HEURISTIC SEARCH: BEST-FIRST (A^* SEARCH)

• Best-first search uses an evaluation function, h(N), which indicates the relative goodness of pursuing that node. If we combine this with the partial path score, we can define a general evaluation function:
  
  f(N) = g(N) + h(N)
  which can be used to evaluate hypotheses as they evolve. If we always pursue the best path according to this evaluation function, what are the merits of this approach? What constraints must be placed on this function to guarantee an optimal solution? How would that solution compare to other search algorithms?
  
  
• A general algorithm for searching such spaces can be defined as follows:
  
  
  
• A search algorithm is said to be admissible if it can guarantee an optimal solution.
  
  
• One possible solution to the traveling salesman problem using best-first search might look like this: