1. A method of establishing a nuclear reactor core loading pattern for loading fuel assemblies and burnable absorbers into a nuclear reactor, said method comprising the steps of: a. providing nuclear data representing fuel assemblies and burnable absorbers in a nuclear reactor core; b. depleting said nuclear data to form a reference core depletion; c. incorporating said nuclear data into a system of equations of a nuclear design quality neutron flux solution; d. defining said system of equations to include constraints which accurately represent the neutron physics of said nuclear reactor, including effects of shuffling said fuel assemblies and of loading burnable absorbers into said reactor; e. employing said system of linear equations as a constraint matrix for a solver and running said solver in order to find an optimum core pattern solution; and f. repeating steps b through e, updating the constraints and objective functions which can be represented as linear constraints within said constraint matrix, in order to satisfy specified engineering requirements and establish an optimum core loading pattern.