Behavioural-based mathematical programming: algorithmics and applications

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The aim of my research is to study, from both the theoretical and computational points of view, decision problems that involve agents with conflicting objectives. To fix ideas, let us consider the problem of setting tolls on the links of a highway. In order to optimize the revenue, one must take into account the behaviour of drivers, who want to minimize their own travel cost. If tolls are low, revenue will be low. If tolls are high, revenue will also be low, due to the low number of drivers for which the highway will be attractive. One must then strike the right balance, taking into account user behaviour. Although it has been shown that, even in that simple setting, the problem is hard to solve, the situation becomes all the more complex when behaviour varies across the population or when congestion occurs. Such problems fit the framework of bilevel mathematical programs, or leader-follower games. In these games, the leader factors into its optimization problem the rational reaction of an adversary or a population impacted by his decisions. This reaction would be the drivers' path choices in our introductory example. This situation is ubiquitous. Indeed, it is the exception that all variables of a problem are controlled by the leader.