1 figaro yet another constraint programming library martin henz, ka boon ng national university of...

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FigaroYet Another Constraint Programming Library

Martin Henz, Ka Boon NgNational University of Singapore

Tobias MüllerUniversität des Saarlandes

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Finite Domain Constraint Programming

A technique for solving combinatorial search and optimization problems.

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S E N D+ M O R E

= M O N E Y

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S E N D+ M O R E

= M O N E Y

0S,…,Y9 S 0M 0

S…Y all different

1000*S + 100*E + 10*N + D

+ 1000*M + 100*O + 10*R + E

= 10000*M + 1000*O + 100*N + 10*E + Y

Modeling

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S E N D+ M O R E

= M O N E Y

0S,…,Y9 S 0M 0

S…Y all different

1000*S + 100*E + 10*N + D

+ 1000*M + 100*O + 10*R + E

= 10000*M + 1000*O + 100*N + 10*E + Y

S N E NN ND NM NO NR NY N

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S E N D+ M O R E

= M O N E Y

0S,…,Y9

S 0M 0

S…Y all different

1000*S + 100*E + 10*N + D

+ 1000*M + 100*O + 10*R + E

= 10000*M + 1000*O + 100*N + 10*E + Y

S {0..9}E {0..9}N {0..9}D {0..9}M {0..9}O {0..9}R {0..9}Y {0..9}

Propagate

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S E N D+ M O R E

= M O N E Y

0S,…,Y9 S 0M 0

S…Y all different

1000*S + 100*E + 10*N + D

+ 1000*M + 100*O + 10*R + E

= 10000*M + 1000*O + 100*N + 10*E + Y

S {1..9}E {0..9}N {0..9}D {0..9}M {1..9}O {0..9}R {0..9}Y {0..9}

Propagate

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S E N D+ M O R E

= M O N E Y

0S,…,Y9 S 0M 0

S…Y all different

1000*S + 100*E + 10*N + D

+ 1000*M + 100*O + 10*R + E

= 10000*M + 1000*O + 100*N + 10*E + Y

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

Propagate

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S E N D+ M O R E

= M O N E Y

0S,…,Y9 S 0M 0

S…Y all different

1000*S + 100*E + 10*N + D

+ 1000*M + 100*O + 10*R + E

= 10000*M + 1000*O + 100*N + 10*E + Y

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}

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

Labeling

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S E N D+ M O R E

= M O N E Y

0S,…,Y9 S 0M 0

S…Y all different

1000*S + 100*E + 10*N + D

+ 1000*M + 100*O + 10*R + E

= 10000*M + 1000*O + 100*N + 10*E + Y

S {9}E {4..7}N {5..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}

E = 4 E 4

Propagate

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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}

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

E = 4 E 4

Labeling

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}

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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}

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

E = 4 E 4

Propagate

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

E = 5 E 5S {9}E {5}N {6}D {7}M {1}O {0}R {8}Y {2}

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S E N D+ M O R E

= M O N E Y

CompleteSearchTree

S {9}E {4..7}N {5..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}

E = 4 E 4

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

E = 5 E 5S {9}E {5}N {6}D {7}M {1}O {0}R {8}Y {2}

E = 6 E 6

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Is That All?

• Complex

symbolic

constraints

• Programmable search

• Trailing vs copying

• Design patterns for constraint programming

• Integration of other search techniques

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

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

E = 4 E 4

S {9}E {6..7}N {7..8}D {2..8}M {1}...

E = 5 E 5S {9}E {5}N {6}D {7}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 Storeclass store {

public:

store();

var newvar(int lo,

int hi);

var getlo(var v);

var gethi(var v);

...

}

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public:

store();

var newvar(int lo,

int hi);

var getlo(var v);

var gethi(var v);

...

}

int main(...) {

store*st=new store();

...}

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public:

store();

var newvar(int lo,

int hi);

var getlo(var v);

var gethi(var v);

...

}

int main(...) {


s = st -> newvar(0,9);

...

y = st -> newvar(0,9);

...}

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public:

store();

var newvar(int lo,

int hi);

var getlo(var v);

var gethi(var v);

...

