Repair and strengthen the economy so there is an abundance of jobs and the homeless population will reduce itself.   Better jobs for the homeless who work but still can't afford a place and you have cut the homeless population by 40%.  Better economy and more people to donate to programs that get the homeless with mental illness and drug addicted off the street and you cut the homeless population by another 40%.  The remaining 20% are not going to do anything to help themselves so let them be, you can't fix stupid.