04/19/23 1

Constraint Programming

for Industrial Applications

H.Simonis

2

What is common among

The production of Mirage 2000 fighter aircraft

The personnel planning for the guards in all French jails

The production of Belgian chocolates

The selection of the music programme of a Pop music radio

station

The design of advanced signal processing chips

The print engine controller in Xerox copiers

They all use constraint programming to solve their problem

3

Constraint Programming - in a nutshell

Declarative description of problems with Variables which range over (finite) sets of values Constraints over subsets of variables which restrict possible value

combinations A solution is a value assignment which satisfies all constraints

Constraint propagation/reasoning Removing inconsistent values for variables Detect failure if constraint can not be satisfied Interaction of constraints via shared variables Incomplete

Search User controlled assignment of values to variables Each step triggers constraint propagation

Different domains require/allow different methods

4

Constraint Satisfaction Problems (CSP)

Combinatorial Optimization Problems

Different problems with common aspects Planning Scheduling Resource allocation Assignment Placement Logistics Financial decision making VLSI design

5

Characteristics of these problems

There are no general methods or algorithms NP-completeness different strategies and heuristics have to be tested.

Requirements are quickly changing: programs should be flexible enough to adapt to these changes

rapidly.

Decision support required co-operate with user friendly interfaces

6

Logic ProgrammingLogic Programming

MathematicsMathematics

Operations Research

Operations ResearchCLP toolsCLP toolsArtificial

Intelligence

ArtificialIntelligence

Constraint propagation

Consistency checking

Demons

Graph theory

Combinatorics

Spatial data structures

Equation solving methods

Predicate logic

Unification

Non-determinism

Simplex & Linear programming

Integer programming

Implicit enumeration

Branch & bound

Flow algorithms

Scheduling methods

Techniques behind CLP

7

Eclipse

Prolog based “constraint toolkit”

Developed first at ECRC, then IC-Parc

Easy to develop new constraint methods

Sets of existing methods/libraries

Basis of problem solvers for PT

Widely used for academic work (> 500 sites)

8

CLP tool history

Prolog III CLP(R) CHIP

Decision Power

CharmeSNI

Prolog

CHIPSEPIA

CHIP lib

CHIP V4

Charme Object

Solver

Pecos

logic based Other base language

CAL

BNR

cc(FD)

EclipseProlog IV

CHIP V5Oz Claire

ALICE

9

Classification of CLP solvers

Computation domain Deterministic solver (search under user control) Efficient methods More than one application

Complete/incomplete decide satisfiability of constraint sets complexity of solver/ simplicity of programs

Methods syntactic: domain independent semantic: domain dependent

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Constraints

Boolean

semanticsyntacticValueselection

Variableselection

Backtracking

Heuristics

ConstraintsolverControl

element

BooleanFinitedomainsRational

Incompletesolver

Completesolver

disequality

numerical

inequalityequality

symbolic

cumulative diffn cycle among

Domain concept

Others Others

Constraint system structure

Interval

Meta-heuristics

sequence

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Computation domains

Finite domains

Linear arithmetic

Boolean

Pseudo Boolean

Non-linear arithmetic

Intervals

Sets, sequences, lists

the initial domains in Prolog III,

CLP(R) and CHIP

12

Incomplete finite domain solver

Domain finite sets of values subsets of natural numbers

Need for enumeration

Classification criteria constraint granularity richness of constraint sets propagation results user definable constraints/control

Methods explicit domain representation bound propagation/ removal of interior values heuristics based on domains

13

Need for global constraints

Y in {2,3}

Z in {1,3}

U in {1,2,3,4}

X in {2,3}

Y

X

Z

U

1

2

3

4

local reasoning, no action global reasoning, detect implications by bi-partite matching

14

Global constraints

Work on sets of variables Global conditions, not local constraints

Semantic methods Operations Research Spatial algorithms Graph theory Network flows

Building blocks (high-level constraint primitives) Multi-purpose As general as possible Usable with other constraints Very strong propagation Acceptable algorithmic complexity

15

Constraint morphology

DifferentDifferent DependencyDependencyTourTourResourceResourceOrderOrder

\=\= >=, distance>=, distance atmost, atleastatmost, atleast circuitcircuit elementelement

alldifferentalldifferent

setupsetupdisjunctivedisjunctive

prod/consprod/conspermutationpermutation

diffndiffn cumulativecumulative sequencesequence

amongamong

cyclecycle casecase

precedenceprecedence

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Search tree visualization

Generation of search tree representation at run-time

Shows parent child relation, failed sub-trees, success nodes

In examples here leaf failure nodes suppressed failure trees not collapsed

Interface a set of simple meta-call predicates

Supported by work in DISCIPL Esprit project Declarative debugging Visualization of constraint programming results

