iOpt Intelligent Optimisation Toolkit

1
iOptIntelligent Optimisation Toolkit

• Raphaël Dorne

C. Voudouris, R. Dorne, A. Liret, C. Ladde, P.
Mills Intelligent Enterprise Technologies, Intelli
gent Systems Lab., BT Exact
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Outline

• iOpt
• iSchedule
• Conclusion

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iOpt Toolkit for Heuristic Search Methods
Application-Specific Frameworks
iOpt
Toolkit
Heuristic Search Framework
Algorithm Visualisation
Problem Modelling Framework
Problem Visualisation
Invariant Library
Invariant Visualisation

• iOpt Main Features
• Java-based system
• Uses one-way constraints for problem modelling
• Incorporates general specialised frameworks
  for building problem models
• Allows the user to build a HS method using a
  library of algorithmic parts
• Independence between problem modelling and
  problem solving
• Visualisation components available for problem
  models/algorithms

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Invariant Library (IL)

• Declarative programming paradigm with the Java
  OO language
• Invariants are one-way functional constraints
• u F(p0,p1,,pn)
• F, a function (Type(pi))n1 ? Type(u)
• A predicate is a Boolean function.
• x ? y z, a ? min(b, c)
• Specialised mark/sweep algorithm
• Very useful to quickly test and undo variable
  assignments
• The Invariant Manager efficiently evaluates the
  consequences of value changes in a network.
• Design patterns compliance (Memento, Observer,
  Composite, Builder, Listener)

input1
input0
inputn
...
Invariant F
output
u
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Constraint Satisfaction Algorithm
Mark Stage

• Two phase constraint satisfaction algorithm
• mark
• evaluate
• During the mark phase all influenced invariants
  are marked for evaluation
• During the evaluation phase all/some marked
  invariants are evaluated
• Lazy/eager evaluation modes
• Smart rules for deciding if an invariant requires
  re-evaluation
• Incremental updates for aggregate invariants
  (e.g. sum, prod)
• User-defined invariant priorities
• Ability to interrupt the evaluate phase based on
  user-defined conditions (e.g. constraint
  violations).

Influenced (i.e. out of date)
Modified
Evaluate Stage
Influenced
Modified
Evaluated
Unnecessarily Evaluated
Affected
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Problem Modelling Framework (PMF)

• Foundation framework for modelling Combinatorial
  Optimisation Problems
• User specifies a COP (X,D,C,F)
• X Decision variables with/without domains
• D value domains
• C Constraints over X
• F Objectives
• PMF concepts
• Variable source invariant with backup facility
• Domain support structure for modifying a set of
  values
• Constraint Boolean invariant
• Objective Real invariant expression of X and C
• Problem handler for the model

Problem Model
Solutions
D. Variables
Constraints
Objective
User
Invariant Network

• Basis for domain frameworks (e.g. Scheduling)
  or specific problem models

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Code example Problem model for Frequency
Assignment

• IntegerDomainVar X new IntegerDomainVarnbAnte
  nnas
• BooleanExp C new BooleanExpnbConstraints
  nbEdges
• beginModelChanges()
• // create decision variables with value domain
  0..f
• for(int i0iltnbAntennasi)
• addDecisionVar(Xi new IntegerDomainVar("0-gt''
  f""))
• // create constraints
• for(int i0ilt nbEdgesi)
• addConstraint(Ci Inv.neq(Xedges0i,Xedge
  s1i))
• // add objective
• addObjective(Inv.toReal(Inv.minus(nbConstraints,In
  v.sum(C))))
• endModelChanges()

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Heuristic Search Framework

• Functionality of common HS algorithms is broken
  down into Parts (i.e. Search Components)
• Part Categories are represented by Java
  Interfaces while specific Parts are defined as
  Java Classes implementing these interfaces
• A HS algorithm is assembled from parts which form
  a tree. Valid trees can be executed on a problem
  model
• The framework can model single solution/population
  methods as well as hybrids of the two.
• Challenge find a good characterisation of
  concepts found within Meta-Heuristic Search
  methods

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Heuristic Solution

• Two types of solution representations
• Vector of objects (decision variables)
• Set of sequences of objects
• Default moves and neighbourhoods based on
• Value assignment to an object (decision variable)
• random, all values, all pairs (X,V)
• swap values
• Change of position of an object
• Move an object randomly, all positions, all
  pairs (P1,P2)
• Swap two objects randomly, all positions, all
  pairs (P1,P2)

