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Informed Search. Informed vs. Uninformed. Uninformed Search: just takes the information available in the problem description Informed Search: Takes additional problem specific properties to guide the search A way of “engineering knowledge” into the search. Best First Search.

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informed vs uninformed
Informed vs. Uninformed
  • Uninformed Search: just takes the information available in the problem description
  • Informed Search: Takes additional problem specific properties to guide the search
    • A way of “engineering knowledge” into the search
best first search
Best First Search
  • A general search strategy
  • Uses an evaluation function f() in deciding which node (in queue) to expand next
  • Note: “best” could be misleading (it is relative, not absolute)
  • Greedy search is one type of Best First Search
  • What’s another you have seen?
greedy search
Greedy Search
  • Use a heuristic h() (cost estimate to goal) as the evaluation function
  • Example: straight-line distance in finding a path from one city to another
  • It is not optimal or complete
  • O(b^m) time and memory
  • But can be acceptable in practice
minimizing total path cost
Minimizing Total Path Cost
  • Use for the evaluation:

f(node) = g(node) + h(node)

where, f is the evaluation function, g is the path from root, and h is the heuristic (estimate to goal)

  • Or, f() = estimate of cheapest path to goal
  • Without h(), the search would be?
  • Without g()?
  • Combine advantages of both…
a search
A* search
  • We can actually guarantee optimality. by using an admissible heuristic:
  • h() is admissible if it never overestimates the cost to reach the goal
  • Example: straight-line distance in the travel problem
why is a optimal
Why is A* Optimal?
  • First we assume f() never decreases along a path (simple modification to the definition f() allows this)
  • Let f* be shortest path length, then
    • A* expands all nodes with f(node) < f*
    • Then some nodes with f(node)=f* before discovering the goal
  • Optimality follows
  • (need to assume some finiteness)
other properties
Other Properties
  • It is complete if finitely many nodes n, with

f(n) <= f* (e.g. finite branch factor and minimum positive distance)

  • No more expansion than other path following search optimal methods
  • Number of nodes can still be exponential within the goal counter (f < f*)
  • Memory is specially a problem (motivates IDA* and SMA*)
heuristics
Heuristics
  • Heuristics can make a big difference
  • Example: for the 8-puzzle problem
    • h1: Incorrect position count
    • h2: Manhatten distance
    • Observation: One dominates the other
  • Often: the higher the value (the under-estimate) the better
  • How about the cost to evaluate h()?
the art and science of heuristic design
The Art (and Science) of Heuristic Design
  • Relax the (constraints of the) problem
    • (so solution costs become under-estimates)
    • E.g. 8-puzzle, Rubic’s cube
  • Pick out state features that are significant for winning
    • E.g. chess, go
  • Other ideas:
    • Use max of multiple admissible heuristics
    • Use statistical heuristics or other (may give up optimality)
when only the goal matters
When only the goal matters
  • In many optimization problems, the path is irrelevant
  • The “goal” state is the solution (the state is described by a set of conditions/constraints, not given)
  • Examples:
    • n-queens
    • traveling salesperson (TSP),
    • constraint satisfaction problems (CSPs) in general
local search
Local Search
  • Take the current state and “locally” change it until you reach a state that satisfies certain conditions
  • It may stop at the goal state/configuration or an optimum state
  • Examples:
    • Hill-climbing (gradient ascent/descent)
    • Simulated Annealing
slide13
TSP: Find the shortest path that

visits all the cities once

choice of neighborhood
Choice of neighborhood
  • In search algorithms, there is usually choices of state and operators
  • In local search: the choice of operators (“actions”) defines a neighborhood and can make a big difference
  • And don’t forget the choice of heuristic
hill climbing
Hill-Climbing
  • Among the successors of the state, pick one that improves the most
  • Can get stuck in local optima, plateaus, or ridges

global

local

value

states

repeated hill climbing
Repeated Hill-Climbing
  • To avoid local optima and other problems, and improve the overall solution found, repeatedly restart the hill-climbing: random restarts
  • The success of hill-climbing depends on the shape of the space “surface”
simulated annealing
Simulated Annealing
  • Instead of restarting, take a random, possibly (locally) bad move
  • Helps get over local optimal
  • A parameter T, “temperature,” determines the probability of choosing a random (not necessarily best) move
  • Higher T, more random moves
  • In annealing, T is lowered gradually (use a “schedule”)
constraint satisfaction problems
Constraint Satisfaction Problems
  • Problem: a number of variable with a number of possible values for each
  • Constraints on the possible variable values
  • Goal state: All constraints are satisfied
  • Example: n-queens, satisfiability, VLSI
heuristics for csps and search
Heuristics for CSPs and Search
  • Variables are incrementally assigned values
  • To limit the branching factor and/or depth searched, use:
    • Most constrained-variable heuristic
    • Most-constraining-variable heuristic
    • Least-constraining-value heuristic
heuristics for csps with local search
Heuristics for CSPs with Local Search
  • Min conflicts: Choose the new variable value resulting in minimum number of with other variables (unsatisfied constraints)
  • N-queens: put the queen in the spot resulting in the minimum number of threats to it
summary
Summary
  • Informed search more powerful than uninformed
  • Two main search techniques of “systematic” search and local-search
  • There is an art to choice of space, operators (actions), and heuristics
  • These choices can make a huge difference