Figaro Yet Another Constraint Programming Library

1
FigaroYet Another Constraint Programming Library

• Martin Henz, Ka Boon Ng
• National University of Singapore
• Tobias Müller
• Universität des Saarlandes

2
Finite Domain Constraint Programming

• A technique for solving combinatorial search and
  optimization problems.

3
S E N D M O R E M O N E Y
4
S E N D M O R E M O N E Y
Modeling

• 0?S,,Y?9
• S ? 0
• M ? 0
• SY all different
• 1000S 100E
  10N D
• 1000M 100O 10R E
• 10000M 1000O 100N 10E Y

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S E N D M O R E M O N E Y
S ? N E ? N N ? N D ? N M ? N O ? N R ? N Y ? N

• 0?S,,Y?9
• S ? 0
• M ? 0
• SY all different
• 1000S 100E
  10N D
• 1000M 100O 10R E
• 10000M 1000O 100N 10E Y

6
S E N D M O R E M O N E Y
Propagate
S ? 0..9 E ? 0..9 N ? 0..9 D ? 0..9 M ?
0..9 O ? 0..9 R ? 0..9 Y ? 0..9

• 0?S,,Y?9
• S ? 0
• M ? 0
• SY all different
• 1000S 100E
  10N D
• 1000M 100O 10R E
• 10000M 1000O 100N 10E Y

7
S E N D M O R E M O N E Y
Propagate
S ? 1..9 E ? 0..9 N ? 0..9 D ? 0..9 M ?
1..9 O ? 0..9 R ? 0..9 Y ? 0..9

• 0?S,,Y?9
• S ? 0
• M ? 0
• SY all different
• 1000S 100E
  10N D
• 1000M 100O 10R E
• 10000M 1000O 100N 10E Y

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S E N D M O R E M O N E Y
Propagate
S ? 9 E ? 4..7 N ? 5..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8

• 0?S,,Y?9
• S ? 0
• M ? 0
• SY all different
• 1000S 100E
  10N D
• 1000M 100O 10R E
• 10000M 1000O 100N 10E Y

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S E N D M O R E M O N E Y
S ? 9 E ? 4..7 N ? 5..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8
Labeling
E ? 4
E 4
S ? 9 E ? 4..7 N ? 5..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8
S ? 9 E ? 4..7 N ? 5..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8

• 0?S,,Y?9
• S ? 0
• M ? 0
• SY all different
• 1000S 100E
  10N D
• 1000M 100O 10R E
• 10000M 1000O 100N 10E Y

10
S E N D M O R E M O N E Y
S ? 9 E ? 4..7 N ? 5..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8
Propagate
E ? 4
E 4
S ? 9 E ? 5..7 N ? 6..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8

• 0?S,,Y?9
• S ? 0
• M ? 0
• SY all different
• 1000S 100E
  10N D
• 1000M 100O 10R E
• 10000M 1000O 100N 10E Y

11
S E N D M O R E M O N E Y
Labeling
S ? 9 E ? 4..7 N ? 5..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8
E ? 4
E 4

S ? 9 E ? 5..7 N ? 6..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8
E 5
E ? 5
S ? 9 E ? 5..7 N ? 6..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8
S ? 9 E ? 5..7 N ? 6..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8
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S E N D M O R E M O N E Y
Propagate
S ? 9 E ? 4..7 N ? 5..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8
E ? 4
E 4

S ? 9 E ? 5..7 N ? 6..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8
E 5
E ? 5
S ? 9 E ? 5 N ? 6 D ? 7 M ? 1 O ? 0 R
? 8 Y ? 2
S ? 9 E ? 6..7 N ? 7..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8
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S E N D M O R E M O N E Y
Complete Search Tree
S ? 9 E ? 4..7 N ? 5..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8
E 4
E ? 4

S ? 9 E ? 5..7 N ? 6..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8
E 5
E ? 5
S ? 9 E ? 5 N ? 6 D ? 7 M ? 1 O ? 0 R
? 8 Y ? 2
S ? 9 E ? 6..7 N ? 7..8 D ? 2..8 M ?
1 O ? 0 R ? 2..8 Y ? 2..8
E ? 6
E 6


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Is That All?
S ? 9 E ? 4..7 N ? 5..8 D ? 2..8 M ?
1...
E 4
E ? 4

• Complex
• symbolic
• constraints
• Programmable search
• Trailing vs copying
• Design patterns for constraint programming
• Integration of other search techniques

S ? 9 E ? 5..7 N ? 6..8 D ? 2..8 M ?
1...
E 5
E ? 5
S ? 9 E ? 5 N ? 6 D ? 7 M ? 1..
S ? 9 E ? 6..7 N ? 7..8 D ? 2..8 M ?
1...
E 6
E ? 6


