Genetic Algorithm with Limited Convergence 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  Linkage adaptation

Genetic Algorithm with Limited Convergence 2 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

Genetic Algorithm with Limited Convergence 3 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 4 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 5 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 6 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  10 5 vs. 5.9  10 8 evaluations

Genetic Algorithm with Limited Convergence 7 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 8 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 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)