Kh Khaled Rasheed Co Comp mputer Science Dept. Uni Universi sity of Georgia ht http://www.cs. s.ug uga.edu/ u/~kha haled
} Genetic al algorithms ◦ Pa Parallel el gen genet etic algo gorithms } Genetic program amming } Evolution strat ategies } Clas assifi fier systems } Evolution program amming } Relat ated topics } Conclus Conclusion ion
} Fit Fitness = Heig ight } Survival al of f the fi fittest
} Mai aintai ain a a populat ation of f potential al so solutions } New solutions ar are generat ated by selecting, combining an and modify fying ex exist sting g so solutions ◦ Crossover ◦ Mutation } Objective fu function = Fitness fu function ◦ Better solutions favored for parenthood ◦ Worse solutions favored for replacement
} ma maximiz imize 2X^ X^2-y+ y+5 where X: X:[0,3],Y:[0,3]
} ma maximiz imize 2X^ X^2-y+ y+5 where X: X:[0,3],Y:[0,3]
} Rep Repres esen enta tati tion } Fi Fitn tnes ess functi tion } Ini Initialization n st strategy } Se Sele lection ion st strategy } Cro Crossover r op operator ors } Mu Mutation op operator ors
} Rep Repres esen enta tati tion } Fi Fitn tnes ess functi tion } Ini Initialization n st strategy } Se Sele lection ion st strategy } Cro Crossover r opera rators rs } Mu Mutation operators } Rep Replacem emen ent t st strategy
} Proportional al selection (roulette wheel) ◦ Selection probability of individual = individual’s fitness/sum of fitness } Ran ank bas ased selection ◦ Example: decreasing arithmetic/geometric series ◦ Better when fitness range is very large or small } Tour Tourna nament nt selection on ◦ Virtual tournament between randomly selected individuals using fitness
} Point crosso ssover (classi ssical) ◦ Parent1=x1,x2,x3,x4,x5,x6 ◦ Parent2=y1,y2,y3,y4,y5,y6 ◦ Child =x1,x2,x3,x4,y5,y6 } Uniform crosso ssover ◦ Parent1=x1,x2,x3,x4,x5,x6 ◦ Parent2=y1,y2,y3,y4,y5,y6 ◦ Child =x1,x2,y3,x4,y5,y6 } Arithmetic crosso ssover ◦ Parent1=x1,x2,x3 ◦ Parent2=y1,y2,y3 ◦ Child =(x1+y1)/2,(x2+y2)/2,(x3+y3)/2
} ch chan ange on one or or mor ore com compon onents } Le Let Child=x1 =x1,x2 x2,P,x3 x3,x4 x4... } Ga Gaussi ussian n mut utation: n: ◦ P ¬ P ± ∆ p ◦ ∆ p: (small) random normal value } Un Uniform mutation: ◦ P ¬ P new ◦ p new : random uniform value } bo bounda dary mutation: ◦ P ¬ Pmin OR Pmax } Bi Binary y mutation=bit flip
} Finds global al optima } Can an han andle discrete, continuous an and mixed var ariab able spac aces } Eas asy to use (short program ams) } Ro Robust t (less sensiti tive to to noise, ill con condit ition ions)
} Relat atively slower than an other methods (not suitab able fo for eas asy problems) } Theory lag ags behind ap applicat ations
} Coar arse-grai ained GA at at high level } Fin Fine-grai ained GA at at low level
} Coar arse-grai ained GA at at high level } Global al par aral allel GA at at low level
} Coar arse-grai ained GA at at high level } Coar arse-grai ained GA at at low level
} Introduced (officially) by John Ko Koza in his bo book (g (gene netic pro progra ramming ng, 1992) } Ea Earl rly attempt pts da date ba back k to the he 50s (e (evolving po popu pulations of bi binary obje bject ct co codes) } Ide Idea is to evolve comput puter r pro progra rams } De Decl clarative p progr gramming l g langu guage ges us usua ually us used d (Lisp) p) } Pr Progr grams a are r e rep epres esen ented ted a as tr trees ees
} A A populat ation of trees ees rep epres esen enting pr programs } Th The e prog ogram ams ar are e com compos osed ed of of el elem emen ents fr from the he FUNCT CTION SET and nd the he TERMINAL SE SET } Th Thes ese e set ets ar are e usual ally fixed ed set ets of of symbol ols } Th The e funct ction on set et for orms "non on-le leaf" n nodes. . (e (e.g .g. + . +,-,* ,*,s ,sin in,c ,cos) } Th The e ter erminal al set et for orms leaf eaf nod odes es. (e. e.g. x, x,3.7, random())
} Fi Fitn tnes ess is usually based ed on I/O tr traces es } Cro Crossover r is implement nted by ra rand ndomly sw swapping su subtrees be between n indi ndividua duals } GP GP usually does not extensively rely on mu mutation ion (random om nod odes s or or su subtrees) } GP GPs are usually generational (sometimes with wi h a gene nera ration n gap) } GP usually uses huge populations (1M M in individ ividuals ls)
} More fl flexible representat ation } Great ater ap applicat ation spectrum } If f trac actab able, evolving a a way ay to mak ake “things” is more usefu ful than an evolving the the “thi “thing ngs”. ”. } Exam ample: evolving a a lear arning rule fo for neural al networks (Am Amr Rad adi, GP , GP98) v vs. . evolving the weights of f a a par articular ar NN.