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FD(CP) Languages and Libraries

• Languages
• CLP(FD)
• Eclipse, CHIP
• CLAIRE new language
• Oz new language
• Libraries
• PECOS LISP
• Ilog Solver C
• Figaro C, under development

Prolog based
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Design Issues

• Languages
• CLP(FD)
• Eclipse, CHIP
• CLAIRE
• Oz
• Libraries
• PECOS
• Ilog Solver

• Syntax
• Integration with
• application programming
• Programming
• propagation algorithms
• Programming search
• strategies
• Programming search
• algorithms

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Representing the Constraint Store

• class store
• public
• store()
• var newvar(int lo,
• int hi)
• var getlo(var v)
• var gethi(var v)
• ...

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Representing the Constraint Store

• class store
• public
• store()
• var newvar(int lo,
• int hi)
• var getlo(var v)
• var gethi(var v)
• ...

int main(...) storestnew store()
...
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Representing the Constraint Store

• class store
• public
• store()
• var newvar(int lo,
• int hi)
• var getlo(var v)
• var gethi(var v)
• ...

int main(...) storestnew store() s
st -gt newvar(0,9) ... y st -gt
newvar(0,9) ...
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Representing the Constraint Store

• class store
• public
• store()
• var newvar(int lo,
• int hi)
• var getlo(var v)
• var gethi(var v)
• ...

int main(...) storestnew store() s
st -gt newvar(0,9) ... y st -gt
newvar(0,9) all_different(st,
s,..,y) ...
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Representing Search Trees

• class node
• public virtual node child(store ,int)0

S ? 9 E ? 4..7 N ? 5..8 D ? 2..8 M ?
1...
E 4
E ? 4

S ? 9 E ? 5..7 N ? 6..8 D ? 2..8 M ?
1...
E 5
E ? 5
S ? 9 E ? 5 N ? 6 D ? 7 M ? 1..
S ? 9 E ? 6..7 N ? 7..8 D ? 2..8 M ?
1...
E 6
E ? 6


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Representing Search Trees

• class naive public node
• private int idxvectorltvargt varsnodesubtree
• public
• naive(vectorltvargt vs,int i,nodet) ...
• node child(storest, int i)
• if (i0)
• st-gttell(varsidx,st-gtgetlo(varsidx))
• return (idx1var.size() ? subtree
• new naive(vars,idx1,subtree))
• else
• st-gttell(varsidx,st-gtgetlo(varsidx)1,
• st-gtgethi(varsidx))
• return new naive(vars,idx,subtree)

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Backtracking

• mark storemark()
• void storebacktrack(mark m)

S ? 9 E ? 4..7 N ? 5..8 D ? 2..8 M ?
1...
E 4
E ? 4

S ? 9 E ? 5..7 N ? 6..8 D ? 2..8 M ?
1...
E 5
E ? 5
S ? 9 E ? 5 N ? 6 D ? 7 M ? 1..
S ? 9 E ? 6..7 N ? 7..8 D ? 2..8 M ?
1...
E 6
E ? 6


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Depth-first Search (backtracking)

• node solve_one(store s,node t)
• if (t NULL) return t
• mark m s-gtmark()
• try return solve_one(s,t-gtchild(s,0))
• catch (Failure)
• s-gtbacktrack(m)
• return solve_one(s,t-gtchild(s,1))

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Stepping Back

• Nothing new so far Oz has programmable search
  algorithms through spaces (Schulte, ICLP97)
  Ilog Solver has IlcManager objects.
• But
• lean stores
• nodes as an abstraction for programming search
  strategies
• more on the basic data structures in the
  proceedings
• moving on Trailing vs. Copying (Schulte, ICLP99)

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Trailing vs Copying

• Trail and backtrack
• Copy and abandon

S ? 9 E ? 4..7 N ? 5..8 D ? 2..8 M ?
1...
E 4
E ? 4

S ? 9 E ? 5..7 N ? 6..8 D ? 2..8 M ?
1...
E 5
E ? 5
S ? 9 E ? 5 N ? 6 D ? 7 M ? 1..
S ? 9 E ? 6..7 N ? 7..8 D ? 2..8 M ?
1...
E 6
E ? 6


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Copying Stores

• Simply copy the store with all variables and
  constraints
• storestore(const store)
• But nodes refer to variables
  their addresses change!

