Constraint Logic Programming Applications

1
Constraint Logic ProgrammingApplications

• Mr. I. Sakellariou
• Intelligent Systems Knowledge Processing Group
  (ISKP)
• http//iskp.csd.auth.gr
• Department of Informatics, Aristotle University
  of Thessaloniki, Greece.

2
Outline

• CLP Applications in Industry
• ISKP Group efforts
• University Exam Scheduling
• Distributed CSP CSPCONS
• Workforce Management
• Distributed Singleton Consistency
• Protein Structure Prediction

3
CLP Applications

• The CLP paradigm has enjoyed a large number of
  applications.
• Commercially available platforms
• SICStus Swedish Institute of Computer Science
• ECLiPSe Originally ECRC, IC-Parc, now CISCO
• CHIP ECRC, now COSYTEC
• There is an increasing number of applications,
  shown by the fact that annual conferences are
  devoted to it (PADP, ICLP, etc).

4
Some Examples of Real World CLP Applications (1/3)

• Options Trading (stock market)
• OTAS system
• Constraint Based Spreadsheets
• Short Term Planning System at Renault
• Cutting stock

5
Some Examples of Real World CLP Applications (2/3)

• Scheduling
• Scheduling activities in Energy Distribution
  network in Spain (PlaNets).
• Planning and Scheduling Aircraft Manufacture at
  Dassault Aviation
• Finds schedules of production lines to meet
  requirements.

6
Some Examples of Real World CLP Applications (3/3)

• Allocation
• aircraft stand allocation (Roissy airport at
  Paris)
• ships allocation in harbour (Hong Kong
  International Terminals)
• Crew rotation
• Nurse planning package (GYMNASTE) assigns shifts
  according to work regulations, laws and
  individual wishes.
• Crew assignment to flights (SAS, British Airways,
  Swissair, TGV Trains FRANCE)

7
CLP Applications in ISKP group
8
Research in ISKP group
9
University Exam Scheduling Application
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Exam Scheduling

• Common problem to University Departments.
• Involves finding an allocation of exams to
  available exam halls, allocation of invigilators,
  etc.
• A number of constraints have to be satisfied.

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Exam Scheduling ProblemResources Data

• General Time related resources
• Starting date Ending Date of exam period
• Holidays
• Exam halls
• Name, capacity, etc
• Availability
• Invigilators and exam setters
• Modules,
• Availability
• Course related
• Semester, number of students participating, etc

12
Exam Scheduling ProblemConstraints

• Exam setters and invigilators
• Invigilator cannot be in two halls
  simultaneously!
• Availability
• Maximum number of exams/day
• Exam halls
• Capacity constraints
• Hall availability
• Module related
• Avoid scheduling two exams of the same semester
  on the same time slot.
• Avoid scheduling same semester exams in the same
  day.

13
Modeling

• Common approach
• Divide Available time periods in slots.
  (1-hour/2-hour, etc)
• Assign an integer to each time slot - exam Hall
  pair.
• Hall 1 1st Exam Day 900-1000 ? 1
• Hall 2 1st Exam Day 900-1000 ? 2
• Easier to state difference constraints.
• Easier to state Hall/Exam setter availabilities
• Easier to state capacity constraints.

14
ECLiPSe-JAVA Implementation

• Constraint Solving
• ECLiPSe IC Library (Integer Constraints)
• Interface JAVA

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Entering Information about Classrooms (Exam Halls)
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Schedule
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Distributed Constraint Logic Programming
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Distributed CLP (Our Current Research)

• The need for distributed constraint logic
  programming systems derives from the fact that
• more efficient implementations
• natural representation of problems that are
  distributed in nature
• production planning in a factory in which
  independent departments must meet their local
  constraints and at the same time co-operate to
  achieve global constraints
• university course scheduling in the case that
  university departments share resources (classes,
  labs, etc)
• implementation of multi-agent systems based on
  CLP.

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Building DCSP Applications

• Currently there are only a few Logic Programming
  platforms that address the problem of building
  DCSP applications (eg. CIAO, OZ).
• Such a platform should include
• Sufficient Communication Primitives
• Support for Constraint Programming
• The Communication Sequential Prolog (CSPCONS)
  addresses both issues.
• Suitable platform for the development and testing
  of distributed constraint applications.
• Developed under the Bilateral Cooperation
  Greece-Hungary 2000-2002 (AUTH-ML).

