Floating offshore wind turbines (FOWTs) are still in the pre-commercial stage and, although different concepts of FOWTs are being developed, cost is a main barrier to commercializing the FOWT system. This article aims to use a shape parameterization technique within a multidisciplinary design analysis and optimization framework to alter the shape of the FOWT platform with the objective of reducing cost. This cost reduction is then implemented in 30 MW and 60 MW floating offshore wind farms (FOWFs) designed based on the static pitch angle constraints (5 degrees, 7 degrees and 10 degrees) used within the optimization framework to estimate the reduction in the levelized cost of energy (LCOE) in comparison to a FOWT platform without any shape alteration–OC3 spar platform design. Key findings in this work show that an optimal shape alteration of the platform design that satisfies the design requirements, objectives and constraints set within the optimization framework contributes to significantly reducing the CAPEX cost and the LCOE in the floating wind farms considered. This is due to the reduction in the required platform mass for hydrostatic stability when the static pitch angle is increased. The FOWF designed with a 10 degree static pitch angle constraint provided the lowest LCOE value, while the FOWF designed with a 5 degree static pitch angle constraint provided the largest LCOE value, barring the FOWT designed with the OC3 dimension, which is considered to have no inclination.