`State space search' is a general and ubiquitous AI activity that includes numerical optimization (e.g. via gradient descent in a real-valued search space) as a special case.

State space search is an abstraction which can be customized for a particular problem via three ingredients:

 1. Some representation for candidate solutions to the problem (e.g.
    permutation of cities to represent a Travelling Salesman Problem
    (TSP) tour, vector of real values for numeric problems).
 2. A
    solution quality measure: i.e. some means of deciding which of two
    solutions is the better. This is typically achieved (for
    single-objective problems) by having via some integer or real-valued
    function of a solution (e.g. total distance travelled for a TSP
    tour). 
 3. Some means of moving around in the space of possible solutions, in a heuristically-informed manner. Derivatives can be used if
    available, or else (e.g. for black-box problems or discrete solution
    representations) the kind of mutation or crossover methods favoured
    by genetic algorithms/evolutionary computation can be employed.

The first couple of chapters of the freely available ["Essentials of Metaheuristics"][1] give an excellent overview and  Michalewicz and Fogel's ["How to Solve It - Modern Heuristics"][2] explains in more detail how numerical optimization can be considered in terms of state-space.


  [1]: https://cs.gmu.edu/~sean/book/metaheuristics/
  [2]: http://www.springer.com/us/book/9783540224945