I mentioned this in another comment reply, but moving the homeless always makes the problem worse. All you have done is created a ghetto where they homeless are now reliant on the handouts, rather than being able to make use of the services provided by the city (transit, etc.)

The only solution that works all the time is integrating the homeless into society. Creating a "step-ladder" that helps people get a roof over their head, and then leverage the city's infrastructure (transit, healthcare, sewer, water, power, etc.) to build themselves a sustainable life.

The ones who fall out of this system are the mental health/addiction sufferers, who then need to be taken care of by the state in some sort of institution. (Which can definitely be out in the countryside, or whatever, because the state has committed to supporting this person for the rest of their life.)

Simply taking the homeless and moving them out to the countryside will ensure they remain a drag on society, since you have removed them from society, and all of the things that society provides.

Ghetto-ization is not the answer. It's way more complex than that.