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To realize the full potential of a gyrotron backward-wave oscillator (gyro-BWO), an energy recovery system was designed using Particle-In-Cell (PIC) simulations and optimized using both a genetic algorithm and PIC simulations. Simulations were carried out to optimize a periodic structure for separation of the spent electron beam and the output radiation produced by a gyro-BWO in the 8.0-9.5 GHz frequency range. The spent electron beam can be collected using a multistage depressed collector. The number and electric potentials of the electrodes were optimized to achieve the best overall recovery efficiency for specific parameters of the spent beam. The 3-D PIC code MAGIC was used to simulate the electrons' trajectories and a genetic algorithm was used to refine the electrode shapes for optimum efficiency.