Help me carry my shopping bags
Pyth, 9 bytes

ehc2osNyQ


Input, output formats:

Input:
[1, 2, 3, 4, 5]
Output:
[1, 2, 4]


Demonstration.

ehc2osNyQ
             Q = eval(input())
       yQ    Take all subsets of Q.
    osN      Order those element lists by their sums.
  c2         Cut the list in half.
eh           Take the last element of the first half.


This works because y returns the subsets in such an order that each subset and its complement are equidistant fom the center. Since the sum of a subset and the sum of its complement will always be equidistant from the center, the list after osNyQ will also have this property. Thus, the center two elements of osNyQ are complements, and must have an optimal split. We extract the first of those two elements and print it.