A Distributed Approach for resolving a Stochastic Dial a Ride Problem with NSGA II

Transportation on demand does not stop facilitating our daily life. In fact, for 40 years the research has contributed to the resolution of the Dial a Ride Problem to improve the service offered to customers. In this research, we contributed to the resolution of a Stochastic Dial a Ride Problem while consider four problems that may inhibit the proper functioning of service Transport on Demand , such as accidents, congestion, inadequate number of places in vehicles and breakdowns. Dial a Ride Problem is known as an NP-hard problem. So the exact resolution with large instances will be very expensive. Therefore, the use of heuristic will be beneficial. In this paper, we present a mathematical model aims to describing and resolving the Stochastic Dial a Ride Problem and the development of a meta-heuristic based on NSGAII hybridized with a stochastic process to minimize the distance traveled by vehicles and the elapsed time also to maximize the quality of service while minimizing the risk that rates that may penalize the smooth functioning of the transport service.