}

int main(...) {


s = st -> newvar(0,9);

...

y = st -> newvar(0,9);

all_different(st,

s,..,y);

...}

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Representing Search Treesclass node {

public: virtual node* child(store *,int)=0;

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

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

E = 4 E 4

S {9}E {6..7}N {7..8}D {2..8}M {1}...

E = 5 E 5S {9}E {5}N {6}D {7}M {1}..

E = 6 E 6

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Representing Search Treesclass naive : public node {

private: int idx;vector<var> vars;node*subtree;

public :

naive(vector<var> vs,int i,node*t) : ... {}

node* child(store*st, int i) {

if (i==0) {

st->tell(vars[idx],st->getlo(vars[idx]));

return (idx+1==var.size() ? subtree :

new naive(vars,idx+1,subtree));

} else {

st->tell(vars[idx],st->getlo(vars[idx])+1,

st->gethi(vars[idx]));

return new naive(vars,idx,subtree);

}}};

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Backtrackingmark store::mark();

void store::backtrack(mark m);

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

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

E = 4 E 4

S {9}E {6..7}N {7..8}D {2..8}M {1}...

E = 5 E 5S {9}E {5}N {6}D {7}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->mark();

try {return solve_one(s,t->child(s,0));}

catch (Failure) {

s->backtrack(m);

return solve_one(s,t->child(s,1));

}

}

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Stepping Back• Nothing new so far; Oz has programmable search

algorithms through spaces (Schulte, ICLP’97); 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, ICLP’99)

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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}...

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

E = 4 E 4

S {9}E {6..7}N {7..8}D {2..8}M {1}...

E = 5 E 5S {9}E {5}N {6}D {7}M {1}..

E = 6 E 6

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Copying Stores• Simply copy the store with all variables and

constraints:store::store(const store*);

• But: nodes refer to variables; their addresses change!

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Labeling Refers to Variablesclass naive : public node {

private: int idx;vector<var> vars;node*subtree;

public :

naive(vector<var> vs,int i,node*t) : ... {}

node* child(store*st, int i) {

if (i==0) {

st->tell(vars[idx],st->getlo(vars[idx]));

return (idx+1==vars.size() ? subtree :

new naive(vars,idx+1,subtree));

} else {

st->tell(vars[idx],st->getlo(vars[idx])+1,

st->gethi(vars[idx]));

return new naive(vars,idx,subtree);

}}};

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Search Refers to Marks



mark m = s->mark();


catch (Failure) {

s->backtrack(m);

return solve_one(s,t->child(s,1));

}

}

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Indirect Addressing

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

Now nodes don’t need to care, whether they work on original or copy.

12345...

12345...

12345...

vars props trail

store

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Depth-first Search (copying)



store s2 = new store(s);


catch (Failure) {

return solve_one(s2,t->child(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->one_step())

if (n==success_node) break;

return n; }

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Stepping Back

• Design patterns for tree search

• More in paper: A Search Toolkit for Constraint Programming (PADL’00)

• Moving on: Constraint programming is just one technique: local search?

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Global Search v1 v2,v1 v2,v1 v2

FF

FT

TF

TT

F? ?T

T??F

??

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FF

FT

TF

TT

F? ?T

T??F

??

v1=F

v1=T

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FF

FT

TF

TT

F? ?T

T??F

??

v1=F

v1=T

v2=F

v2=T

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FF

FT

TF

TT

F? ?T

T??F

??

v1=F

v1=T

v2=F

v2=T

v2=F

v2=T

solution

Search Tree

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Local Search v1 v2,v1 v2,v1 v2

FF

FT

TF

TT

F? ?T

T??F

??

v1=F

v1=T

v2=F

v2=T

v2=F

v2=T

solution

consider only fullassignments ofvariables to values

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Local Search

FF

FT

TF

TT

Search Space

v1 v2,v1 v2,v1 v2

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Local Search

v1 v2,v1 v2,v1 v2

FF

FT

TF

TTinitial assignment

neighborhood

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Local Search

local move

FF

FT

TF

TT

v1 v2,v1 v2,v1 v2

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Local Search

v1 v2,v1 v2,v1 v2

local move

FF

FT

TF

TT

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Local Search

v1 v2,v1 v2,v1 v2

solution found

FF

FT

TF

TT

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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

1 figaro yet another constraint programming library martin henz, ka boon ng national university of...

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