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Labeling Refers to Variables

• class naive public node
• private int idxvectorltvargt varsnodesubtree
• public
• naive(vectorltvargt vs,int i,nodet) ...
• node child(storest, int i)
• if (i0)
• st-gttell(varsidx,st-gtgetlo(varsidx))
• return (idx1vars.size() ? subtree
• new naive(vars,idx1,subtree))
• else
• st-gttell(varsidx,st-gtgetlo(varsidx)1,
• st-gtgethi(varsidx))
• return new naive(vars,idx,subtree)

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Search Refers to Marks

• node solve_one(store s,node t)
• if (t NULL) return t
• mark m s-gtmark()
• try return solve_one(s,t-gtchild(s,0))
• catch (Failure)
• s-gtbacktrack(m)
• return solve_one(s,t-gtchild(s,1))

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Indirect Addressing
store

• only use indices in arrays to address variables,
  propagators and marks

vars
props
trail
1 2 3 4 5 . . .
1 2 3 4 5 . . .
1 2 3 4 5 . . .
Now nodes dont need to care, whether they work
on original or copy.
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Depth-first Search (copying)

• node solve_one(store s,node t)
• if (t NULL) return t
• store s2 new store(s)
• try return solve_one(s,t-gtchild(s,0))
• catch (Failure)
• return solve_one(s2,t-gtchild(s,1))

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Stepping Back

• Indirect addressing allows copy and
  trailing-based search
• Possibly interesting combinations of the two to
  be explored
• Moving on Memory policy just one dimension in
  the design space for search algorithms.

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Dimensions in the Design Space for Search
Algorithms

• Exploration depth-first search,
  limited-discrepancy search,...
• Memory policy copying, trailing,...
• Optimization branch-and-bound, restart
  optimization,...
• Interaction first, last, all solution search,
  tracing,...
• Visualization Oz Explorer like search tree
  visualization

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STK Software Engineering of Inference Engines

• STK originally developed for Oz
• Allows to separate design dimensions into modules
• Software architecture ensures reusability of
  components
• STK ideas will be at the heart of Figaro

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Example Exploration and Interaction

• Exploration is defined by a class that extends
  the abstract class exploration.
• class exploration
• public virtual node one_step()0

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Example Exploration and Interaction

• Exploration is defined by a class that extends
  the abstract class exploration.
• class exploration
• public virtual node one_step()0
• Interaction calls one_step according to the
  desired mode of interaction.
• node first(exploration e)
• node n
• while (n e-gtone_step())
• if (nsuccess_node) break
• return n

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Stepping Back

• Design patterns for tree search
• More in paper A Search Toolkit for Constraint
  Programming (PADL00)
• Moving on Constraint programming is just one
  technique local search?

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Global Search
??

• v1 ? v2,v1 ? v2,v1 ? v2

F?
?T
T?
?F
FT
TT
FF
TF
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Global Search
??
v1F

• v1 ? v2,v1 ? v2,v1 ? v2

F?
?T
v1T
T?
?F
FT
TT
FF
TF
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Global Search
??
v1F

• v1 ? v2,v1 ? v2,v1 ? v2

F?
?T
v1T
T?
v2T
?F
v2F
FT
TT
FF
TF
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Global Search
??
v1F

• v1 ? v2,v1 ? v2,v1 ? v2

F?
?T
v1T
T?
v2T
?F
Search Tree
v2F
FT
v2T
TT
FF
v2F
solution
TF
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Local Search
??
v1F

• v1 ? v2,v1 ? v2,v1 ? v2

F?
?T
v1T
T?
v2T
?F
consider only full assignments of variables to
values
v2F
FT
v2T
TT
FF
v2F
solution
TF
43
Local Search

• v1 ? v2,v1 ? v2,v1 ? v2

FT
Search Space
TT
FF
TF
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Local Search

• v1 ? v2,v1 ? v2,v1 ? v2

neighborhood
FT
initial assignment
TT
FF
TF
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Local Search

• v1 ? v2,v1 ? v2,v1 ? v2

FT
TT
FF
local move
TF
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Local Search

• v1 ? v2,v1 ? v2,v1 ? v2

FT
TT
FF
TF
local move
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Local Search

• v1 ? v2,v1 ? v2,v1 ? v2

FT
TT
FF
solution found
TF
48
Observations

• Data structures needed for constraint programming
  are the same as in local search.
• Integration of CP and LS has been approached
  before.
• Stephen Won, MS thesis supervised by Jimmy Lee
  (1997)

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Stepping Back (for good)

• Viewing constraint programming as a collection of
  design patterns.
• Flexible memory policy through indirect
  addressing
• Figaro initiative
• library for discrete problem solving and
  optimization
• local search and constraint programming (LP,IP?)
• designed by researchers for researchers
• open source, current contributors N U Singapore,
  partners CUHK, PSL

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Figaro (very last slide)

• Figaro, an offspring of Mozart
• F I nite domain
• GA dget for combinatorial
• p RO blem solving