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A Platform for DCLP Applications CSPCONS
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CSPCONS (1/3)

• Our approach involves extending the Communicating
  Sequential Prolog II System to support Constraint
  Logic programming (CSPCONS).
• CS-Prolog II, is
• a UNIX implementation of the standard Prolog that
  was developed by ML (Hungary).
• originally developed for transputers (parallel
  processors)
• was ported to UNIX during an EU funded
  INCO-Copernicus project (ExperNet).

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CSPCONS (2/3)

• This approach was followed because CSP II offers
  among other things
• Parallelism through the use of independent
  sequential Prolog processes that communicate via
  a message passing mechanism over channels.
• Real time features
• TCP/IP communication capabilities between other
  instances of CSP-II programs and external
  applications
• Implementation is robust and has been tested on a
  real world application.

23
CSPCONS Processes

• Self driven execute a single Prolog call.
• Event driven respond to events.
• Inter-Process Communication
• Message Passing, though channels.
• Event Passing, by explicit (programmer) or
  implicit (system) event generation.
• TCP/IP Communication
• Extension of inter-process message passing
  scheme, but asynchronous

24
CSPCONS Application
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TCP/IP Mechanism Notions

• CSP-Port, entry point for all incoming messages
• Connection, where all outgoing messages are
  directed.
• Both are linked with local channels.

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Constraints in CSPCONS

• The original language has been extended to
  provide support for constraints.
• Constraints are being incorporated as external
  libraries, implemented in C, thus allowing the
  implementation of any constraint domain.
• Constraint libraries for linear and finite
  domains have been developed.

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CSPCONS Constraints Schema

• CSP-Process (core) handles all Prolog specific
  tasks, maintains the solver instances and
  dispatches all constraint related calls to the
  solver. Each core can be connected to up to 4
  solvers.
• The Solver performs all constraint satisfaction
  tasks, ie. maintains the set of constraints, the
  variable domains and applies when appropriate the
  consistency algorithms. The Solver returns the
  results to the core.

(Up to 4 Solver Libraries)
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Current Status and Future Work

• Current version of CSPCONS, includes
• Finite Domain Solver (AC-2000 propagation,
  all_different global constraint, etc).
• Experimental Linear Equations Solver
• Platforms
• Solaris
• Linux
• Windows
• Future Work
• Improve Solver
• Include more global constraints
• Test on more Applications

29
Distributed Workforce Management (DIWOMS)
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Distributed Workforce Management System (DIWOMS)
(1/2)

• Problem definition
• allocation of jobs to workers, in such a way that
  the total number of assigned tasks is maximised,
  with the minimum transition time between tasks.
• Multiple time constraint travelling salesman
  problem
• Problem Data
• 250 jobs, geographically distributed, 118
  technicians, with different attributes (skill,
  start/end time), 11 bases where the technicians
  belong to, skill constraints for each job, travel
  time and a cost function determining the quality
  of the solution.

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The BT Problem
Spatial visualization of Jobs, Bases and Personnel
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A Three Phase Solving Approach

• A clustering phase
• Partitioning the problem to a number of
  subproblems of less complexity.
• Each subproblem is assigned to an agent.
• A solving phase
• Agents independently solve each subproblem.
• A patching phase
• Agents cooperate to find the final job
  assignments.

33
Implementation

• Each base is modeled as an agent.
• All agents execute the same algorithm.
• Each agent is implemented as a CSPCONS process.
• Communication during the clustering and
  optimization phase is achieved via channels.
• Solution phase uses the CLP primitives of
  CSPCONS
• find_job_details(JobID,Start,Duration)-
  job(JobID,Type,Duration,_), job_limits(Type,MinSta
  rt,MaxStart), clp_constraint(Start in
• MinStart..MaxStart).

34
Results

• Implemented in a Sun E 450
• 4 Processors, 2GB RAM, Solaris 2.8
• Solution is near the optimal reported in the
  literature.

35
Final Solution (technician tours) and Clusters
(generated during the first phase) visualized
over the problem area
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Distributed Singleton Consistency (DSAC)
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Singleton Arc Consistency

• Singleton Arc Consistency (SAC)
• (Debruyne-Bessière 1997)
• Basic Idea
• For every value di of a variable xi that is
  consistent, the sub-problem P obtained by
  restricting the domain Di to di is consistent.
• Any value that fails to satisfy the above is
  removed from the domain, i.e. if the sub-problem
  is determined to be inconsistent then the value
  is removed.
• Characteristics of the Algorithm
• Enforces stronger consistency than most AC
  algorithms, i.e. removes a larger set of values.
  
• Costly application.
• Solution Distributed execution of the SAC
  algorithm.

