We derive and apply a methodology for the initialization of velocity and transport fields in complex multiply-connected regions with multiscale dynamics. The result is initial fields that are consistent with observations, complex geometry and dynamics, and that can simulate the evolution of ocean processes without large spurious initial transients. A class of constrained weighted least squares optimizations is defined to best fit first-guess velocities while satisfying the complex bathymetry, coastline and divergence strong constraints. A weak constraint towards the minimum inter-island transports that are in accord with the first-guess velocities provides important velocity corrections in complex archipelagos. In the optimization weights, the minimum distance and vertical area between pairs of coasts are computed using a Fast Marching Method. Additional information on velocity and transports are included as strong or weak constraints. We apply our methodology around the Hawaiian islands of Kauai/Niihau, in the Taiwan/Kuroshio region and in the Philippines Archipelago. Comparisons with other common initialization strategies, among hindcasts from these initial conditions (ICs), and with independent in situ observations show that our optimization corrects transports, satisfies boundary conditions and redirects currents. Differences between the hindcasts from these different ICs are found to grow for at least 2-3 weeks. When compared to independent in situ observations, simulations from our optimized ICs are shown to have the smallest errors.