We consider the problem of minimization of the energy consumed by an electrical vehicle performing quite long travels with slopes. The model we address here, takes into account the electrical and mechanical differential equations of the vehicle. This yields a mixed-integer optimal control problem that can be approximated, using a methodology based on some decomposition steps, by an integer nonlinear global optimization problem. In Merakeb et al (2014), an efficient Branch and Bound algorithm was proposed to solve this problem but only for flat and short travels (100m). In this paper, we show that this algorithm can be extended to solve more operational cases. Firstly, we consider the case of long travels and propose a new Branch and Bound based method for which two powerful heuristics for computing bounds have been developed. Secondly, we deal with routes presenting slopes and develop a new algorithm that allows to efficiently deal with this kind of situations. Note that the main difficulty lies in determining where the changes of slopes occur. A particular attention was devoted to the add of constraints about the acceleration of the vehicle to the optimal control problem in order to provide realistic optimal solutions. Numerous numerical results validating our operational approach are reported.
View Branch and Bound based methods to minimize the energy consumed by an electrical vehicle on long travels with slopes