What is the solution to this problem: Possibility of electing a minority president (one who does not have an absolute majority of popular votes)
There is no way to rule out the possibility of electing a "minority president" while using the current Electoral College system. The possibility of a minority president is one of the major arguments against the current system.
In order to make such a scenario less likely, the most logical thing to do would be to split up the states' electoral votes proportionally. In other words, a candidate getting 52% of a state's popular vote would get 52% of its electoral votes. This would be a bit tricky, though, because most states do not have enough electoral votes to be able to divide them that finely. (Washington has 9 electoral votes -- 52% of that is 4.68, so how do you divide them).
The way to make it completely impossible to have a minority president is to have a national popular vote. You would also have to have a provision for a runoff election in case too many candidates split the vote (like in 1992) and no one got 50%.