1. CSE P573 Introduction to Artificial Intelligence Class 1 Planning & Search
INTRODUCE MYSELF
Relative new faculty member, but 20 years in AI research
Interests: Efficient ways to represent and reason with commonsense knowledge
GO OVER SYLLABUS
HAND OUT SEATING CHART
Henry Kautz
Autumn 2004

2. Tonight (6:40) What is artificial intelligence?
(7:00) Outline of course
(7:10) Planning
(7:20) State-space search
(7:40) Constraint satisfaction
(8:00) Exercise: creating & solving planning problems

3. What is Artificial Intelligence?

4. Outline of Course Topics Textbook Coursework Information
search & planning
game playing
logic & knowledge representation
natural language processing
probabilistic reasoning
robotics
rule learning
neural networks
reinforcement learning
local search & genetic algorithms
Textbook
Russell & Norvig, Artificial Intelligence, A Modern Approach, 2nd Ed
Skim before class; re-read afterward
Coursework
weekly assignments (80%)
take home final (20%)
Information

5. Planning Input Description of initial state of world
Description of goal state(s)
Description of available actions
Optional: Cost for each action
Output
Sequence of actions that converts the initial state into a goal state
May wish to minimize length or cost of plan

6. Classical Planning Atomic time Deterministic actions
Complete knowledge
No numeric reward (just goals)
Only planner changes world

7. Route Planning State = intersection
Operators = block between intersections
Operator cost = length of block
States = cities
Start state = starting city
Goal state test = is state the destination city?
Operators = move to an adjacent city; cost = distance
Output: a shortest path from start state to goal state
SUPPOSE WE REVERSE START AND GOAL STATES?

8. Blocks World Control a robot arm that can pick up and stack blocks.
Arm can hold exactly one block
Blocks can either be on the table, or on top of exactly one other block
State = configuration of blocks
{ (on-table G), (on B G), (clear B), (holding R) }
Operator = pick up or put down a block
(put-down R) put on table
(stack R B) put on another block
State = configuration of blocks: ON(A,B), ON(B, TABLE), ON(C, TABLE)
Start state = starting configuration
Goal state test = does state satisfy some test, e.g. “ON(A,B)”?
Operators: MOVE x FROM y TO z
or PICKUP(x,y) and PUTDOWN(x,y)
Output: Sequence of actions that transform start state into goal.
HOW HARD if don’t care about number of actions used? POLYNOMIAL
HOW HARD to find smallest number of actions? NP-COMPLETE
Suppose we want to search BACKWARDS from GOAL?
Simple if goal COMPLETELY specified
NEED to have a DIFFERENT notion of STATE if goals are PARTIALLY SPECIFIED

9. State Space Planning = Finding (shortest) paths in state graph
put-down(R)
stack(R,B)
pick-up(R)
pick-up(G)
stack(G,R)

10. STRIPS Representation
(define (domain prodigy-bw)
(:requirements :strips)
(:predicates
(on ?x ?y)
(on-table ?x)
(clear ?x)
(arm-empty)
(holding ?x))

11. goal may be a partial description
Problem Instance
(define (problem bw-sussman)
(:domain prodigy-bw)
(:objects A B C)
(:init
(on-table a) (on-table b) (on c a)
(clear b) (clear c) (arm-empty))
(:goal
(and (on a b) (on b c))))
goal may be a partial description

12. delete effects – make false
Operator Schemas
(:action stack
:parameters (?obj ?under_obj)
:precondition
(and (holding ?obj) (clear ?under_obj))
:effect
(and (not (holding ?obj))
(not (clear ?under_obj))
(clear ?obj)
(arm-empty)
(on ?obj ?under_obj)))
add effects – make true
delete effects – make false

13. Blocks World Blackbox Planner Demo

14. Planning Algorithms Direct Space-State Search Depth-First
Breadth-First
Best-First A*
Constraint Satisfaction
Davis-Putnam Procedure

15. A General Search Algorithm
Search( Start, Goal_test, Criteria )
Open = { Start }; Closed = { };
repeat
if (empty(Open)) return fail;
select Node from Open using Criteria;
if (Goal_test(Node)) return Node;
for each Child of node do
if (Child not in Closed)
Open = Open U { Child };
Closed = Closed U { Node };
Closed list optional

16. Criteria = shortest distance from Start
Breadth-First Search
Search( Start, Goal_test, Criteria )
Open = { Start }; Closed = { };
repeat
if (empty(Open)) return fail;
select Node from Open using Criteria;
if (Goal_test(Node)) return Node;
for each Child of node do
if (Child not in Closed)
Open = Open U { Child };
Closed = Closed U { Node };
Criteria = shortest distance from Start

17. Depth-First Search Search( Start, Goal_test, Criteria )
Open = { Start }; Closed = { };
repeat
if (empty(Open)) return fail;
select Node from Open using Criteria;
if (Goal_test(Node)) return Node;
for each Child of node do
if (Child not in Closed)
Open = Open U { Child };
Closed = Closed U { Node };
Criteria = most recently visited (implies: greatest distance from Start)

18. Criteria = shortest estimated (heuristic) distance to goal
Best-First Search
Search( Start, Goal_test, Criteria )
Open = { Start }; Closed = { };
repeat
if (empty(Open)) return fail;
select Node from Open using Criteria;
if (Goal_test(Node)) return Node;
for each Child of node do
if (Child not in Closed)
Open = Open U { Child };
Closed = Closed U { Node };
Criteria = shortest estimated (heuristic) distance to goal

