in the following, the Bloch modes have been calculated using the plane wave expansion method [@mpb-art]. The minimized SM (i.e., the inverse locality) of the Wannier functions in the first eight bands are displayed for four different, random distributions of the initial Bloch phases. As expected, the optimal locality obtained using the CG method depends crucially on the choice of the initial phases. This is an indication that the SM of the Wannier functions possesses several local minima.

![Locality ($1/\mathcal{S}_{n}$) of the SM-optimized Wannier functions as a function of GA generation for the Sq-D structure, TM polarization, 3rd band (top) and for the Sq-A structure, TE polarization, 5th band (bottom). The dashed, green line shows the locality of the best-localized Wannier function in each generation. Every 100 generations, these Wannier functions served as a starting point for the subsequent CG optimization step (red crosses). On the right hand side, the modulus square of the SM-optimized Wannier function is shown for an early (top: 40000th, bottom: 38300th) and a later (top: 60000th, bottom: 100000th) generation, respectively.[]{data-label="fig:ga_sm"}](all-g-tm-sm "fig:"){width="0.95\columnwidth"}\
![Locality ($1/\mathcal{S}_{n}$) of the SM-optimized Wannier functions as a function of GA generation for the Sq-D structure, TM polarization, 3rd band (top) and for 