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The aim of the presented study is to optimize the different classes of high-temperature superconducting (HTS) DC cables for improving their performances in a cryo-electric aircraft considering their weight, peak temperature during faults, and the ratio of current passing through each tape to the critical current of HTS tapes. These terms were interpreted into three objective functions, and a multi-objective optimization algorithm known as non-dominated sorting genetic algorithm II was used to find the optimal solution clusters. The cable optimization was conducted for different former materials by changing the former thickness and radius. Results showed that the DC HTS cables with aluminum former have the lowest weight while cables with copper formers have the best thermal performance against faults.