Evolutionary algorithms are stochastic search and optimization heuristics derived from the classic evolution theory, which are implemented on computers in the majority of cases.

1. Evolutionary Algorithms

2. Evolutionary Algorithms (EA)
• EA are stochastic search and optimization
heuristics derived from the classic evolution
theory, which are implemented on computers
in the majority of cases.

3. Basic Idea
• If only those individuals of a population
reproduce, which meet a certain selection
criteria, and the other individuals of the
population die, the population will converge to
those individuals that best meet the selection
criteria.
• Population dynamics follow the basic rule of
Darwin evolution theory, which can be described
in short as the “survival of the fittest.”

4. General EA Process

5. Classification of EA/CA Methods
Genetic Algorithm
(GA)
Genetic
Programming (GP)
Evolutionary
Strategy (ES)
Evolutionary
Programming (EP)
Learning Classifier
System (LCS)

6. Related Search Heuristics
Hill Climbing
Particle
Swarms (PS)
Simulated
Annealing (SA)
Tabu Search
(TS)
Ant Systems
(AS)

7. EA Analogy Foundations
Individual
Selection
Crossover
Mutation

8. Genetic Algorithm (GA)
• A search heuristic that mimics the process of
natural selection*.
* Wikipedia

9. GA – Individual
• GA individuals store the solution attributes
not directly in clear type but in a coded
representation.
– Bit-String: consists of L bits, which are clustered
into words wi. In a simple version all words are of
equal length l.
– The decoded words w are the solution attributes
x, which are to be optimized. Each attribute xi is
assigned to the word wi.

10. Standard Binary Coding
• A simple binary decoding method for a real number
attribute xi with the upper bound of oj and the lower
bound of uj with the length l from the word wi could
be:
• wi,n gives the nth bit of the word wi

11. GA – Fitness
• After the fitness for every individual ai of the
population A(s) has been calculated, the best
individuals of the population A(s) are selected
to be the parents of the next generation
A(s+1).

12. GA – Selection
• A commonly selection method is the roulette
wheel selection:
– an individual ai of the population A(s) is assigned to a
small part on a wheel of chance. The size pi of this
part is proportional to the calculated fitness Φi.
– The wheel is then tossed as many
times as parents are needed to
create the next generation and each
winning individual is copied into the
parent population B(s).

13. GA – Crossover
• The descendants are created by performing sexual
recombination (crossover) and mutation.
• Crossover exchanges genes, coding the solution
attributes, between the parents to generate the
descendants.
– Instead of DNA, the Bit-String of the parents is cut at a
position chosen by chance and the single parts are mixed
and chained again
to build the
Bit-Strings of the
descendants.

14. GA – Mutation
• After the descendants are created by sexual
recombination, the descendants are mutated.
• This resembles the naturally occurring
accidents that can happen when DNA is
copied. Mutation on the Bit-String occurs by
shifting single bits in the Bit-String selected by
chance.

15. GA
• After undergoing these creation and altering
processes, the descendants form the next
generation A(s+1).
• The generational process is repeated until a
satisfying solution for the given target
function is found.

16. Evolutionary Strategy (ES)
• An optimization technique based on ideas of
adaptation and evolution. It belongs to the
general class of evolutionary computation or
artificial evolution methodologies*.
* Wikipedia

17. ES as a Phenotype Oriented Approach
• ES method emphasizes the phenotype of an
individual and that it omits any additional
coding. Because of this, the crossover and
mutation methods have to change the real
value of an attributes and not an abstract
coded representation
• This phenotype-oriented approach allows
further optimization of the altering operators.

18. ES – Individual
• An ES individual consists in most cases of a
vector of n real numbers, the decision
parameters that are to be optimized:
• The strategy parameters are stored in an
additional vector of n real numbers:

19. ES – Fitness
• We use one strategy parameter σi for each
decision parameter xi.
• σi assigns a standard deviation to the
phenotype mutation for each decision
parameter, which is equal to the mean size of
a mutation step.

20. ES – Selection
• A deterministic selection procedure is used to
select the possible parents for the next
generation.
• Only λ best individuals are selected from a
population A(s) that is of size μ and used for
the parent population B(S).
• This approach is called the (μ, λ) strategy.

