CSCI5240 - Combinatorial Search and Optimization with Constraints

Tutorial 11

Today covers

• Asg 10

• Propagator

• Submission Format

Knight’s Tour

move(x, y, n)?x

y

nreturns whether (x, y)

is a legal move on a n*n chessboard

Today covers

• Asg 10

• Propagator

• Submission Format

Propagator

A class to process a constraint to a particular level (of consistency). It checks and “updates” a constraint as needed

Posting a constraint is essentially posting relevant propagators

Propagator of less

less(home, x, y);

rel(home, x, IRT_LE, y);

Propagator

Constraint

Propagator

Propagator

PostingEvents to trigger propagation

Subscription: when particular events of variable happened, the propagator is called

Use IntView

View

x

IntVar x

IntVar s(x)

IntArgs t[0] = x

IntView v(x)

variable implementation

different interfaces

Access or Modifier domain through view

Accessor Modifier

x.in(int)

x.min()

x.max()

x.val()

x.size()

x.assigned()

x.eq(home, int)

x.nq(home, int)

x.le(home, int)

x.lq(home, int)

x.gr(home, int)

x.gq(home, int)

• Int::PC_INT_VAL: a value has been assigned to the variable, that is the variable is bounded

• Int::PC_INT_BND : the minimum (maximum) of the domain of the variable has increased (decreased)

• Int::PC_INT_DOM : the domain of the variable has been modified

Events

Modifying the domain

D(x) = {1, 2, 3, 4}

x.le(home, 4)

D(x) = {1, 2, 3}

Events triggered

D(x) = {2, 3}

D(x) = {2}

x.gr(home, 1)

x.nq(home, 3)Int::PC_INT_VAL

Int::PC_INT_DOMInt::PC_INT_BND

Int::PC_INT_DOMInt::PC_INT_BND

Int::PC_INT_DOMInt::PC_INT_BND

Propagator

Disposal

Cancel the subscriptions

Propagator

Copying

Propagator

not necessary

Propagator

related to a particular consistency level

AC_revise

AC Propagation on less

Domain Reduction

equivalently

Propagation

further propagation needed

propagation failure

x0.le() removes all values in variable x0 that are larger than x1.max()

no more propagations

needed

Used as constraint less

Outside the propagator class Less

now the function less() behaves as a constraint

Write your own propagator• Determine a consistency notion (e.g., AC)

• Link the propagator with events that may make the constraint “inconsistent” (e.g., Int::PC_INT_BND)

• Implement the propagate() function

examine whether a support exists for each domain value

remove unsupported domain values accordingly (x.le(), x.nq(), …)

• Modify those basic necessary components accordingly: constructor, dispose(), copy function, post()

Today covers

• Asg 10

• Propagator

• Submission Format

Submission Format

• Q1

• File: knight.cpp

• Command: ./knight

output all solutions, each in a line

Submission Format• Q2

• File: nqueen.cpp

• Command: ./nqueen -search 1 n (first-fail, mimum-domain-value)

./nqueen -search 2 n (first-fail, median-domain-value)

output the first solution

runtime and numbers of failures are recorded in tables

Submission Format• Q2

• File: nqueen_min.mzn

• Command: mzn-gecode nqueen_min.mzn -D “n=xxx;”

• Output: Output the first solution of the n-Queens problem using the first-fail, minimum-domain-value heuristic

• File: nqueen_med.mzn

• Command: mzn-gecode nqueen_med.mzn -D “n=xxx;”

• Output: Output the first solution of the n-Queens problem using the first-fail, median-domain-value heuristic

Submission Format

• Q2

• File: comparison.txt

contains all tables for comparison

Submission• 2 cpp files, 2 mzn files, and 1 txt file (result comparison)

• Strictly follow the naming rules for filenames, option values and running commands

• Include compiling and linking commands as comments at the bottom of your program file (if applicable)

• Compress all files into one

• Send to xmhuang@cse.cuhk.edu.hk

• Subject: CSCI5240-Asg9-sid

• Due: Dec 11

Grading• Modelling

Clearness (variables and domains, what do they stand for)

Correctness (size and bounds)

• Programming

Correctness (the constraint specified, running results)

Readability (use comment, delete unused code)

Programming style (good block structure)