Optimization of the vehicle routing problem with demand responsive transport using the NSGA-II algorithm

Demand Responsive Transport (DRT) systems emerge as an alternative to deal with the problem of variable demand, or even unpredictable, occurring in conventional urban transport systems. It can be seen in some practical situations such as public transport in rural areas, wherein in some situations, there is no way to predict demand. This paper addresses the Vehicle Routing Problem with Demand Responsive Transport (VRPDRT), a type of transport which enables customers to be taken to their destination like a taxi or minibus in order to reduce operating costs and to meet customer needs. A multiobjective approach is proposed to VRPDRT in which five different objective functions are used. These functions are aggregated in three new functions resulting in a three-objective formulation for VRPDRT. When using a three objective approach, that formulation allows a better understanding of the company and human perspectives while permitting to solve the resulting problem in an efficient way. The proposed three-objective optimization problem is solved using a random method of generating solutions and an algorithm considered state of the art, the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The sets of solutions are compared using the Set Coverage Metric. The results show that the NSGA-II algorithm could obtain sets of solutions with better values for all objective functions used also called the non-dominated solutions set.