDP which we called SPDPTWPD (Selective PDP with Time Windows and Paired Demands). In this variant, the precedence constraints (paired demands) and the choice of sites to be served (selective aspect) must be considered. We proposed a hybrid genetic algorithm to deal with the multi-objective SPDPTWPD. We tested our proposed approach on benchmark instances and the obtained results show its efficiency.