Optimization of nuclear fuel reloading by the homogenization method

In this paper we apply the homogenization method to the optimization of the position of fuel assemblies in a nuclear reactor core. For this type of problem the state equation is a system of diffusion equations for the neutron flux. Homogenization theory allows us to relax a truly discrete optimization problem into a continuous and well-posed optimization problem. The latter one is solved by using classical methods of optimal control. A discrete admissible distribution of assemblies is recovered by a numerical penalization technique. The main advantage of homogenization is that the resulting reloading pattern is guaranteed to be near optimal whatever the initial guess.