In this article, a hybrid predictive control (HPC) strategy is formulated for the real-time optimisation of a public transport system operation run using buses. For this problem, the hybrid predictive controller corresponds to the bus dispatcher, who dynamically provides the optimal control actions to the bus system to minimise users' total travel time (on-vehicle ride time plus waiting time at stops). The HPC framework includes a dynamic objective function and a predictive model of the bus system, written in discrete time, where events are triggered when a bus arrives at a bus stop. Upon these events, the HPC controller makes decisions based on two well-known real-time transit control actions, holding and expressing. Additionally, the uncertain passenger demand is included in the model as a disturbance and then predicted based on both offline and online information of passenger behaviour. The resulting optimisation problem of the HPC strategy at every event is Np-hard and needs an efficient algorithm to solve it in terms of computation time and accuracy. We chose an ad hoc implementation of a Genetic Algorithm that permits the proper management of the trade-off between these two aspects. For real-time implementation, the design of this HPC strategy considers newly available transport technology such as the availability of automatic passenger counters (APCs) and automatic vehicle location (AVL) devices. Illustrative simulations at 2, 5 and 10 steps ahead are conducted, and promising results showing the advantages of the real-time control schemes are reported and discussed.

A hybrid predictive control formulation based on evolutionary multi-objective optimization to optimize real-time operations of public transport systems is presented. The state space model includes bus position, expected load and arrival time at stops. The system is based on discrete events, and the possible operator control actions are: holding vehicles at stations and skipping some stations. The controller (operator) pursues the minimization of a dynamic objective function to generate better operational decisions under uncertain demand at bus stops. In this work, a multi-objective approach is conducted to include different goals in the optimization process that could be opposite. In this case, the optimization was defined in terms of two objectives: waiting time minimization on one side, and impact of the strategies on the other. A genetic algorithm method is proposed to solve the multi-objective dynamic problem. From the conducted experiments considering a single bus line corridor, we found that the two objectives are opposite but with a certain degree of overlapping, in the sense that in all cases both objectives significantly improve the level of service with respect to the open-loop scenario by regularizing the headways. On average, the observed trade-off validates the proposed multi-objective methodology for the studied system, allowing dynamically finding the pseudo-optimal Pareto front and making real-time decisions based on different optimization criteria reflected in the proposed objective function compounds.