In this work, a framework was designed and implemented for optimizing the reactor core loading pattern of a representative European Pressurized Water Reactor (EPR) core. The paper focuses on optimizing the equilibrium cycle, encoded in the proposed matrix-based version. Optimizations were conducted for 1/8 and 1/4 symmetry, with the goal of maximizing average burnup of the core while simultaneously maintaining or improving the nuclear enthalpy rise hot channel factor, neutron leakage, and average fuel assembly burnup. The optimization utilized a genetic algorithm, parallel simulated annealing, and a proposed hybrid version. The results showed that each algorithm could, within several dozen iterations, propose a solution comparable to the reference within the defined objective function, demonstrating significant potential to reduce the time needs and engineering efforts to improve and design industrial fuel loading patterns.