Informed Search

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# Informed Search - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Informed Search' - alina

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Presentation Transcript

### 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
• 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
• 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
• 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()?
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?
• 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
• 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 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
• 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
• 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
• 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:
• Simulated Annealing
TSP: Find the shortest path that

visits all the cities once

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
• 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
• 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
• 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
• 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
• 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
• 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
• 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