Distributed Approch Using NSGAII Algorithm to Solve the Dynamic Dial a Ride Problem A. RADDAOUI, I. ZIDI, K. ZIDI, K. GHEDIRA Abstract— THE DRP (dial a ride problem) consists on determining and planifiying the operated tours of vehicles in order to satisfy the user’s requests hoping to become origin’s points to destination’s points. The DRP is bind to NP- difficult problems, in order to solve it, many researchers have been used multi objective approached methods; actually our approach consists on reducing the number of vehicles, reducing the route’s time and increasing the customer’s number. In this paper, we propose our contribution which is a distributed approach based on a multi-agent system( made to decompose the problem and to model the heterogeneous vehicle), and an instance of the genetic algorithm (NSGAII). The process of the proposed approach is shown through an illustrative example. Keywords- Distributed GA NSGAII, Mutli-objectve Simulated Annealing Algorithm, DRP, Multi-objective algorithm, DRP, SMA. I. INTRODUCTION The DRP (Dial a Ride Problem) consists in determining and planning the tours operated by vehicles in order to satisfy user’s requests wishing to be transported from origin to destination. In this paper, we propose our contribution of DRP responsive transport with the use of a distribution of the genetic algorithm NSGA II (DNSGAII). The DRP consists on responding the actual transport’s requests via the vehicles ‘fleet under a number of feasibility and functioning constraints. DRP is a problem belonging to the NP-difficult class [1]. The accurate methods are unable to solve this kind of problem in a reasonable time especially when the problem is so big [2]. In this case, we are obliged to use methods that permit us to find an approached solution in an acceptable time. It is about the heuristics and meta- heuristics, like those which are based on genetic algorithm, simulated annealing and taboo searches. A.Raddaoui is with the University of Tunis, SOIE-Management Hight Institue, 41, Liberty street Le Bardo 2000, Tunisie (e-mail: alayaraddaoui@gmail.com ). I.Zidi is with the University of Gafsa, Faculty of Sciences of Gafsa, Zarroug, Gafsa 2112, Tunisie (e-mail: zidi.issam@gmail.com ). K.Zidi is with the University of Gafsa, Faculty of Sciences of Gafsa, Zarroug, Gafsa 2112, Tunisie (e-mail: kamel_zidi@yahoo.fr ). K.Ghedira is with the University of Tunis, SOIE-Management Hight Institue, 41, Liberty street Le Bardo 2000, Tunisie (e-mail: khaled.ghedira.isg.rnu.tn ). II. RELATED WORKS A DARP (Dial-a-Ride Problem) is an extension of the PDP where the goods are individuals, leading to some additional technical constraints due to transport of persons for example, the fact of having a single point of embarkation by landing point and vice versa, and the obligation to comply with specific deadlines. Dial a Ride Problem or Demand Responsive Transport (DRT) as defined by common road transport, is a special case of DARP where service quality can be measured in terms of comfort and friendliness, ergonomics, forms of trajectory in relation with origins and destinations, considered the requests in real time, etc… [3]. Generally, a DRP is an extension of the PDP (Pickup & Delivery Problem) in which the freight is replaced by the transport of persons [4]. In the article [5] we find a more detailed of the state of the art of this problem. The DRP has been extensively studied in the literature. We distinguish several variants of the DRP. Indeed, there are DRP with or without time windows and dynamic and static DRP. In the case of dynamic DRP, the problem is usually treated as a succession of static problem [6]. The majority of research works has been focused on the static DRP while for example [7] have solved the dynamic DRP. When the problem is of small size, we tend to use exact methods to solve it. In this context we mention the work of Psaraftis who used an exact algorithm of dynamic programming to solve the problem with a single vehicle [2]. He studied the case where there are windows of time imposed at points of departure and arrival for each demand. Again using the exact methods, we find the work who resolved the DRP with the method of Branch and Bound. With the increasing of requests for transportation in a DRP, the researchers thought the problem with heuristic and meta-heuristic methods. These methods allow reaching an acceptable solution of the problem in the reasonable time. In this context, we cite the main work such as Mauri et al, where the authors solved a multi-objective DRP [8]. They applied their approach on data derived from the benchmark presented in [9]. Indeed, they developed a simulated algorithm based on three local search methods. Cordeau et al, have applied the tabu search algorithm to solve the problem. For transportation problems at actual demand, Garix et al, have developed an inserting method for transportation on demand problem located in a low density rural area “Cental Country of the Doubs, Franche-Comte” [10]. Nabaa et al, have solved a dynamic DRP using a distributed scheduling algorithm [6]. This algorithm is applied to a succession of static problems representing the basic problem. Proceedings of the World Congress on Engineering and Computer Science 2013 Vol I WCECS 2013, 23-25 October, 2013, San Francisco, USA ISBN: 978-988-19252-3-7 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) WCECS 2013