A new approach for the optimal distribution of assemblies in a nuclear reactor

The aim of this paper is to propose a new approach for optimizing the position of fuel assemblies in a nuclear reactor core. This is a control problem for the neutronic diffusion equation where the control acts on the coefficients of the equation. The goal is to minimize the power peak (i.e. the neutron flux must be as spatially uniform as possible) and maximize the reactivity (i.e. the efficiency of the reactor measured by the inverse of the first eigenvalue). Although this is truly a discrete optimization problem, our strategy is to embed it in a continuous one which is solved by the homogenization method. Then, the homogenized continuous solution is numerically projected on a discrete admissible distribution of assemblies.