The floating wind turbine support structure design problem is complicated by conflicting technical objectives and innumerable platform geometry options. Previous support structure optimization studies have been limited in their ability to evaluate the full design space due to their adherence to certain assumptions about the physical platform configuration. The present work is an effort toward developing an alternative form of the support platform optimization problem one that abstracts details of the platform geometry and deals instead with hydrodynamic performance coefficients in order to provide a more complete and intuitive exploration of the design space. A basis function approach, which represents the design space by linearly combining the hydrodynamic performance coefficients of a diverse set of basis platform geometries, was taken as the most straightforward way of physically constraining the platform hydrodynamic performance. Candidate designs are evaluated in the frequency domain using linearized coefficients for the wind turbine, platform, and mooring system dynamics. The platform hydrodynamic coefficients are calculated according to linear hydrodynamic theory. The optimization objective is to minimize the nacelle acceleration under several operating conditions. Optimization results for a slack catenary mooring system indicate the benefits of combining submerged volume with a widely dispersed water plane area. Results for a tension leg mooring system are consistent with conventional TLP designs. The intent is to use these results as starting points for more traditional platform parameter optimization. Examination of the possible physical interpretations of linearly combining basis platform coefficients reveals that certain aspects of this approach may have poor physicality. This points to the need to expand this first attempt with more sophisticated ways of representing the constrained hydrodynamic performance variables. (C) 2014 Elsevier Ltd. All rights reserved.