Understand behaviour of different strategies

17

Search tree tool

Menubar

Panel

Tree view

OtherViews,here domainstate

Info Area

18

Initial Credit 8

4 2 1

2 1 1

1

Local Search

Credit Search

Solution

*

credit([X1..X10],8,10,my_delete,

my_indomain,

4,part(1,2)),

Example of tree search

04/19/23 19

Success Stories for Constraint Logic Programming

COSYTEC – IC-Parc

20

Overview

Hardware design

Compilation

Financial problems

Placement

Cutting problems

Stand allocation

Air traffic control

Frequency allocation

Network configuration

Product design

Production step planning

Production sequencing

Production scheduling

Satellite tasking

Maintenance planning

Product blending

Time tabling

Crew rotation

Aircraft rotation

Transport

Personnel assignment

Personnel requirement

planning

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Five central topics

Assignment Parking assignment Platform allocation

Network Configuration

Scheduling Production scheduling Project planning

Transport Lorry, train, airlines

Personnel assignment Timetabling, Rostering Train, airlines

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Stand allocation

HIT (ICL Hong-Kong) assign ships to berths in container harbour developed with ECRC’s version of CHIP then using DecisionPower (ICL) first operational constraint application (1989-90)

APACHE (COSYTEC) stand allocation for airport

Refinery berth allocation (ISAB) where to load/unload ships in refinery

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AIR FRANCE - APACHE

Stand allocation system Originally developed for Air France, CDG2 Packaged for large airports

Complex constraint problem Technical & operational constraints Incremental re-scheduler

Cost model Max. nb passengers in contact Min. towing, bus usage

Benefits and status Quasi real-time re-scheduling KAL, Turkish Airlines

24

Network configuration

RiskWise (PT)

Locarim (France Telecom, COSYTEC) cabling of building

Planets (UCB, Enher) electrical power network reconfiguration

Load Balancing in Banking networks (ICON) distributed applications control network traffic

Water Networks (UCB, ClocWise)

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RiskWise

Traffic analysis/optimization for IP networks

Find out end-to-end communication flows in the

network of an ISP

Suggest changes in network which optimize

investment

Handle incomplete data

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Production scheduling

Atlas (Monsanto) Herbizide production

Cerestar (OM Partners) Glucose production

KAPSS (Mitsubishi Chemical) offset printing plates

Trefi Metaux (Sligos) heavy industry production scheduling

Michelin rubber blending, rework optimization

27

DASSAULT - PLANE

Assembly line scheduling developed by Dassault Aviation for Mirage 2000 Jet/ Falcon business jet

Two user system production planning 3-5 years commercial what-if sales aid

Optimisation requirement to balance schedule minimise changes in production rate minimise storage costs

Benefits and status replaces 2 week manual planning operational since Apr 94 now used in US for business jets

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FINA - FORWARD

Oil refinery production scheduling joint development by TECHNIP and COSYTEC incorporates ELF FORWARD LP tool

Schedules daily production crude arrival -> processing -> delivery design, optimize and simulate

Product Blending explanation facilities handling of over-constrained problems

Status generic tool developed in 240 man days operational since June 94 Operational at FINA, ISAB, BP

29

Transport

By Air AirPlanner (PT) Daysy (Lufthansa) Pilot (SAS)

By Road Wincanton (IC-Parc) TACT (SunValley) EVA (EDF)

By Rail CREW (Servair) COBRA (NWT)

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EDF- EVA

Transportation of nuclear waste developed by GIST + COSYTEC plans evacuation and transport for 54 sites

Constraints availability of transport vehicles and vessels no and capacity of storage tanks compatibility of waste to vessels size of convoy, time

Status operational since Oct 94 6 month plan in 5 minutes

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SERVAIR - CREW

Crew rostering system assign service staff to TGV train timetable joint implementation with GSI

Problem solver generates tours/cycles assigns skilled personnel

Constraints union, physical, calendar

Status operational since Mar 1995 cost reduction by 5%

32

Personnel Planning

RAC (IC-Parc)

OPTISERVICE (RFO)

Shifter (ERG Petroli)

Gymnaste (UCF)

MOSAR (Ministère de la JUSTICE)

33

RFO - OPTI SERVICE

Assignment of technical staff to tasks overseas radio broadcasting network - Radio France Outre-mer joint development by GIST and COSYTEC 250 journalists and technicians

Features schedule manually, check, automatic rule builder to specify cost formulas

