Designing gradients coils with arbitrary geometries has been realized by matrix inversion optimization techniques. Use of a truncated singular value decomposition (SVD) is promising because magnetic field accuracies are controlled by choosing the appropriate SVD eigenmodes. However, in the SVD method, the gradient performances, such as inductance and power dissipation, cannot be optimized. Here we proposed a new strategy to optimize a desired coil performance. A key feature is the use of a genetic algorithm to optimize the appropriate combination of SVD eigenmodes. The concept is demonstrated for a biplanar geometry, and would be readily applicable to arbitrary geometries.