Hybrid adaptive predictive control for a dynamic pickup and delivery problem including traffic congestion

Abstract

This paper presents a hybrid adaptive predictive control approach to incorporate future information regarding unknown demand and expected traffic conditions, in the context of a dynamic pickup and delivery problem with fixed fleet size. As the routing problem is dynamic, several stochastic effects have to be considered within the analytical expression of the dispatcher assignment decision objective function. This paper is focused on two issues: one is the extra cost associated with potential rerouting arising from unknown requests in the future, and the other is the potential uncertainty in travel time coming from non-recurrent traffic congestion from unexpected incidents. These effects are incorporated explicitly in the objective function of the hybrid predictive controller. In fact, the proposed predictive control strategy is based on a multivariable model that includes both discrete/integer and continuous variables. The vehicle load and the sequence of stops correspond to the discrete/integer variable, adding the vehicle position as an indicator of the traffic congestion conditions. The strategy is analyzed under two scenarios. The first one considers a predictable congestion obtained using historical data (off-line method) requiring a predictive model of velocities distributed over zones. The second scenario that accepts unpredictable congestion events generates a more complex problem that is managed by using both fault detection and isolation and fuzzy fault-tolerant control approaches. Results validating these approaches are presented through a simulated numerical example.