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Tunable terahertz absorbers based on graphene frequency selective surfaces are designed using well-established evolutionary optimization techniques. Randomly initialized hill climbing (RHC) algorithm is applied to find the design with the broadest bandwidth. The effects of three factors including the substrate loss, structuring the substrate and using double layer patches are examined. The optimum structure with broadest operation bandwidth consists of a perforated lossy substrate with a single layer patch and offers 1.95 THz absorption bandwidth around 2 THz central frequency leading to 100% fractional bandwidth.