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Distributed Singleton Arc Consistency

• Reduce execution time by distributing work to be
  done to a number of agents.
• A society of agents apply the SAC algorithm on
  the problem variables.
• Each agent applies SAC on a subset of the
  original set of variables (responsibility set)
• Removed values are communicated via message
  passing.
• Different Broadcasting Policies can be applied.
• A Scheduler is responsible for detecting
  termination.

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DSAC Agents
Termination Control Messages
Value Removal Messages
Responsibility Set
40
Impementing DSAC

• First Version
• Java Constraint Library for implementing
  constraints.
• Pathwalker lib for communication between agents.
  
• Experiments
• 3 Sun Ultra-5
• 1 Sun Enterprise 450 (4 Processors)

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SpeedUp
42
Implementation in CSPCONS

• The DSAC algorithm is simple and requires no
  major modifications to the underlying
  implementation platform.
• Network of SUN Workstations
• All measurements concern wall time.
• Problems
• Golomb Rulers
• A set of m different integers such that the
  m(m-1) differences between the integers are
  distinct.
• The length of the ruler is minimum.
• Quasigroup Completion
• Completing a partially filled Latin Square.

43
Experimental Results Golomb Rulers
44
Experimental Results Latin Squares
45
Conclusions and Future Work

• Distributed Singleton Consistency improves
  significantly the performance of the algorithm.
• Simple but efficient.
• Easy to implement.
• Future Work
• More "intelligent" assignment of responsibility
  sets.
• Heuristics during the application of SAC in each
  agent.

46
Protein Structure Prediction in CLP

• A Recent Approach

47
Recent Approach to Protein Folding

• The approach follows a lattice model (fcc).
• Proposed in
• A. Dovier, M. Burato, and F. Fogolari.Using
  Secondary Structure Information for Protein
  Folding in CLP(FD). In Proc. of Workshop on
  Functional and Constraint Logic Programming,
  ENTCS vol. 76, 2002.
• A. Dal Palù, A. Dovier, and F. Fogolari.
  Constraint Logic Programming approach to protein
  structure prediction. BMC Bioinformatics 2004,
  5186, 30 November 2004.
• A. Dal Palu', A. Dovier, and E. Pontelli.
  Heuristics, Optimizations, and Parallelism for
  Protein Structure Prediction in CLP(FD). To
  appear in PPDP'05.

48
Proteins

• A protein is a list of linked units called
  aminoacids.
• There are 20 different kinds of aminoacids
• Alanine (A) Cysteine (C) Aspartic Acid (D)
  Glutamic Acid (E) Phenylalanine (F) Glycine (G)
  Histidine (H) Isoleucine (I) Lysine (K) Leucine
  (L) Methionine (M) Asparagine (N) Proline (P)
  Glutamine (Q) Arginine (R) Serine (S) Threonine
  (T) Valine (V) Tryptophan (W) Tyrosine (Y)
• Typical length of a protein is 100-500 units.
• Protein Structure Prediction
• Predicting the 3D structure of proteins, given
  their primary and secondary structure

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Protein Structure

• Protein Structure Prediction
• Predicting the 3D structure of proteins, given
  their primary and secondary structure
• Primary structure
• sequence of aminoacids (residues)
• Secondary Structure
• a-helix, ß-sheets
• ssbonds (disulfide bridges from cystein residues)
• Tertiary Structure
• Admissible spatial positions of each aminoacid in
  3D
• State of minimum free energy (Anfinsen
  thermodynamic hypothesis)

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Optimization Problem

• Optimization Problem
• Since the tertiary structure is the state with
  the minimum free energy
• Define the energy function, that in general
  depends on distances between residues and their
  type.
• Minimize the energy function
• Assumptions
• Aminoacids are considered as a whole (sphere).
• Consecutive amino acids have a fixed distance.
• Energy function is the sum of energy
  contributions of non-consecutive aminoacids.
• Energy contribution given by a potentials matrix
  for each combination of aminoacids.

51
Potentials Matrix (part)
52
Problem Description-Constraints

• Given a sequence of aminoacids that constitute
  the protein.
• s1, s2, s3, ... sn
• For aminoacid si define a point ltx,y,zgt that
  represents its position in 3D space.
• x,y,z real numbers
• x,y,z integer numbers (lattice models)
• Two constraints
• consecutive aminoacids in chain have a fixed
  distance (next )
• two aminoacids cannot have the same position

53
Problem Description-Energy Function

• Non-consecutive aminoacids contribute to the
  energy when are in contact, i.e. have a distance
  less than a given threshold (are in contact).
• Energy function

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Modeling Space-Lattice Model

• Face-Centered Cubic Lattice Model (fcc model)
  (G. Raghunathan and R. L. Jernigan. 1997)
• Cubes of size 2.
• Distance between residues ?2
• Residues are on
• Central point of face
• Vertices

