Very well explained. Thanks. And its how I understand it. I see search as having to do with combinatorial exploration and optimization as having to do with exploring vector spaces. You switch to heuristics in search when the space is too big or complex. But I also think that for suitable generalizations of the term one can view search as optimization or vice versa for reasoning purposes. I think there is something philosophical to be said about the fact that metaheuristics work as well as they do.