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Search Component for Local Search Methods
SearchComponent
SingleSolutionMethod
Neighborhood
NeighborhoodSearch
Selector
CompositeNeighborhoodSearch
CompositeSingleSolutionMethod
CompositeNeighborhood
DecisionVariableSelector
SingleNeighborhoodSearch
GenerationSingleSolutionMethod
ValueSelector
SwapMoveNeighborhood
BestImprovement
LocalSearch
PositionSelector
AssignMoveNeighborhood
BestMove
SearchRestart
InsertMoveNeighborhood
DecisionVariableValueSelector
CircularFirstImprovement
PerturbationSolutionMethod
DecisionVariablePositionSelector
FirstImprovement
Options Random_order Index_order Sorted_Order
FirstLegalMove
RestartFirstImprovement
ThresholdNeighborhoodSearch
InvariantSimulatedAnnealing
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Algorithm Hill climbing
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Algorithm Simulated Annealing
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Algorithm Tabu Search
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Generic Hybrid GATS for Frequency Assignment
PopulationHeuristicSearch
CompositePopulationMethod
CompositePopulationMethod
GenerationPopulationMethod
MutationPopulationMethod
CrossoverPopulation Method
FAPConstructiveGeneration
SelectionPopulationMethod
SingleSolutionMethodMutation
FAPCrossover
SUSSelection
LocalSearch
Tabu Search Subtree
BestMoveNeighbourhoodSearch
FAPNeighbourhood
DomainAssignmentTabu
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Code example hill climbing 1/2

• // right branch initial generation
• GenerationSingleSolutionMethod myRSSG new
  VectorSolutionRandomGeneration()
• // left branch local search
• // neighborhood
• AssignMoveNeighborhood myNeighborhood new
  AssignMoveNeighborhood()
• DecisionVariableIndexSelector decisionVariableSele
  ctor new DecisionVariableIndexSelector()
• decisionVariableSelector.setMovesVersion(Selector.
  RANDOM_ORDER)
• ValueIndexSelector valueIndexSelector new
  ValueIndexSelector()
• valueIndexSelector.setMovesVersion(Selector.RANDOM
  _ORDER)
• myNeighborhood.add(decisionVariableSelector)
• myNeighborhood.add(valueIndexSelector)
• // neighborhood search
• BestMoveNeighborhoodSearch myRMNS new
  BestMoveNeighborhoodSearch()
• myRMNS.setNeighborhood(myNeighborhood)

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Code example hill climbing 2/2

• // local search
• LocalSearch myLS new LocalSearch()
• myLS.setNeighborhoodSearch(myRMNS)
• myLS.setThreshold(0.0)
• // connect the two branches
• CompositeSingleSolutionMethod myCSSM1 new
  CompositeSingleSolutionMethod()
• myCSSM1.setMaxIterations(1)
• myCSSM1.addMethod(myRSSG)
• myCSSM1.addMethod(myLS)
• // root of the algorithm
• SingleSolutionHeuristicSearch mySSHS new
  SingleSolutionHeuristicSearch()
• mySSHS.setSingleSolutionMethod(myCSSM1)
• mySSHS.setSearchTitle("Hill Climber")
• mySSHS.setMinimisation(true)
• mySSHS.setInfeasibilityAllowed(true)
• mySSHS.setPrintLevel(Global.HS_LEVEL3Global.HS_LE
  VEL4)

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Other features of HSF

• Objective Function
• Support dynamic modification of the objective
  function (GLS)
• Several objective functions in a same algorithm
  (MinimiseConflictsLocalSearch)
• Personal objective function
• Support Evaluator evaluation by simulation
• Delta matrix facility
• Flexibility
• Several algorithms linked together
• Minimisation/Maximisation
• Feasible/Infeasible search space
• Stopping conditions at search component level
• Integration of specific treatments within an
  algorithm

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iOpts Visual ToolsA. Problem VisualisationB.
Algorithm Visualisation/Monitoring C. Heuristic
Search Builder
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Problem Model Visualisation
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Algorithm Visualisation

• Set-up
• Set Search Component parameters
• Run several Heuristic Searches in a row

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Algorithm Monitoring

• Control
• Behaviour of the algorithm
• gt Heuristic Search debugger/configurator

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The Case for Heuristic Search Builder

• NFL theorem (Walpert Mac ready 95)
• Reuse metaheuristics and HSF framework
• Easily adapt existing/quickly create new
  algorithms
• Avoid the need to understand HSF architecture
• Objective No need to type a single line of code

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Defining Heuristic Search Builder

• Visual tool to fully build an algorithm
• Database of algorithmic parts
• Drag-and-drop components to build algorithm
• XML facility to load/save (partial) algorithm
• Not a compiler but follow an MVC approach

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Heuristic Search Builder - Configuration
Parameters table
Search components table
Menu bar
Current heuristic search
Validity check
Variables table
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Heuristic Search Builder - Composition
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HSB/HSF Communities

• Inter- or intra-organization Lab./Company

Algorithmic Parts Database (Java code)
HSB
Developers
Users

• search algorithms/parts databases
• exchange of java code/XML files via email, web
  server,

Algorithms Database (XML files)
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Experiments Graph Coloring instances
1 Dorne Hao 98, Galinier Hao 98, Morgenstern
96. 2 Michel Van Hentenryck 98.
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iSchedule Intelligent Scheduling Framework
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Introduction to iSchedule