55
Closer Look to the FCC model
56
Constraints

• X,Y,Z variables for each aminoacid.
• Position Restrictions
• xyz is even.
• Given two consecutive aminoacids si, si1 (next)
• xi-xi1 ? 0,1, yi-yi1 ? 0,1, zi-zi1 ?
  0,1
• xi-xi1 yi-yi1 zi-zi1 2
• Two non-consecutive amino acids must have a
  distance of more than a lattice unit
• (xi-xj)2 (yi-yj)2 (zi-zj)2 gt 2

57
Constraints

• Admissible angles between 3 consecutive
  aminoacids
• FCC model 60, 90, 120, 180
• Allowed 90, 120 (volumetric energetic cons)
• Constraint concerning angles
• scalar product between vectors Vi-1,i and Vi,i1
• Scalar product should be 0,1
• Constraints concerning secondary structure
• two animoacids with an ss-bond must be close.
• strands
• helix

58
Example of Modeling A Constraint in CLP(FD) (1/2)

• The Next Constraint
• next(X1,Y1,Z1,X2,Y2,Z2)-
• domain(DX,DY,DZ,0,1),
• DX X1-X2,
• DY Y1-Y2,
• DZ Z1-Z2,
• DXDYDZ 2.

59
Example of Modeling A Constraint in CLP(FD)

• The non-next constraint
• non_next(X1,Y1,Z1,X2,Y2,Z2)-
• Dx (X1-X2) (X1-X2),
• Dy (Y1-Y2) (Y1-Y2),
• Dz (Z1-Z2) (Z1-Z2),
• sum(Dx,Dy,Dz, gt, 2).

60
SS Bond Constraints

• SS Bond
• ssbond(X1,Y1,Z1,X2,Y2,Z2)-
• Dx abs(X1-X2),
• Dy abs(Y1-Y2),
• Dz abs(Z1-Z2),
• Dx lt 4,
• Dy lt 4,
• Dz lt 4.

61
Energy Function

• Reified constraint
• ...
• El in 0,Pot,
• DX abs(X1 - X2),
• DY abs(Y1 - Y2),
• DZ abs(Z1 - Z2),
• 2 DX DY DZ ltgt El Pot.

62
Search

• Variable Selection
• Assign value to variables adjacent to ground
  vars.
• Bounded Block Fails Heuristic
• Block sublist of vars that are unbound
• Try labeling in each block in turn.
• If labeling in a block fails, backtracking to the
  previous block.
• If a block fails too many times (threshold)
  backtracks not to the previous but to one before
  that.

63
Results

• Implementation in SICStus Prolog
• Tested up to proteins of size 80.
• Time varies between 1sec and 10 hours on a PC.
• Parallel CLP version.
• Future Directions
• New Heuristics
• New dedicated global constraints/solver.

64
Protein Prediction Structure in CSPCONS

• Initial Experimental Version
• Porting original code to CSPCONS
• AIMS
• Investigating benefits from applying DSAC in the
  problem.
• Investigating new heuristics.
• Re-writing non-linear constraints to linear.
• New Modeling?

65
References

• Constraint Programming In Pursuit of the Holy
  Grail Roman Bartak
• Survey Practical Applications of Constraint
  Programming, Mark Wallace.
• Constraint Logic Programming, Pascal van
  Hentenryck
• Constraint Logic programming A survey, J. Jaffar
  and Lassez.
• Parallel and Constraint Logic Programming, I.
  Vlahavas, P. Tsarcopoulos and I. Sakellariou,
  Kluwer Academic Publishers
• Constraint Programming for Industrial
  Applications, H. Simonis presentation.
• Ideal architecture of residue packing and its
  observation in protein structures. Protein
  Science, 62072-2083, 1997. G. Raghunathan and R.
  L. Jernigan. 1997
• A. Dovier, M. Burato, and F. Fogolari.Using
  Secondary Structure Information for Protein
  Folding in CLP(FD). In Proc. of Workshop on
  Functional and Constraint Logic Programming,
  ENTCS vol. 76, 2002.
• A. Dal Palù, A. Dovier, and F. Fogolari.
  Constraint Logic Programming approach to protein
  structure prediction. BMC Bioinformatics 2004,
  5186, 30 November 2004.
• A. Dal Palu', A. Dovier, and E. Pontelli.
  Heuristics, Optimizations, and Parallelism for
  Protein Structure Prediction in CLP(FD). To
  appear in PPDP'05.

66
Constraint Logic ProgrammingApplications

• Thanks.