All possible loading patterns for a nuclear reactor core are searched and optimized for compliance with design constraints. The fuel inventory is divided into a few batches according to coarse levels of reactivity. A recursive enumeration process identifies patterns meeting selected core position constraints, which can be user modified to adjust the search space size. For the batch loading patterns satisfying the constraints, the batches are divided into several smaller batches. A sensitivity matrix linearizing the relationship between fuel assembly position and the depletion model is processed through mixed integer linear programming with branching and bounding to identify an optimal daughter loading pattern. The process is repeated through several levels of batch refinement and selection of optimal daughter patterns, including a level where burnable absorbers are assigned to feed assemblies, until the individual fuel assembly level is reached. The multiple optimal patterns remaining provide a range of solutions.