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ID2204: Constraint Programming

Christian Schulte!"!#$%&'()&#*"'

Software and Computer SystemsSchool of Information and Communication TechnologyKTH Royal Institute of TechnologyStockholm, Sweden

mailto:[email protected]

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1030405416 *?110@4/012)7=,&8+&9')A.=-%+$2)*7B2)CBD 3E

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Program model as scriptdeclare variablespost constraints (creates propagators)define branching

Solve scriptbasic search strategyGist: interactive visual search

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Script is class inheriting from class Spacemembers store variables regarded as solution

Script constructorinitialize variablespost propagators for constraintsdefine branching

Copy constructor and copy functioncopy a Script object during search

Exploration takes Script object as inputreturns object representing solution

Main functioninvokes search engine

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array of integer variables stores solution

1030405416 *?110@4/012)7=,&8+&9')A.=-%+$2)*7B2)CBD 13

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constructor: initialize variables, post

constraints, define branching

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copy constructor and copy function

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J variables created in this script (space)

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8 variables

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take values between 0 and 9

(digits)

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J refer to variables by their letters

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1030405416 *?110@4/012)7=,&8+&9')A.=-%+$2)*7B2)CBD 1K

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Defined in namespace 7($,'(

Check documentation for available constraints

Take script reference as first argumentwhere is the propagator for the constraint to be posted!script is a subclass of Space (computation space)

1030405416 *?110@4/012)7=,&8+&9')A.=-%+$2)*7B2)CBD 50

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Equations of the formc1 x1 cn xn = dinteger constants: ci and dinteger variables: xi

In Gecode specified by arraysintegers (?#.A4+2K civariables (?#.@34A443;F)?#.@34A4+2K xi

Not only equations?Z[\a]F)?Z[\X]F)?Z[\baF)?Z[\7ZF)?Z[\b]F)?Z[\7]equality, disequality, inequality (less, greater, less or equal, greater or equal)

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1030405416 *?110@4/012)7=,&8+&9')A.=-%+$2)*7B2)CBD 51

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Other options for posting linear constraints are available: minimodeling support

linear expressionsBoolean expressionsmatrix classes

See the examples that come with Gecode

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1030405416 *?110@4/012)7=,&8+&9')A.=-%+$2)*7B2)CBD 56

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Which variable to choosegiven order ?X[\@AZ\XhXasmallest size ?X[\@AZ\9?ga\:?Xsmallest minimum ?X[\@AZ\:?X\:?X

How to branch: which value to choosetry smallest value ?X[\@Ab\:?Xsplit (lower first) ?X[\@Ab\9Gb?[\:?X

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update all variables needed

for solution

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create a new copy of the space

during cloning

1030405416 *?110@4/012)7=,&8+&9')A.=-%+$2)*7B2)CBD 5K

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Required during explorationbefore starting to guess: make copywhen guess is wrong: use copydiscussed later

Copy constructor and copy function neededcopy constructor is specific to scriptupdates (copies) variables in particular

1030405416 *?110@4/012)7=,&8+&9')A.=-%+$2)*7B2)CBD @0

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Always same structure

Important!must update the variables of a script!

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Variablesdeclare as membersinitialize in constructorupdate in copy constructor

Posting constraintsCreate branchingProvide copy constructor and copy function

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Returning solutions one by one for scriptBk9 depth-first search`A` branch-and-boundZ(2.34.F)bB9

Interactive, visual search7"2.

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create root space for search

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create search engine (takes

clone of 5)

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root space not any longer

needed

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search first solution and

print it

1030405416 *?110@4/012)7=,&8+&9')A.=-%+$2)*7B2)CBD 60

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1030405416 *?110@4/012)7=,&8+&9')A.=-%+$2)*7B2)CBD 63

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A graphical tool for exploring the search treeexplore tree step by steptree can be scaleddouble-clicking node prints information: inspectionsearch for next solution, all solutions

Best to play a little bit by yourselfhide and unhide failed subtrees

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>&8+)A.,$$'8="+

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Find distinct digits for letters, such that

and +,-./ maximal

0.-1

2 +,03

4 +,-./

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Similar, please try it yourself at homeIn the following, referred to by 9(#':,2.:,#(;

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Principlefor each solution found, constrain remaining search for better solution

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Argument = refers to so far best solutiononly take values from =never mix variables!

Invoked on object to be constrained

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Result-only search enginesBk9F)`A`

Interactive search engine7"2.

Best solution search uses constrain-method for posting constraintSearch engine independent of script and constrain-method

*hwwlqj 3udfwlfdo«...

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