21. ES – Crossover
• Two different methods to mix two
selected parents (e1 and e2) from B(s):
– Discrete crossover: used for the decision
parameters.
• A descendant c either inherits the attribute xi
from one or the other parent.
• The actual parent that supplies an attribute can
be chosen arbitrarily.
– Intermedium crossover: used for strategy
parameters.
• The descendant c is assigned a σi value that is
the mean of the corresponding σi of both
parents.
• This method has a concentration effect.

22. ES – Mutation
• Strategy parameters are mutated according to:
• N(0,1) is an evenly distributed random number with the range
[0,1] that is generated for each mutation per individual.
• Nj(0,1) is also an evenly distributed random number with the
range [0,1], but this number is generated for each σi.
• τ1 and τ2 are exogene strategy parameters.
• The new mutation step size σ’i is used to mutate the decision
parameters xi:

23. ES
• The descendants form the next generation
A(s+1) after undergoing these altering
processes.
• Again the generational process can be
repeated until a satisfying solution is found.

24. Genetic Programming (GP)
• An evolutionary algorithm-based methodology inspired by
biological evolution to find computer programs that
perform a user-defined task. Essentially GP is a set of
instructions and a fitness function to measure how well a
computer has performed a task. It is a specialization of
genetic algorithms (GA) where each individual is a
computer program. It is a machine learning technique used
to optimize a population of computer programs according
to a fitness landscape determined by a program's ability to
perform a given computational task*.
* Wikipedia

25. GP – Individual
• Designed to store computer programs in such
a way that they can be optimized using an
evolutionary approach.
• The computer programming language LISP
was used to code computer programs into an
individual.

26. GP – Fitness
• Evaluated by executing the program under
varying conditions and the behavior or the
output of the program can be used to
estimate the fitness.

27. GP – Selection
• Tournament selection:
– Parents are selected by doing multiple small
tournaments between members of A(s).
– For each tournament n arbitrarily selected
individuals from the population A(s) are put into a
tournament group.
• Then the best individual of the tournament
group is selected as possible parent and
copied into the parent population B(s).

28. GP – Crossover
• Performed by selecting
two sub trees by chance
from the parents and
exchange them to
create the descendants.

29. GP – Mutation
• Performed by selecting a sub tree of the
descendant by chance and to exchange the
sub tree with an arbitrary generated new sub
tree.
• The GP program trees tend to rapidly increase
in size during the evolutionary process. This
effect is called bloat and it causes the increase
of computation effort, since the programs that
are to be evaluated become more complex.

30. Evolutionary Programming (EP)
• Evolutionary programming is one of the four
major evolutionary algorithm paradigms. It is
similar to genetic programming, but the
structure of the program to be optimized is
fixed, while its numerical parameters are
allowed to evolve*.
* Wikipedia

31. EP – Individual
• EP individuals (each representing whole
species) is only determined by the given
optimization problem and underlies virtually
no restrictions regarding the data types that
can be processed.

32. EP – Selection
• EP uses a mixture of tournament selection and
the best of selection as in ES.
• For each individual ai a tournament group of n
individuals selected by chance from A(s), then the
number of individuals of that tournament group
that are inferior to ai, regarding the fitness is
determined and assigned as score to ai.
• The λ individuals with the highest score are
selected as parents B(s).

33. EP – Mutation
• EP mutation operator is problem or data type
specific, because each problem can use
different attribute data types for the
individuals.

34. Learning Classifier Systems (LCS)
• A machine learning system with close links to
reinforcement learning and genetic
algorithms*.
• The method of LCS is based on the GA
method, only the Bit-String representation of
the individuals was changed that they can
represent generalizing rules.
* Wikipedia

35. LCS – Individual
• Able to learn simple “if {condition} then {action}”
style rules by learning from feedback information
given by an environment or supervisor.
• The condition and the action parts of the rules
are coded like the GA in Bit-Strings.
– Only the alphabet of the condition part was extended
from the basic binary alphabet {0,1} to {0,1,#}.
• The ‘#’ symbol represents a ‘don’t care’ to allow
generalization of conditions.

36. LCS – Fitness
• Individuals are evaluated in two phases:
– Performance phases (red), where the individuals
interact with the environment.
– Reinforcement phase (blue), where the individuals
are rewarded for good performance.

37. Performance and Reinforcement
Phases of LCS evaluation

38. LCS – Fitness
• The performance and reinforcement phase
can be repeated several times to ensure
correctly assigned fitness values of the rules
evaluated. Then the accumulated fitness can
be used to perform a single GA generation
step.

39. Thank You
Q & A