1. HeuristicLab 3.0
Modeling EAs

2. Modeling Algorithms what is an algorithm? 3 main aspects
instructions
sequence of execution
result
we have to model
operators modifying data
graphs of operators representing the sequence of execution
"A finite set of unambiguous instructions performed in a prescribed sequence to achieve a goal, especially a mathematical rule or procedure used to compute a desired result. Algorithms are the basis for most computer programming."
© The American Heritage Dictionary of the English Language

3. Modeling Algorithms scopes operators form an n-ary tree structure
contain variables
operators
form a graph structure
represent basic instructions of algorithms
manipulate scopes (modify variables and/or sub-scopes)
decide which operators are executed next

4. Modeling Algorithms basic operators EmptyOperator
does nothing
SequentialProcessor, ParallelProcessor
executes its sub-operators on its scope
SequentialSubScopesProcessor, ParallelSubScopesProcessor
executes all its sub-operators on the corresponding sub-scopes
UniformSequentialSubScopesProcessor, UniformParallelSubScopesProcessor
executes its first sub-operator on all sub-scopes
ConditionalBranch
depending on a boolean value executes its first or second sub-operator on its scope
StochasticBranch
with a predefined probability executes its first or second sub-operator on its scope
VariableInjector
injects its local variables into the scope
Sorter
sorts its sub-scopes depending on a sorting criterion

5. Modeling Evolutionary Algorithms
abstract EA
basic operations
initialization, evaluation, selection, crossover, mutation, replacement
Initialization
Terminate?
Selection
Crossover
Mutation
Evaluation
Replacement

6. Modeling Evolutionary Algorithms
scopes form a hierarchical structure
very suitable for representing hierarchical structure of EA populations
a scope may represent a population, a solution, a part of a solution, …
operators work on different levels
to switch levels use
(Uniform)SequentialSubScopesProcessor
(Uniform)ParallelSubScopesProcessor …
Meta-Population Level
Population Level
Solution Level
Sub-Solution Level

7. Initialization set global variables create sub-scopes
inject variables representing global parameters of an algorithm
population size, mutation rate, number of elites, number of generations, …
VariableInjector
inject PRNG
RandomInjector
use special operators to inject variables representing the problem instance
for example: TSPInjector
create sub-scopes
one sub-scope for each population, individual, etc.
SubScopesCreater
initialize populations, individuals, etc.
use sub-scopes processors to iterate over all sub-scopes
apply special operators to create randomly generated individuals
for example: RandomPermutationGenerator

8. Evaluation calculate and inject quality value for each individual
use sub-scopes processors to iterate over all scopes representing an individual
apply problem-specific evaluation operator
for example: RoundedEuclideanPathTSPEvaluator
SingleObjectiveEvaluatorBase
base class for all single-objective evaluation operators
evaluates the quality value of an individual depending on the variables in the scope by calling abstract method Evaluate
adds a new double variable "Quality" to the scope
if a quality value already exists it is overwritten

9. TSP SGA Example … PRNG TSP Data Population Size Mutation Rate Elites
Evaluated Solutions …
SequentialProcessor
RandomInjector
PRNG
TSP Data
PRNG
TSPInjector
TSPRoundedEuclidean DistanceMatrixInjector …
VariableInjector
Permutation
Quality
Permutation
SubScopesCreater
UniformSequential
SubScopesProcessor
SequentialProcessor
RandomPermutation
Generator
DistanceMatrixPathTSP
Evaluator
Counter
Sorter
Main Loop

10. Selection separate sub-scopes into two groups
insert a new level in the scope tree
copy/move selected sub-scopes
use sub-scopes processors to work on selected scopes
basic selection operators
LeftSelector, RightSelector, RandomSelector
copy/move n sub-scopes from left or right or randomly
quality-based selection operators
selection is based on a double value (quality) in each sub-scope
ProportionalSelector, LinearRankSelector, TournamentSelector

11. Selection …
Remaining
Selected

12. Crossover & Mutation depend on solution encoding crossover mutation
effect variables contained in scopes
crossover
merge groups of n sub-scopes to one new sub-scope
for example: SinglePointCrossover, OrderCrossover
mutation
manipulate a scope
for example: FlipManipulator, InversionManipulator

13. TSP SGA Example … S … R S … R S … R S … R S … R S … R S … R Main Loop
ProportionalSelector
SequentialSubScopes
Processor
EmptyOperator
Replacement
SequentialProcessor
OrderCrossover
Termination ?
UniformSequential
SubScopesProcessor
Sorter …
Parents S … R
Selected S … R
Selected S … R
Children S … R
Selected S … R
Children S … R
Children S … R
Children
SequentialProcessor
StochasticBranch
InversionManipulator
DistanceMatrixPathTSP
Evaluator
Counter

14. Reduction reverse operation to selection join sub-scopes again
remove level in the scope tree
move sub-scopes on level up
basic reduction operators
LeftReducer, RightReducer, MergingReducer
take sub-scopes from left, right or all groups …

15. Replacement merge parents and children
use selection/reduction operators
select parents that should stay and discard all others (elitism)
select children that should replace and discard all others
merge both groups

16. TSP SGA Example … R S … R S … … … … … … … … R S … R S Replacement
SequentialSubScopes
Processor
SequentialProcessor
LeftSelector
RightReducer
SequentialProcessor
RightSelector
LeftReducer
MergingReducer … R S … R S … … …
Remaining Children …
Next Generation …
Remaining Parents …
Children
Parents …
Children
Parents … R S … R S
Sorter

17. Modularization
operator graphs grow quite quickly and become hard to handle
modularization of operator graphs is necessary
use special operator that wraps a whole operator graph
algorithms contain problem-specific parts
for example: TSPInjector, RandomPermutationGenerator, DistanceMatrixPathTSPEvaluator, …
how to build a generic SGA template that can be parameterized with all necessary problem-specific operators?
CombinedOperator
contains an operator graph
may inject its sub-operators into its scope
executes the whole operator graph on its scope
OperatorExtractor
placeholder operator
extracts and executes an operator with a predefined name from the scope
variable lookup goes up in the scope tree until a matching operator is found

18. DistanceMatrixPathTSP
TSP SGA Example
CombinedOperator
TSPInjector
RandomPermutation
Generator
DistanceMatrixPathTSP
Evaluator
CombinedOperator
SequentialProcessor
RandomInjector
ProblemInitializer
VariableInjector
SubScopesCreater
UniformSequential
SubScopesProcessor
SolutionGenerator
Evaluator
Counter
Sorter

19. Demonstration