} Ex Extre tremely y slow } Very poor han andling of f numbers } Very lar arge populat ations needed
} Ge Gene netic programming ng with h line near geno nomes s (W (Wolfgang Ba Banzaf) ◦ Kind of going back to the evolution of binary program codes } Hyb Hybrids of GP P and other methods that be better handl dle numbe bers: ◦ Least squares methods ◦ Gradient based optimizers ◦ Genetic algorithms, other evolutionary computation methods } Ev Evolving things other than programs ◦ Example: electric circuits represented as trees (Koza, AI in design 1996)
} Were invented to so solve numerical optimization pr probl blem ems } Or Originated in Europe in the 1960s } In Initially: two-me memb mber or (1+1) ES: S: ◦ one PARENT generates one OFFSPRING per GENERATION ◦ by applying normally distributed (Gaussian) mutations ◦ until offspring is better and replaces parent ◦ This simple structure allowed theoretical results to be obtained (speed of convergence, mutation size) } Later Later: en enhan anced ed to to a a (µ+1) st strategy which incorporated crosso ssover
} Sc Schwefe fel l in introd oduced the mu mult lti- me memb mbered ESs Ss now ow denot oted by y (µ µ + λ ) ) an and (µ, , λ ) } (µ, , λ ) E ES: Th : The p e paren ent gen t gener erati tion i is di disjoint nt fro rom the he chi hild d gene nera ration } (µ µ + + λ ) ) ES: Some of the pa parents may be be se selected to o "prop opagate" to o the child ge generati tion
} Real al val alued vectors consisting of f two par arts: ◦ Object variable: just like real-valued GA individual ◦ Strategy variable: a set of standard deviations for the Gaussian mutation } This structure al allows fo for "Self- ad adap aptat ation“ of f the mutat ation size ◦ Excellent feature for dynamically changing fitness landscape
} In mac achine lear arning we seek a a good hy hypo pothe thesis } The hypothesis may ay be a a rule, a a neural al network, a a program am ... etc. } GAs an and other EC methods can an evolve rules, NNs, program ams ...etc. } Clas assifi fier systems (CFS) ar are the most explicit GA bas ased mac achine lear arning to tool.
} Ru Rule a e and m mes essage s ge system tem ◦ if <condition> then <action> } Ap Apporti tionmen ent o t of c cred edit s t system tem ◦ Based on a set of training examples ◦ Credit (fitness) given to rules that match the example ◦ Example: Bucket brigade (auctions for examples, winner takes all, existence taxes) } Ge Genetic algorithm ◦ evolves a population of rules or a population of entire rule systems
} Ev Evolves a population of rules, the final po popu pulation is used d as the rule and d message sy syst stem } Di Dive versity maintenance among rules is hard } If If done well converges faster } Ne Need to specify how to use the rules to cl clas assify ◦ what if multiple rules match example? ◦ exact matching only or inexact matching allowed?
} Eac ach individual al is a a complete set of f ru rules or r comp mplete te soluti tion } Avoids the har ard credit as assignment pr probl blem } Slow becau ause of f complexity of f spac ace
} Clas assical al EP evolves fi finite stat ate mac achines (or similar ar structures) } Relies on mutat ation (no crossover) } Fitness bas ased on trai aining seq sequen ence( e(s) s) } Good fo for sequence problems (DNA) an and prediction in time series
} Add a a stat ate (with ran andom tran ansitions) } Delete a a stat ate (reas assign stat ate tran ansitions) } Chan ange an an output symbol } Chan ange a a stat ate tran ansition } Chan ange the star art stat ate
} No specific representation } Similar to Evolution Strategies ◦ Most work in continuous optimization ◦ Self adaptation common } No crossover ever used!
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