A system is provided that determines optimal movements of fuel assemblies in a nuclear reactor, such as a traveling wave reactor (TWR). Such a system may be capable of modeling core operations and fuel moves in parallel to determine optimal fuel cycle moves responsive to one or more constraints, including, but not limited to core criticality and location of a deflagration wave within an operatingreactor core. According to one embodiment, the optimal solution may be determined using a branch search to simulate possible fuel moves.