1. Chap.12 Practical Planning
CS570 Artificial Intelligence
Kwang-hyung Lee

2. 12.1 Practical Planners
12.1 Practical Planners
Spacecraft assembly, integration, and verification
1. Hierarchical plans
2. Complex conditions
3. Time
4. Resources
Job Shop Scheduling
Scheduling for space missions
Buildings, aircraft carriers and beer factories

3. 12.2 Hierarchical Decomposition
Solution at a high level abstraction
[Go(Supermarket),Buy(Milk),Buy(Bananas),Go(Home)]
It is a long way from instruction fed to the agent’s effectors
A low level plan
[Forward(1 cm),Turn(1 deg),Forward(1 cm), ……]
Hierarchical decomposition : an abstract operator can be decomposed into a group of steps
ex) Abstract operator: Build(House)
decomposed operators : obtain Permit,Hire Builder,Construction, Pay Builder
Primitive operator:executed by the agent

4. Hierarchical planning work
12.2 Hierarchical Decomposition
Hierarchical planning work
(1) provide an extension to the STRIPS for nonprimitive operator
(2) modify the planning algorithm to allow the replacement of a nonprimitive operator with its decomposition

5. 12.2 Hierarchical Decomposition
*Extending STRIPS
(1) partition operators into primitive and nonprimitive operators
nonprimitive : Install(FloorBoards)
primitive : Hammer(Nail)
(2) decomposition method
Decompose(o,p) : An operator o is decomposed into a plan p

6. Decomposition of o into p
12.2 Hierarchical Decomposition
Decomposition of o into p
The decomposed plan p correctly implements an operator if it is complete and consistent :
1. p must be consistent (no contradiction)
2. Every effect of o must be asserted by at least one step of p
3. Every precondition of the steps in p must be achieved by a step in p or be one of the preconditions of o

7. *Modifying the planner
12.2 Hierarchical Decomposition
*Modifying the planner
Modification of planner POP into HD-POP
(1) a way to decompose nonprimitive operators
(2) the algorithm takes a plan as input, rather than just a goal

8. SELECT-NONPRIMITIVE:selects a nonprimitive
12.2 Hierarchical Decomposition
SELECT-NONPRIMITIVE:selects a nonprimitive
CHOOSE-DECOMPOSITION:picks a decomposition method
The fields of the plan are altered :
STEPS :Add steps, remove Snonprimitive
BINDINGS :Add variable binding constants
Ordering:Call RESOLVE-THREATS
Links: Si c Snonprim Si c Sm : a step of method

9. 12.3 Analysis of Hierarchical Decomposition
Abstract solution : a plan containing abstract operators, but consistent and complete
downward solution:if p is an abstract solution and there is a primitive solution
upward solution:if an abstract plan is inconsistent then no primitive sol.

10. Hierarchical planning,
12.3 Analysis of Hierarchical Decomposition
if a planner(nonhierarchical) has to generate n-step plan(where b is branching factor), it takes time O(bn)
Hierarchical planning,
sb steps at d=1
bs at d=2
ibs2 = O(bsd) (from i=1 to d)

11. Plan b is inconsistent , but it can be into a consistent plan
12.3 Analysis of Hierarchical Decomposition
The Gift of the Magic
A poor couple:he has a gold watch, she has long hair.
Plan b is inconsistent , but it can be into a consistent plan
The upward solution property does not hold

12. *Decomposition and Sharing
12.3 Analysis of Hierarchical Decomposition
*Decomposition and Sharing
Merge each step of the decomposition into existing plan
Divide-and-conquer approach:solve each subproblem and then combine it into the rest
Sharing steps while merging
Ex) enjoy a honeymoon and raise a baby
(1) decomposition
get married and go on honeymoon
get married and have a baby
(2) merge
share the step “get married”

13. *Decomposition and approximation
12.3 Analysis of Hierarchical Decomposition
*Decomposition and approximation
Hierarchical decomposition
nonprimitive operator => primitives
Hierarchical planning(approximation hierarchy, abstraction hierarchy)
It takes an operator and partitions its precondition according to their criticality level Op(ACTION:Buy(x), EFFECT : Have(x)  Have(Money), PRECOND:1:Sells(store,x)  :At(store)  :Have(Money))

14. 12.4 More Expressive Operator Description
*Conditional effects
ex) block world in section 11.8
Two operators were needed
Op(ACTION:Move(b,x,y), PRECOND : On(b,x)  Clear(b)  Clear(y), EFFECT:On(b,y)  Clear(x)  On(b,x)  Clear(y))
Op(ACTION:MoveToTable(b,x), PRECOND : On(b,x)  Clear(b), EFFECT:On(b,Table)  Clear(x)  On(b,x))
initial situation:On(A,B) goal :clear(B)

15. 12.4 More Expressive Operator Description
Move A to the table or to somewhere else? : premature commitment in Move(b,x,y)
To eliminate it, we include conditional effect “effect when condition” : Q when P Op(ACTION:Move(b,x,y), PRECOND : On(b,x)  Clear(b)  Clear(y), EFFECT:On(b,y)  Clear(x)  On(b,x)  Clear(y) when yTable)

16. *Universal quantification
12.4 More Expressive Operator Description
*Universal quantification
ex) block world
clear(b) x Block(x)  On(x,b)
ex) shopping problem
Carry(bag, x, y) : (effect) all objects that are in the bag are at y and are no longer at x. Op(ACTION:Carry(bag,x,y), PRECOND:Bag(bag)  At(bag,x), EFFECT:At(bag,y)  At(bag,x)  I Item(i)  (At(i,y)  At(y) when In(I,bag))