Transcript Slide 1
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
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Linkage adaptation
Genetic Algorithm with Limited Convergence
Messy Genetic Algorithms (mGAs)
Inspiration from the nature
evolution starts from the simplest forms of life
mGAs 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
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Genetic Algorithm with Limited Convergence
mGA’s codings
Tagged alleles
Variable-length strings: (name1, allele1) … (nameN, alleleN)
((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
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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
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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 (lk)2k O(lk) 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
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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
number of genes in common
fmGA vs mGA
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tournaments are held only between strings that have a threshold
150-bit long problem, 305-bit deceptive function
1.9105 vs. 5.9108 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
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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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Genetic Algorithm with Limited Convergence