• Framework dedicated to Scheduling
• Synthesis of expertise in Scheduling problems
• Vehicle Routing
• Job Shop Scheduling
• Workforce Scheduling
• NG-Dynamic Scheduler (Work manager)
• Fully based on iOpt technology
• Problem Model based on PMF
• Algorithms based on HSF/CSF
• High level Framework
• Resource, task, time window, timeline,
• gt Schedules tasks allocation to resources

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iSchedule Architecture for VRP
Modelling
Solving
VRP solution
Extensions for VRP Modelling
Specific parts for VRP Algorithms
iSchedule
Schedule Modelling Framework
Scheduling Algorithms
Heuristic Search Framework
Problem Modelling Framework
iOpt
Invariant Library
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Scheduling Framework (iSchedule)

• Incorporates classes for modelling scheduling
  problems with unary resources
• Extension/Specialisation of the Problem Modelling
  Framework
• Classes included are
• Task,
• Resource,
• Break,
• Start/End Activities and others
• Support for dynamic scheduling problems
• Addition/deletion of tasks/resources/time windows
  etc.
• Event notifications of changes allow to define
  dynamic scheduling meta-strategies
• Models developed using SF
• VRP, JSSP, WSP

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Timelines

• Activity interactions with the timelines
• adds/removes/requires capabilities
• requires/produces state
• requires capacity (pos. or neg.)
• Resource constraints on the timelines
• essential/possible capabilities
• minimum/maximum capacity
• possible states

State Timeline
Warm Oven
Hot Oven
Heat Oven
Bake Pastries A
Bake Pastries B
Capacity Timeline
max
Capability Timeline
min
Task A
Task B
Skill A
Essential Skills
Possible Skills
Skill B
Skill C
Skill D
Pick up Tool
Return tool
Task which requires tool
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Task Constraints
cost

• Task Time Windows
• ends/starts at
• ends/starts between
• ends/starts between with a target time
• Task Precedence Relations
• Task A ends/starts after end/start Task B
• Task A ends/starts after end/start Task B with
  delay
• Parallel Tasks
• Task A and B start together/within a time limit
• Task Resource Relations
• same/different resource

lst
est
tst
Task
Task A
Task B
t
Task A
Task B
Task A
Task B
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Other Modelling Facilities 1/2

• Predefined Objectives
• unallocated tasks (QoS)
• task delays (QoS)
• overtime (Cost)
• fixed cost for using resource (Cost)
• fixed cost for using specific resource for
• specific activity (QoS/Cost)
• specific travel (QoS/Cost)
• travel/setup time based costs (Cost)
• service time based costs (Cost)

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Other Modelling Facilities 2/2

• User-Defined Service Model
• Resource - Task compatibility,
• Fixed/Variable service costs,
• Service Duration
• User-Defined Setup (i.e. Travel) Model
• Resource - Route compatibility,
• Fixed/Variable travel costs,
• Travel Duration

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Algorithms Facilities
Heuristic Search Framework
Heuristic Search
Heuristic Solution SchedulingSolution
Heuristic Problem HP_Schedule
iSchedule Framework
External Company Framework...

• fitness value, feasibility, incremental updates,
• flexibility, schedule change (insert task, swap
  tasks, )

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Algorithm Facilities 1/2

• Solution representation
• Set of sequences
• Neighbourhood
• Generic from iOpt insert, swap tasks
• Specific to iSchedule (cf. next slide)
• Meta-heuristics and other components from iOpt
• Simulated Annealing, GAs, tabu search,
• Best move, First/Best improvement

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Algorithm facilities 2/2
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Algorithm Hill climbing
HP_Schedule (HP)
Optimised Heuristic Solution
Single Solution Heuristic Search
Composite Single Solution Method
Schedule Constructive Generation
Local Search
(HP HS)
(Initial) ScheduleSequencesSolution (HS)
Best Move Neighbourhood Search
move
Insert Move Move Neighbourhood
Swap Move Neighbourhood
Segment Move Neighbourhood
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Algorithm Hill climbing
HP_Schedule (HP)
Optimised Heuristic Solution
Single Solution Heuristic Search
Composite Single Solution Method
Schedule Constructive Generation
Local Search
(HP HS)
(Initial) ScheduleSequencesSolution (HS)
Perform All Composite Neighbourhood Search
First Improvement Neighbourhood Search
Best Move Neighbourhood Search
move
move
Swap Move Neighbourhood
Insert Move Neighbourhood
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Schedule Visualisation
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Experiments Vehicle Routing Problem
1 Metaheuristic Approaches for the Vehicle
Routing Problem with Time windows A survey, M.
Gendreau and O. Bräysy, Mic2003, Kyoto, Japan 2
Fast Local SearchGuided Local Search (max. time
10800 sec. (3 hours)), Survey performed by
Patrick Mills (12th out of 21 papers)
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Conclusion

• iOpt/iSchedule is a complete framework of tools
  to quickly and easily develop solution for
  optimisation/satisfaction scheduling problems.
• Acquiring iOpt/iSchedule (evaluation license,
  academic license, commercial license).

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• Thank you !
• QA