Genetic Algorithm with Limited Convergence
‹#›
Simple Selectorecombinative GAs
Scale poorely on hard problems
(multimodal, deceptive, high
degree of subsolution interaction, noise, ...)
, largely the result of
their mixing behaviour
Inability of SGA to correctly identify and adequately mix the appropriate
BBs in subsequent generations
Exponential computation complexity of SGA
Crossover operators
or other exchange emchanisms are needed
such that adapt to the problem at hand
Linkage adaptation
Genetic Algorithm with Limited Convergence
‹#›
Messy Genetic Algorithms
(mGAs)
Inspiration
from the nature
evolution starts from the simplest forms of life
mGA
s
depart from SGA in four ways:
messy codings
messy operators
separation of processing into three heterogeneous phases
epoch

wise iteration to improve the complexity of solution
Genetic Algorithm with Limited Convergence
‹#›
mGA
’
s codings
Tagged alleles
Variable

length strings: (name
1
, allele
1
) … (name
N
, allele
N
)
((4,0) (1,1) (2,0) (4,1) (4,1) (5,1))
Over

specification
multiple gene instances (gene 4)
majority voting
–
would express deceptive genes too readily
first

come first

served (left to right expression)

positional priority
Underspecification
missing gene instances (gene 3)
average schema value
–
variance is too high
competitive template
–
solution locally optimal with respect to k

bit
perturbations
Genetic Algorithm with Limited Convergence
‹#›
Messy operators: cut & splice
Cut
–
divides a single string into two parts
Splice
–
joins the head of one string with the tail of the other one
When short strings are mated
–
probability of cut is small
mostly the
string will be just spliced
the strings’ length is doubled
When long string are mated
–
probability of cut is large
one

point
crossover
Genetic Algorithm with Limited Convergence
‹#›
Three heterogeneous phases
Initialization
Enumerative initialization of the population with all sub

strings of a certain
length
k
<<
l
(
l
k
)2
k
O
(
l
k
) computations
Guaranteed that all BBs of certain size are present in the population
Primordial phase
Only selection used to dope the population with good BBs
Good linkage groups are selected before their alleles are allowed to be
mixed
Juxtapositional phase
selection + cut&splice
Mixing of the BBs
Genetic Algorithm with Limited Convergence
‹#›
Fast messy genetic algorithms
Probabilistically complete enumeration
Population of strings of length
l
’ close to
l
is generated
Assumption: each string contains many different BBs of length
k
<<
l
Building block filtering
extracts highly

fit and effectively linked BBs
repeats (1)
selection
and (2)
gene deletion
only
O
(
l
) computations
to converge
Extended thresholding
tournaments are held only between strings that have a
threshold
number of genes in common
fmGA vs mGA
150

bit long problem, 30
5

bit deceptive function
1.9
5
vs. 5.9
8
evaluations
Genetic Algorithm with Limited Convergence
‹#›
Gene expression messy GA

gemGA
Messy ???
No variable

length strings
No under

or over

specification
No left

to

right expression
Messy use of heterogeneous phases
of processing in gemGA
Linkage learning phase

first identifies linkage groups
Mixing phase
–
selection + recombination
exchanges good allele combinations within those groups to find
optimal solution
Genetic Algorithm with Limited Convergence
‹#›
gemGA: The idea
Linkage learning phase
Transcription I (antimutation)
Each string undergoes
l
one

bit perturbations
Improvements are ignored ?!? (bit does not belong to optimal BB)
Changes that degrade the structure are marked as possible linkage groups
candidates
Ex.: two 3

bit deceptive BBs 111 101
marked not marked
(degrades) (improves)
Transcription II
Identifies the exact relations among the genes by checking nonlinearities
IF
f
(
X’
i
) +
f
(
X’
j
) !=
f
(
X’
ij
) THEN link(
i,j
)
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