Collision with Andromeda Galaxy According to Hubble's law, the universe is expanding and this expansion is proportional to distance between the two objects and thus objects are moving away at a very fast rate,  then why is it predicted that after 4 billion years the Milky Way shall collide with Andromeda galaxy?
As you say, expansion is proportional to distance. And in fact, compared to the size of the (observable) Universe, Andromeda and our Milky Way are close together. Indeed, farthest objects are now more than 20 billion Ly from us, whereas Andromeda is only 2.5 million Ly away. That is a 1/10000 factor.

The space expansion between them is not enough to set them apart, because of their general motion. On small scale (until galaxy cluster scale), the motion is primarily ruled by gravity. Galaxy cluster are in fact the largest gravitationally bound systems we know. 


  They typically contain no more than 50 galaxies in a diameter of 1 to 2 megaparsecs


Since Andromeda is the closest galaxy, it is inside "our" galaxy cluster, and stays bound to ours by gravity.