One of the most fruitful notion of generalized solution in optimization and combinatorics is [linear programming relaxation][1]. Quoting from the wikipedia article: In mathematics, the linear programming relaxation of a 0-1 integer program is the problem that arises by replacing the constraint that each variable must be 0 or 1 by a weaker constraint, that each variable belong to the interval [0,1].




  [1]: http://en.wikipedia.org/wiki/Linear_programming_relaxation