19. Best-First with Manhattan Distance ( x+  y) Heuristic
53nd St
52nd St G
51st St S
50th St
10th Ave
9th Ave
8th Ave
7th Ave
6th Ave
5th Ave
4th Ave
3rd Ave
2nd Ave

20. Non-Optimality of Best-First
53nd St
52nd St S G
51st St
50th St
10th Ave
9th Ave
8th Ave
7th Ave
6th Ave
5th Ave
4th Ave
3rd Ave
2nd Ave

21. Properties Depth First Simple implementation (stack)
Might not terminate
Might find non-optimal solution
Breadth First
Always terminates if solution exists
Finds optimal solutions
Visits many nodes
Best First
Always terminates if heuristic is “reasonable”
Visits many fewer nodes
May find non-optimal solution

22. A*
Criteria: minimize (distance from start) (estimated distance to goal)
Implementation: priority queue
f(n) = g(n) h(n)
f(n) = priority of a node
g(n) = true distance from start
h(n) = heuristic distance to goal

23. Optimality of A*
Suppose the estimated distance is always less than or equal to the true distance to the goal
heuristic is a lower bound
heuristic is admissible
Then: when the goal is removed from the priority queue, we are guaranteed to have found a shortest path!

24. Maze Runner Demo

25. Planning Heuristics General idea: solve an easier “relaxed” problem
Blocks World
Number of blocks out of place
Ignores complication of “trapped” blocks
General STRIPS Planning
Number of false goal propositions (not admissible)
Delete all preconditions from actions; solve easier relaxed problem; use length of solution (admissible)

26. Tonight (6:40) What is artificial intelligence?
(7:00) Outline of course
(7:10) Planning
(7:20) State-space search
(7:40) Constraint satisfaction
(8:00) Exercise: creating & solving planning problems

27. Constraint Propagation Problems (CSP)

28. Constraint Satisfaction
Find assignment(s) to a set of variables that satisfies (makes true) a set of constraints on those variables
Example: variables = real numbers
constraints = linear equations
x + 2y + z = 3 x – y + z = 0 -x - y – 2z = 7
Satisfied by x=10, y=1, z=-9

29. Constraint Satisfaction
Find assignment(s) to a set of variables that satisfies (makes true) a set of constraints on those variables
Example: variable = true/false (Boolean)
constraints = propositional logic formulas
(x  y) (x  z) (y  z)
Satisfied by {x=False, y=True, z=True}
{x=True, y=False, z=True}
{x=True, y=True, z=True}

30. Constraint Satisfaction
Find assignment(s) to a set of variables that satisfies (makes true) a set of constraints on those variables
Example: variable = true/false (Boolean)
constraints = propositional logic formulas
(x  y) (x  z) (y  z)
Satisfied by {x=0, y=1, z=1}
{x=1, y=0, z=1}
{x=1, y=1, z=1}

31. Special Syntactic Forms
General propositional logic
((q r)  s))   (s  t)
Conjunction Normal Form (CNF)
( q  r  s )  ( s   t)
Binary clauses: 2 literals per clause
( q  r) ( s   t)
Unit clauses: 1 literal per clause
( q) (s)
Before going into some specific proof systems, let us
define some important special syntactic forms of
sentences in propositional logic.

32. Planning as a Logical CSP
Choose a maximum time step K
Variables for each ground fact for each time step:
(on R B 1)
(on R B 2)
(on R B 3)
Variables for each ground action for each time step:
(pick-up R 1)
(pick-up R 2)
(pick-up R 3)

33. Initial & Goal State Formulas
Assert initial state hold at time 1
Variables for each ground fact for each time step:
(on R B 1)  (on B G 1)  (on-table G 1) 
(hand-empty)  (clear R 1)
Assert goals hold at time K (e.g. 5)
(on R G 5)

34. Action Formulas
For each time step: If an action occurs, its preconditions hold
(pickup R 3)  (on-table R 3)
(pickup R 3)  (hand-empty 3)
For each time step after the first: If a fact holds, it was either just added by an action or maintained from the previous state
(on R G 3)  [ (stack R G 2) 
(maintain (on R G) 2) ]
The precondition of maintain is that fact:
(maintain (on R G) 3)  (on R G 2)
(maintain (on-table R) 3)  (on-table R 2)

35. Mutual Exclusion Formulas
Actions and maintains whose preconditions or effects conflict cannot happen at the same time
(pickup R 3)  (pickup G 3)
(pickup R 3)  (pickup B 3)
(pickup R 3)  (maintain (hand-empty) 3)
(pickup R 3)  (maintain (on-table R) 3)
That’s it!
The TRUE action variables in a satisfying solution are a plan!
SATPLAN – Winner of 2004 AI Planning System Competition

36. Solving SAT: Davis-Putnam
DPLL( wff ):
for each unit clause (P) [resp. ( P)]
set P to true [resp. to false]
simplify other clauses
if empty clause then return false
if no clause left then return solution
choose a unassigned variable Q
if DPLL( wff U {(Q)} ) return solution
else return DPLL( wff U {( Q)} )
Backtrack search over partial variable assignments
Worst case O(2n)

37. In-Class Exercise Form groups of 3 Open a browser on
Follow: Lectures & Assignments, Shakey Domain
Launch x-windows and ssh
Login to attu
Launch: xterm& xterm&
In one xterm: cd /cse/courses/csep573/04au/planning/blocks
blackbox -o domain.pddl –f bw-sussman.pddl
(8:30) SHARE representation
(8:50) SHARE solutions