Constraint Programming
2001 Edition
Jan Maluszynski and Ulf Nilsson
TCSLAB, LiU
{janma, ulfni}@ida.liu.se
http://www.ida.liu.se/~ulfni/cp2001
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Course organization
Date
11 Sep
18 Sep
25 Sep
2 Oct
9 Oct
16 Oct
23 Oct
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Content
Organization, motivation, limitations, etc.
Basics (Ch 1+2)
Finite domain constraints (Ch 3)
Logic programming (optional) (Ch 4)
Modelling with FD-constraints (Ch 5, 8)
Interval constraints
Available systems
Lect
UN
JM
JM
UN
UN
JM
PP
2
Course organization (cont’d)
Date
30 Oct
6 Nov
13 Nov
20 Nov
27 Nov
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Content
Constraints for system design
Constraint Handling Rules
Survey of HAL
Reserve
Solutions to exercises
Lect
KK
??
??
---
3
Course organization (cont)
Obligatory course assignments (23 Oct) with
deadline 20 Nov, and examination 27 Nov
Course credit points 4
Literature:
K. Marriott and P. Stuckey
Programming with Constraints: An Introduction
MIT Press, 1998.
+ handouts and on-line manuals
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A simple definition
 Constraint programming is the study of
computational systems based on constraints.
 Constraints are roughly systems of equations,
inequations and disequations over some
algebraic structure.
The idea of constraint programming is to solve
problems by encoding the problem as a set of
constraints and exploring solutions to the
constraints.
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Typical problem
Processes A-D may start at times 1,2,3,4,5,6,7
Process A uses 3 resources during 2sec
Process B uses 1 resource during 4sec
Process C uses 2 resources during 1sec
Process D uses 2 resources during 1sec
There are 4 resources
Process A must finish before C can start
When are A, B, C, D earliest finished?
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Overview
Constraints, basics, operations, domains
Focus on finite domains, intervals
Constraint logic programming
Modeling and applications
Systems
CLP-systems
Systems for defining constraints CHR, HAL
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Constraints
A constraint problem consists of a set of
problem variables ranging over some domain
and a set of constraints restricting the values
that may be assigned to the variables.
Example:
x in {1,2,3}, y in {2,3,4,5}, 2x = y
Examples of domains:
Reals/rationals, intervals, finite domains,
Booleans, sets, monoids (strings) etc
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Methods for constraint solving
Reals/rational constraints
Gauss-Jordan elimination + Simplex
Real/Rational intervals
interval narrowing, box consistency,
Gauss-Seidel elimination, interval Newton method,
Booleans
for example, operations on BDD’s
Finite domains
arc, node and path consistency methods
constraint propagation (forward checking, look-ahead)
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Optimization
Finding a solution which satisfies constraints and
minimizes/maximizes objective function
Different types
combinatorial optimization of discrete (finite
domain) variables
linear optimization for continuous variables
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Different constraint systems
Real/rational constraints: CLP(R), CLP(Q)
CLP(R), Sicstus Prolog, CHIP
Finite domains constraints: CLP(FD)
Sicstus Prolog, CHIP
Boolean constraints: CLP(B)
Sicstus Prolog, CHIP
Interval constraints: CLP(I)
CLP(BNR), Numerica, Prolog IV
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Systems discussed in the course
SICStus Prolog
Chip 5.2
Prolog IV
CHR
HAL
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The programming paradigm
Logic
programming
Constraint
satisfaction/solving
CLP
Optimization
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Logic programming
Logic (relations) for problem description
Declarative description style (problem
description separated from its solving)
Unification (a kind of constraint solving)
Builtin search
Constraint programming does not need LP !!!
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Some applications
Spatial and temporal problems
Placment and layout
Manpower planning
Scheduling
Resource allocation
Configuration management
Verification (e.g. correctness, safety+liveness)
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Placement/Layout
A window contains a number of widgets. As
the window is shrinking or growing the
widgets have to be repositioned while
satisfying certain constraints (e.g. certain
widgets must always be visible or must be in
a certain relation to other widgets). Given a
certain window size, produce a layout that
satisfies the constraints.
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Scheduling
A conference consists of 11 sessions of equal length.
The program is to be organized as a sequence of slots,
where a slot contains up to 3 parallel sessions:
1. Session 4 must take place before Session 11.
2. Session 5 must take place before Session 10.
3. Session 6 must take place before Session 11.
…
8. Session 6 must not be in parallel with 7 and 10.
9. Session 7 must not be in parallel with 8 and 9.
10. Session 8 must not be in parallel with 10.
Minimize the number of slots.
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Job shop scheduling
There are n jobs and m machines. Each job
requires execution of a sequence of operations
within a time interval, and each operation Oi
requires exclusive use of a designated machine
Mi for a specied amount of processing time pi.
Determine a schedule for production that satisfies
the temporal and resource capacity constraints.
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Manpower planning
Airport Counter Allocation problem: Allocate
enough counters and staff (the number
depends on the aircraft type) to each flight.
The counters are grouped in islands and for
each flight all assigned counters have to be in
the same island. The staff has working
regulations that must be satisfied (breaks
etc).
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Black-box vs Glass-box solvers
Most systems rely on non-extensible, black-box
constraint solvers
Efficiency unpredictable
Hard to debug
Some systems facilitate defining new constraints
and solvers (glass-box approach)
Improved control of propagation and search
Examples CHR, HAL, ...
Then again, most problems are NP-complete...
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