The Vehicle Routing Problem (VRP)  consists in determining a set of tours for a fleet of vehicles, which must respect various constraints and be of least cost. This combinatorial optimization problem is particularly important due to its large set of applications.
In practice, the VRP often involves dealing with parameters that are known with some uncertainty. This uncertainty may concern for instance the customer demands or the travel times. Classically, probability theory has been used to take into account the uncertainty . This is known as stochastic optimization.
In recent decades, alternative theories to probability theory have emerged to represent and more finely manage the different origins (randomness and lack of knowledge) of uncertainty. Among these, the Belief Function Theory (BFT)  enjoys a certain maturity, with various applications .
In previous work [5, 6], we have shown the relevance and feasibility of an evidential treatment, that is to say based on the BFT, of uncertainties in the VRP. The proposed models were obtained by extending the main approaches (so-called chance constraints and recourse) developed in stochastic optimization. In addition, we have implemented approximate solving methods allowing us to find good quality solutions in a reasonable time to the complex optimization problems obtained.
Within the framework of this PhD project, we propose to pursue this work in three main directions. At the modelling level, refined approaches, taking more advantage of the expressiveness of the framework of belief functions, should be explored. This includes exploiting more cautious decision criteria, such as those analyzed in , in order to compare and order, potentially only partially, the solutions. The study of the proposed models is also to be deepened. In particular, it is necessary to determine the uncertain variables on which it would be interesting to act (for example to reduce the uncertainty or the value, in the sense of relations between belief functions ) in order to improve the solutions. Finally, at the solving level, the belief function approximation methods used , which reduce the complexity, need to be refined in order to obtain better quality solutions. The adaptation of exact solving methods  is also envisaged.