Optimization minimize overtime, temporary staff compute cost of schedule

Status operational since 1997 installed worldwide in 8 sites

Now used for other companies TSR Canal+

04/19/23 34

Case Study: Semi Process Industry

35

ATLAS (Monsanto, Antwerp)

Scheduling system in chemical factory herbicide manufacturing and packaging integrated inventory control system

Life system first phase operational since July 93 second phase operational since March 94 major revision in 98 (SAP connection)

Developed jointly by OM Partners (Antwerp) COSYTEC

Multi-user PC/UNIX system multiple schedulers co-operative behavior

36

Gr

G

F1

F2

Dr

L1

L2

L3

L4

PackagingFormulation

raw material

intermediate products

Holdingarea

Manufacturing Process

Outside

finishedproducts

37

ProductionPurchasing

Users

SchedulersFactory

PackagingFormulation

ProductionSchedule

Shop floor data

Sales forecast(6 month horizon)

Stock level

Data baseupdateplanned/realized

Orders(delay 1day to 4 weeks)

Arrivals(lead time 3 weeks)

Dynamic Scheduling Environment

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ProductionPurchasing

Re-scheduling Formulation

Re-scheduling Packaging

New Schedule

Users Priorityorders

Visualization ofschedule

(stock level,delays,

down times...)

Productionproblems

Old scheduleFine tuningof sequence medium/long

termimpact

shortterm

reaction

Scheduling Process

SchedulersFactory

PackagingFormulation

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IBM - VMAntwerp

IBM - MVSSAS

Brussels

ORACLE

X 25

USA

Ethernet PlannerFactory

SchedulerFormulation

SchedulerPackaging

Productionmanager

Purchasing

Users PC / XWindowsGUI

HP UNIX

SchedulingCHIP

Architecture

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The system

Connection to other systems Data download/upload from/to local and remote mainframes End-user connection via PCs

Data base Local on UNIX machine ORACLE SQL standard Forms/reports facilities

Multi-user tool Multiple schedulers for parts of production Inventory control Production Multiple scenarios; one schedule

41

Constraint solver

Constraints handled Machine choice Sequence/ machine dependent set-up Manpower limits Component consumer constraints Finished product producer constraint Producer/consumer constraints for intermediate products Production planning for batch part

Number of batches for intermediate products Optimum batch sizing

Limited stock levels

42

The Cumulative global constraint

Cumulative constraint– Resource limits over periods of time– Upper/lower limits– Soft/hard limits– Gradual constraint relaxation

Application– Resource restrictive scheduling, producer consumer constraints,

disjunctive schedule, manpower constraints, overtime

cumulative

43

Cumulative

Methods obligatory parts task intervals available space many more (25000 lines of C code)

Concepts one constraint may be used for different purposes

44

The Diffn global constraint

Diffn constraint– non overlapping areas on n-dimensional rectangles– distances between rectangles– limit use of areas– relaxation

Application– layout, packing, resource assignment, setup,

distribution planning, time-tabling

diffn

45

Diffn

Methods obligatory parts region intervals max flow on assignment available space many others (32000 lines of C code)

Concepts

46

The Cycle global constraint

cycle

Cycle constraint– Finds cycles in directed graphs with minimal cost– Assign resources, find compatible start dates

Applications– Tour planning, personnel rotation, distribution

problems, production sequencing

47

Cycle

Methods connected components bi-partite matching non-oriented graph concepts shortest/longest paths micro-rules many others (38000 lines of C code)

Concepts

48

ATLAS - Summary

End-user system Direct manipulation Constraints not visible to user Changes/strategies expressed via interface

Complex scheduling problem Real-life, not pure problem Interaction/conflicts between constraints Incremental expression with constraints

Development effort (250 days) Integration Data base reporting Graphical interface Problem solver

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The CHIP system: Constraints and ...

CHIP

XGIPQUIC

CHIP

Application

EMC/CLIC CHIP++

Application

Objects

Solvers

o b je c ts

lo ad sa ve

io db lis t g an tt d ia gram

cre a te set g e t

p an e l

d a ta m od e l

50

Behind the scene

CHIP kernel 175000 lines Prolog 15000 Core Constraints 20000 Global Constraints 140000

Interfaces 5000 lines CLIC EMC QUIC

XGIP graphics 20000 lines

Graphics libraries 17000 lines

51

A typical decision support

application

o b je c ts

lo ad s a ve

io db lis t g an tt d ia g ram

c re a te s e t g e t

p an e l

d a ta m od e l

dB

GUI

LibrariesReporting

Solver

DATA

52

Application framework

Building blocks - data management and GUI description, upload, download, windows, Gantt chart, lists, diagrams,

panels

Built on top of comprehensive data model single point of reference, maintenance, extensions

General enough for different application domains manufacturing, transport, chemical, human resources

Obvious benefits code size, application quality, development speed, decreased

maintenance, etc.

