The last decades have seen a surge of interest in optimization problems that take into consideration different forms of uncertainties. Indeed, many real-life problems require finding a (sub-) optimal solution without knowing in advance very precise values for all input data. For instance, uncertainties can arise from unpredictable environmental conditions that can influence the demand, the cost, or the availability of certain products. In other applications, the uncertainties can concern the decision variables: it can even be difficult to determine in advance the feasibility/existence of certain candidate solutions.
Successful existing approaches to deal with uncertainty include stochastic programming or robust optimization methods. This PhD subject is devoted to a new framework of addressing uncertainty: the theory of belief functions. This is a very convenient framework to represent and combine uncertain information (evidence) in a relatively natural manner. While more classical stochastic optimization methods consider that uncertainty can be be described using exact probabilistic laws, the belief functions are more useful to formalize non-random uncertainty with no precise distribution laws. As such, we will use this framework to address belief-based uncertainty in optimization. Over a longer term, the goal is to develop a versatile and flexible framework of addressing this type of uncertainty in optimization. These methods will be applied to the vehicle routing problem.