Sep 05, 2003
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- What makes a good heuristic?
        - h(n) = 0 for all goal nodes n
        - h(n) should satisfy triangle inequality
                - h(n) <= c(n,n') + h(n')

- Consistent heuristics
        - those that satisfy triangle inequality

- Monotone heuristics
        - using these, path costs never decrease

- Consistency implies monotonicity
        - if a heuristic is not consistent, A* might
          explore some bad paths over and over again

- Time complexity of finding optimal solutions
        - If h(n) = h*(n), linear, march on unchallenged
        - If h(n) = 0, exponential
        - If h(n) <= h*(n), still exponential but in
          the difference between the heuristics

- Comparing heuristics
        - h1 being more informed than h2

- A* is optimally efficient for any given heuristic
        - different from saying A* is optimal
          (i.e., leads to the optimal solution)
        - this means that no algorithm using the same
          heuristic can do better than A*

- Making A* more efficient
        - mainly w.r.t. space complexity
        - Just as BFS:DFID, we get  A*:IDA*
        - increase trees, not by depth but by f()

- Read up yourself
	- RBFS
	- SMA*


- Other classes of search algorithms
        - iterative improvement
                - e.g., 8-queens problem
                - e.g., finding minimum of a function

- Iterative improvement 
        - "faith based"
        - difficult to get guarantees
        - local maxima, plateaus

- Other approaches
        - simulated annealing
                - "cooling schedule"
        - genetic algorithms
                - "crossover" and "mutation"
                  operators

- Ironically, some of the most famous algorithms
  in AI are iterative improvement algorithms!
        - we will encounter them soon!