53

Data model

o b je c ts

lo ad sa ve

io db lis t g an tt d ia g ram

c re a te se t g e t

p an e l

d a ta m od e l

Single point of reference

Object model expressed in CHIP++

Meta program generates dB model, hooks to GUI

Provides I/O to save and load object model

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Needs of an industrial system

Lines of code for a live application

Development speed, tools, risk

Integration

User interface

Solver a must

db/integration46%

library14%

solver9%

static6%

other6%

graphics19%

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Benefits of CLP approach

Short development time Fast prototyping Refining of modelling Same tool used for prototyping/production

Compact code size Ease of understanding Maintenance

Compositional development Changing requirements are localized No need to understand all aspects of problem to add/change constraint

Good performance Fast answer Good results Optimal solutions rarely required

Adapt solution to problem, not vice versa Bespoke application development

04/19/23 56

The Future: Constraint Application Generators

CHIP Factory

57

Approach

CHIP Factory

Program generator for C++

CHIP constraint library

Generates (complete)

application from

specification data model user interface data base solver

58

Problem Description

Example application from LISCOS Project (BASF)

Two stage, continuous process scheduling problem

First stage production intermediate products (10) batch based process campaign based schedule setup times/costs on one line

Intermediate product storage producer/consumer constraints

Second stage production finished products (100) machine choice, machine restrictions variable production rates on machines

59

Problem Description (2)

60

Object Model

MachineChosen

DeletedItemdbKey : intclassName : atomclassKey : int

WarningdbKey : intattribute : atomexplanation : atomreference : atom

MachinedbKey : intdescription : atomseqNr : intnr : intTask

dbKey : intstart : dateend : dateduration : timestartVar : dvarendVar : dvardurationVar : dvar

resource

MachineChoicenrMachines : intparallel : int

DisjMachine

DisjTaskqty : int

IntermediateSetupdbKey : intvalue : int

MachineChoiceTaskresourceVar : dvarqty : int

ProducerConsumer

IntermediateProductdbKey : intbatchSize : intcolor : colordescription : atominitialStock : intspeed : int

from

to

SpeeddbKey : intvalue : time

FinishedProductdbKey : intcolor : colordescription : atominitialStock : int

61

MachineChosen

DeletedItemdbKey : intclassName : atomclassKey : int

WarningdbKey : intattribute : atomexplanation : atomreference : atom

MachinedbKey : intdescription : atomseqNr : intnr : intTask

dbKey : intstart : dateend : dateduration : timestartVar : dvarendVar : dvardurationVar : dvar

resource

MachineChoicenrMachines : intparallel : int

DisjMachine

DisjTaskqty : int

IntermediateSetupdbKey : intvalue : int

MachineChoiceTaskresourceVar : dvarqty : int

ProducerConsumer

IntermediateProductdbKey : intbatchSize : intcolor : colordescription : atominitialStock : intspeed : int

from

to

SpeeddbKey : intvalue : time

FinishedProductdbKey : intcolor : colordescription : atominitialStock : int

GUI Design

list

chart

gantt

62

Constraint Model

DisjTask constraints

MachineChoiceTask constraints

DisjMachine resource constraint

Machine choice resource constraint

Producer/Consumer constraint

63

DisjTask constraints

post(end_var == start_var + duration_var)

post(duration_var == solver.convertDurationToDomain(duration))

64

MachineChoice constraint

diffn_entries(entries);

forall(task,machine_choice_task,

entries.add(task.start_var,task.resource_var,task.duration_var,1)

);

diffn_post(entries)

65

Finished Application

66

Summary

Large scale problems can be solved with CLP

Very high level language + framework allows rapid

development in industrial terms

Complex, customer specific conditions can be handled

Global constraints allow Expression Resolution of complex problems

Most important Ease of modelling Speed of development Reactivity to customer demands

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Some pointers

Constraint Archive www.cs.unh.edu/ccc/archive

Constraints Journal www.wkap.nl/journals/constraints

Principles and Practice of Constraint Programming www.cs.ualberta.ca/~ai/cp CP99 in Washington,DC/ CP2000 in Singapore

Practical Application of Constraint Technologies and Logic

Programming www.practical-applications.co.uk/PACLP99

On-line guide to Constraint Programming (R. Bartak) http://kti.mff.cuni.cz/~bartak/constraints

K. Marriott, P.J. Stuckey Programming with Constraints: An Introduction, MIT Press, 1998