The ants are not the reason aphids are on your plants, but the presence of aphids is why the ants are there. Aphids prefer plants with lush, green growth most often plants that are growing in soils that have an excess of Nitrogen. The simplest means of eliminating aphids from any plant is sharp water sprays to knock them off, long term however is to look closely at the soil and fix that.
Far too many people do not understand why ants are here and far too many people encourage the fear of ants far too many people have.

deej85, I do not believe that the translucent eggs are those of aphids. My reason for saying so is that egg laying by aphids is done in the fall. Whatever color they may be when deposited usually darkens as spring and hatch time approaches. I would not associate aphids with a compost bin; they usually migrate to the young, tender plant tissue. In view of all this, I'd take a second look at the insect ID.