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Set 3: Informed Heuristic Search

ICS 271 Fall 2016

Kalev Kask

Basic search scheme

• We have 3 kinds of states

– explored (past) – only graph search

– frontier (current)

– unexplored (future) – implicitly given

• Initially frontier=start state

• Loop until found solution or exhausted state space

– pick/remove first node from frontier using search strategy

• priority queue – FIFO (BFS), LIFO (DFS), g (UCS), f (A*), etc.

– check if goal

– add this node to explored,

– expand this node, add children to frontier (graph search : only

those children whose state is not in explored list)

– Q: what if better path is found to a node already on explored list?

What is a heuristic?

Heuristic Search

• State-Space Search: every problem is like search of a map
• A problem solving agent finds a path in a state-space graph from start

state to goal state, using heuristics

h= 253

h= h= Heuristic = straight-line distance

State Space for Path Finding on a Map

Greedy Search Example

State Space of the 8 Puzzle

Problem 1 2

4 5 6 7 8

h1=4 h1=

h1 = number of misplaced tiles

h2=9 h2=

h2 = Manhattan distance

What are Heuristics

• Rule of thumb, intuition
• A quick way to estimate how close we are to the

goal. How close is a state to the goal..

• Pearl: “the ever-amazing observation of how much

people can accomplish with that simplistic, unreliable

information source known as intuition .”

8 - puzzle

• h1(n): number of misplaced tiles
• h2(n): Manhattan distance
• h3(n): Gaschnig’s
• Path-finding on a map
• Euclidean distance h 1 (S) =? 8 h 2 (S) =? 3+1+2+2+2+3+3+2 = 18 h 3 (S) =? 8

Heuristic Functions

• 8 - puzzle
  • Number of misplaced tiles
  • Manhattan distance
  • Gaschnig’s
• 8 - queen
  • Number of future feasible slots
  • Min number of feasible slots in a

row

• Min number of conflicts (in

complete assignments states)

• Travelling salesperson
  • Minimum spanning tree
  • Minimum assignment problem

C

A D

E

F

B

Best-First (Greedy) Search: f(n) = number of misplaced tiles

Greedy Best-First Search Example

Greedy Best-First Search Example

Greedy Best-First Search Example

Problems with Greedy Search

• Not complete

– Gets stuck on local minimas and plateaus

• Infinite loops

• Irrevocable

• Not optimal

• Can we incorporate heuristics in systematic

search?