04/24/23 1

Applications of Constraint Programming

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)

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

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

7

Logic Programming

Mathematics

Operations ResearchCLP toolsArtificial

Intelligence

Constraint propagationConsistency checkingDemons

Graph theoryCombinatoricsSpatial data structuresEquation solving

methods

Predicate logicUnificationNon-determinism

Simplex & Linear programmingInteger programmingImplicit enumerationBranch & boundFlow algorithmsScheduling methods

Techniques behind CLP

8

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)

9

Example problem

Solve the cryptarithmetic puzzle

Each character represents a digit Different characters have different values Numbers do not start with 0

SEND +MORE------ MONEY

10

Example: Model

top:-[S, E, N, D, M, O, R, Y] :: 0..9, alldifferent([S, E, N, D, M, O, R, Y]), S \= 0, M \= 0, 1000 * S + 100*E + 10*N + D +1000*M + 100*O + 10*R + E =10000 *M + 1000*O + 100*N + 10*E + Y, labeling([S, E, N, D, M, O, R, Y]).

Variable definition

Constraints betweenvariables

Search routine

11

Constraint reasoning

Simplification (each variable occurs once) 1000*S in {1..9}+ 91*E in {0..9} + D in {0..9} + 10*R in {0..9} = 9000*M in {1..9}

+900*O in {0..9} + 90*N in {0..9} + Y in {0..9}

Evaluation lhs/rhs lhs in 1000..9918 rhs in 9000..89919

Merging of sides constraint in 9000..9918

Consequence M = 1 S = 9 O in {0..1}

Propagation of alldifferent O = 0

12

Reasoning

Re-evaluation of equality 1000*9+ 91*E in {2..8} + D in {2..8} + 10*R in {2..8} = 9000*1

+900*0 + 90*N in {2..8} + Y in {2..8} lhs in 9204..9816, rhs in 9182..9728, eq in 9204..9728 N \= 2, E \= 8

Re-evaluation, ... Continuing the process gives

M = 1, S = 9, O = 0, E in 4..7, N in 5..8, D in 2..8, R in 2..8, Y in 2..8

13

Starting labeling

First variable is E, first value is 4 Propagation on equality gives

1000*9+ 91*4 + D in {2..8} + 10*R in {2..8} = 9000*1 +900*0 + 90*N in {5..8} + Y in {2..8}

results in N = 5, D = 8, R = 8, Y = 2

Propagation on alldifferent fails Backtracking to last choice

14

First alternative

Next value for E is 5 Propagation on equality gives

1000*9+ 91*5 + D in {2..8} + 10*R in {2..8} = 9000*1 +900*0 + 90*N in {5..8} + Y in {2..8}

results in N = 6, R = 8

Constraint propagation (alldifferent + equality) gives D = 7, Y = 2

Problem solved

15

Points to remember

Even small problems create complex propagation chains The same constraint can be woken several times in the same

propagation loop The order in which constraints are woken has an influence on

the speed, but not on the result Propagation continues until no further information is obtained Search (under user control) required to find ground solution Basic structure of finite domain program always the same

define variables define constraints user defined search

typical: pick variable and find value

04/24/23 16

Success Stories for Constraint Logic Programming

COSYTEC – IC-Parc

17

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

18

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

19

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

20

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

21

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)

22

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

23

FRANCE TELECOM - LOCARIM

Intelligent cabling system for large buildings developed with Telesystemes for France Telecom

Application input scanned drawing specify requirements

Optimization minimize cabling, drilling Reduce switches shortest path

Status operational in 5 Telecom sites generates quotations

24

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

25

ATLAS (Monsanto)

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 system multiple schedulers co-operative behavior

Gr

G

F1

F2

Dr

L1

L2

L3

L4

PackagingFormulation

raw material

Holdingarea

Out finishedproducts

26

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

27

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

28

Transport

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

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

By Rail CREW (Servair) COBRA (NWT)

29

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

30

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%

31

Personnel Planning

RAC (IC-Parc) OPTISERVICE (RFO) Shifter (ERG Petroli) Gymnaste (UCF) MOSAR (Ministère de la JUSTICE)

32

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+

33

Rostering

Ministère de la JUSTICE Rostering of prison guards Help to determine personnel needs Simulation / Calculation of anonymous rosters Provisional plans for one year Development by Cisi and COSYTEC 10 regional sites for 200 prisons Objectives :

planning obtained in minutes was 3 weeks manually

reduction of overtime cost improved personnel satisfaction reduction of days lost

04/24/23 34

Case Study: A complex transportation problem

35

TACT: Transport planning and resource scheduling

Transport planning and scheduling for SVF/Cargill UK delivering chicken/turkeys from farms to factories JIT arrival at factory combined

planning scheduling assignment

multi-resource problem, interaction between resource types

Developed by COSYTEC Operational since 2/95 Revising decision making process

formalizing current procedures spread knowledge inside company

36

Problem

Satisfy order book with available resources Transport Qty of Type from Source

to Sink

Schedule operations Assign resources to activities

Depot Tour generation Start in depot Connect orders to tours Use of passive transport End in depot

37

Integrated transport problem

Loading Teams, Drivers, Forklifts, Lorries

Transport Drivers, Lorries, Forklifts

Unloading Drivers, Personnel, Storage Area, Lorries

Cleaning Personnel, Lorries, Forklifts

38

Menubar

List

Gantt chart

Application Look

Details and status

39

Solver Architecture

Orders

Plan

Schedule

Assignment

How many trips?

When to leave or to arrive?

Who is doing what?

40

Planning

How many trips are required lorry types drag trailers transport restriction volume/weight limits

Merging of orders same source/sink same type

Fork lift requirements resource needed for loading take out with first trip bring back with last trip optimization

41

Scheduling

On departure side all trips for same order must be

scheduled together no gaps no concurrency loading times depend on team, lorry type

and product

On arrival side JIT schedule producer/consumer behavior very limited storage area limited storage time minimum stock level required

42

Producer/Consumer Behavior

43

Assignment

Find compatible resources for each activity multiple resource problem interaction between resources conflict resolution

Respect constraints working time rest periods work load

Balance use of resources of same type teams drivers

Minimize use of outside resources

44

User control

The user is in command modification of constraints choice of strategies relaxation of constraints

Different priorities of various users in-time delivery use of resources need for overtime balancing work load

Need for compromise Improved reactivity

events rescheduling

45

Problem solver

Large scale, complex model Inter-related problem solvers Use of global constraints essential

cumulative diffn cycle

Explanation facilities meta programming (Prolog feature) relaxation of global constraints possible in CHIP

Re-scheduling/re-use of existing solution Constraint solver / constraint check

46

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

47

Cumulative

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

Concepts one constraint may be used for different purposes

48

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

49

Diffn

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

Concepts

50

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

51

Cycle

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

Concepts

52

Evaluation

Operational since spring 1995 Scheduling speed

8 hours manual work 15 min with TACT application

Return on investment (estimated by customer) in 6 month transport fleet constant at increasing demand

Push button solution little manual interaction

Application has stayed up-to-date for last five years new types of lorries changing status of catching teams ...

53

Statistics

10 month project duration study, specification development implementation

36000 lines of CHIP code complete application in CHIP except AS/400 interface to ORACLE

7000 lines of code for solver explanation facilities automated constraint relaxation specialized lower bound calculation

54

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

55

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