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" 0 _2$\ +}T{Xb$P`A[,M!5m2$AOܙ"n2$"%wVtb$ QB`R7965lz 0e0e     A@ A5% 8c8c     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||S"`f3f3@8 Zʚ;E*6ʚ;g4KdKd0ppp@ <4!d!d 0L&<4dddd 0L&<4BdBd 0L&2*___PPT9 z?T+ @Neville & Sibley: SIGAda HoustonO =:&Developing a Generic Genetic Algorithm''<QMelvin Neville & Anaika Sibley Northern Arizona University Flagstaff, AZ 86011 RR : IntroductionMelvin Neville, CSE faculty Artificial Life Evolution of intelligence Biological neural net modeling Anaika Sibley, CSE student ASCI-PALS research (DOE) b99 e/  IntroductionhCSE 470: Introduction to Intelligent Systems Neural Nets, Fuzzy Logic, Genetic Algorithms Building tools&-<-<OutlineIntroduction: Who we are and context Genetic and Evolutionary Algorithms Biological analogies Genetic vs Evolutionary Algorithms Our version Sine function model Conclusions: algorithm, teaching, Ada NIX'IC' $fZ9Genetic and Evolutionary Algorithms: Biological AnalogiesBiological inspiration: evolution and Mendelian genetics Gene and Allele  Parameter variations Chromosome  Linkage among parameters Mutation  Allele alterations Crossover  evading local minima& %Biological AnalogiesBiological inspiration: evolution and Mendelian genetics Evolution: Selection and  fitness Role of chance? Problem of local minima (maxima) 6DIDI,& U Biological AnalogiesChromosomes and Genes$ Biological Analogies and Crossover Biological AnalogieshEvolutionary Paradigm: The cycle Selection among variants  More fit : Better chance to survive to reproduce Their alleles more represented Mutation and crossover increase variation&!! "Genetic vs Evolutionary AlgorithmsMajor distinctions per Michalewicz Representation: GA: Bit vector ES: Floating-point vector Selection: GA: Repetitive random selection with fitness influence ES: Fitness function without replacementb#) `#) `  &"Genetic vs Evolutionary AlgorithmsMajor distinctions per Michalewicz (cont.) Timing of mutation and crossover: GA: After next generation selected ES: Before next generation selected Probabilities of mutation and crossover: GA: Constant ES: Can alter from generation to generationl+"G)9#"G)9  '"Genetic vs Evolutionary AlgorithmsMajor distinctions per Michalewicz (cont.) Handling  illegal offspring: GA: Penalize re fitness ES: Discard or ImpossibleD+2#2 X( Our VersionOur algorithm: 1. Initialize the generation counter to 0 2. Initialize the population of entities 3. Iterate through generations until some stopping criterion met0) Our VersionVOur algorithm: 3. Iterate through generations 3.1 Increment generation counter 3.2 Each  winner produces same # children 3.3 Each child subject to chance mutation 3.4 Each child has chance of crossover 3.5 The children are evaluated 3.6 The most fit are selected for the next generation ( winners )D* Our Version_Our parameters and data structures: NumWin ChildPerWin Winners list Children list PriorityQueue($<$<,$ 1 Our Version#Our parameters and data structures:2The Sine Function ModelDTaylor s series: f(y+h) = h0f(y)/0! + h1f (y)/1! + h2f  (y)/2! + h3f   (y)/3! + h4f    (y)/4! + & Sine series: sin x = x1/1!  x3/3! + x5/5!  x7/7! + & RU +              4The Sine Function ModelfProblem: to  evolve the coefficients of the Sine Series Subproblems: Initial coefficient values? Evaluation of  fitness ? Interpretation of mutation? Interpretation of crossover?&FnFn9 p5The Sine Function ModelDInitial coefficient values? Set to zero (they go in both directions)&))6The Sine Function ModelEvaluation of fitness? Formula: Coefficients evaluated every N (5) degrees range 0 .. 90 degrees: sum square divergences from math library sin() Evaluation with initial coefficients of 0.0: 9.5000< 7The Sine Function ModelEvaluation of fitness? Evaluation with  perfect coefficients: 0.0000 The  perfect Coefficients (power of x): 0 => 0.0000000 4 => 0.0000000 1 => 1.0000000 5 => 0.0083333 2 => 0.0000000 6 => 0.0000000 3 => -0.1666667 7 => -0.0001984RZ(Z Z)ZZ8The Sine Function ModelInterpretation of mutation? 0 .. multiple genes can be selected Alteration in coefficients by +/- delta-values Delta-coefficient file: 0 => 0.1 4 => 0.002 1 => 0.05 5 => 0.0004 2 => 0.02 6 => 0.00006 3 => 0.008 7 => 0.00001VZkZeZ3 }9The Sine Function ModelInterpretation of crossover? Random choice of organisms involved Random choice of pairings Random choice of single point of breakage:hO  :Lessons Learned: The AlgorithmParameters of run: NumWin = 20 Winners, ChildPerWin = 20 20000 maximum cycles Eval at end: 0.000456 (start: 9.5000) Coefs: 0 => -0.0000000 -0.0000000 1 => 0.9500000 1.0000000 2 => 0.0600000 0.0000000 3 => -0.1360000 -0.1666667xZ;ZKZWZ;/UP !wK2Lessons Learned: ParametersuChange the Parameter Values Vary the number of Winners Vary the number of Children Create Multiple Runs Graph Results67#7#L1Seven Differing Runs M3Seven Differing Children =!Lessons Learned: The AlgorithmBreakdown of the evaluation: Angle (deg) Evolved sin Library sin 0 0.0000 0.0000 5 0.0833 0.0872 10 0.1669 0.1736 30 0.4921 0.5000 60 0.8691 0.8660 90 1.0015 1.0000*,ZZ>"Lessons Learned: The AlgorithmNeed to change deltas Need to shake free of local minima Change crossover mechanism? Alter population sizes? Domain knowledge very important694 94 @$Lessons Learned: Ada*Hard typing Linked-list structure GenericsA%Lessons Learned: AdaKHard typing: Student reaction (C++ and Java) The compiler as (stern) friend& ? ?B&Lessons Learned: AdaKLinked-list Updating problem: Node contents = pointer (thru GetContents())(.-= C'Lessons Learned: AdaJLinked-list Updating problem: Copy node contents (thru Get/SetContents())(-,< I/Lessons Learned: AdaLLinked-list Updating problem: Direct access to (non-encapsulated) Contents (/.J0Lessons Learned: AdalGenerics: Powerful but complicated Allow tying together complicated instantiation relationships (see paper) < b bH. ConclusionsGenetic Algorithms potentially powerful Final results may be stall at local minimum Domain knowledge important Ada: definite strengths Ada: particular problems,oF+The Sine Function ModelTaylor s series: f(y+h) = h0f(y)/0! + h1f (y)/1! + h2f  (y)/2! + h3f   (y)/3! + h4f    (y)/4! + & Euler s formula: eix = cos x + i sin x Substitute: Euler s formula with y=z,h=ix => eixez Evaluate at z = 0 ZXZZZ Z:Z    #       tE" G-The Sine Function Model^Substitute: f(z + ix)z=0 = cos x + i sin x = (ix)0ez/0! + (ix)1ez/1! + (ix)2ez/2!  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