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High current storage rings, such as the Z operating mode of the FCC-ee, require superconducting radio frequency (RF) cavities that are optimized with respect to both the fundamental mode and the dangerous higher order modes. In order to optimize the shape of the RF cavity, a constrained multi-objective optimization problem is solved using a massively parallel implementation of an evolutionary algorithm. Additionally, a frequency-fixing scheme is employed to deal with the constraint on thedoi:10.18429/jacow-icap2018-tupag14 fatcat:k6kdvrza4bhrrndazc5ngl22vm