INFORMED SEARCH METHODS

Best-First Search
	expand the least-cost node of the search tree

Greedy Search
	expand the node considered closest to solution state

	(This is greedy because it always takes the biggest 
	bite first.)

Best-First is provably optimal and complete but can be 
slow, while the greedy algorithm is neither optimal nor 
complete.

A* Search

	expand the node with lowest expected total path cost
	(sum the cost of path to node with perceived 
	distance to solution)

	Perceived distance must be computed with an 
	admissible heuristic (a function that never 
	overestimates the actual cost).

	monotonic function

	A* is optimal and complete



			HEURISTIC FUNCTIONS

How do we estimate distance to goal state?

How do we generate admissible heuristics?

For a problem computing a trip in physical space we can 
use point-to-point distances since the actual 
distance travelled must be at least that far.

Eight-Puzzle Problem

	Potential heuristics:

		h1 = Number of tiles not in correct place
		(each one will have to move to solve problem)

		h2 = Sum the distances of the tiles from goal positions.
		(each tile must move at least this far in solution)

	h2(state) >= h1(state)
	h2 dominates h1

	Both of these admissible functions are example of relaxing 
	assumptions or constraints in the original problem.

If no single admissible function seems good, you can use a 
whole bunch:

	h(n) = max(h1(n), h2(n), ... h?(n))
	but remember to consider cost of computation 




		ITERATIVE IMPROVEMENT ALGORITHMS

Generate a complete solution and iteratively improve the 
solution through modification.

Advantage to search:
	keep only one state in memory

Hill-Climbing
	local maxima, plateaux, ridges

Random-Restart Hill-Climbing
	hill-climbing from different start positions
	how many restarts?

Hill-Climb and Jump
	get to a local maxima and jump ...

Simulated Annealing
	Introduce random moves with probabilistic chance of 
	taking move that decreases current position.

	Probability that move down will be taken is function 
	of "badness" and time (t).

	As t becomes large, this is almost like hill-climbing.