A framework for simple evolutionary algorithms. Provided with a function for
evaluating a genome's fitness, a function for probabilistic selection among a
pool of genomes, and recombination and mutation operators,
runEA will run an
EA that lazily produces an infinite list of generations.
AI.SimpleEA.Utils contains utilitify functions that makes it easier to write
the genetic operators.
- runEA :: [Genome a] -> FitnessFunc a -> SelectionFunction a -> RecombinationOp a -> MutationOp a -> StdGen -> [[(Genome a, Fitness)]]
- type FitnessFunc a = Genome a -> [Genome a] -> Fitness
- type SelectionFunction a = [(Genome a, Fitness)] -> Rand StdGen [Genome a]
- type RecombinationOp a = (Genome a, Genome a) -> Rand StdGen (Genome a, Genome a)
- type MutationOp a = Genome a -> Rand StdGen (Genome a)
- type Fitness = Double
- type Genome a = [a]
Runs the evolutionary algorithm with the given start population. This will
produce an infinite list of generations and
takeWhile should be
used to decide how many generations should be computed. To run a specific
number of generations, use
let generations = take 50 $ runEA myFF mySF myROp myMOp myStdGen
To run until a criterion is met, e.g. that an individual with a fitness of at
least 19 is found,
takeWhile can be used:
let criterion = any id . map (\i -> snd i >= 19.0) let generations = takeWhile (not . criterion) $ runEA myFF mySF myROp myMOp myStdGen
A fitness functions assigns a fitness score to a genome. The rest of the individuals of that generation is also provided in case the fitness is in proportion to its neighbours.
A selection function is responsible for selection. It takes pairs of genomes and their fitness and is responsible for returning one or more individuals.
A recombination operator takes two parent genomes and returns two children.
A mutation operator takes a genome and returns an altered copy of it.
The aim of this OneMax EA is to maximize the number of
1's in a bitstring.
The fitness of a
bitstring i simply s defined to be the number of
1's it contains.
import AI.SimpleEA import AI.SimpleEA.Utils import Control.Monad.Random import Data.List import System.Environment (getArgs) import Control.Monad (unless)
numOnes function will function as our
FitnessFunc and simply returns the number of
in the string.
numOnes :: FitnessFunc Char numOnes g _ = (fromIntegral . length . filter (=='1')) g
select function is our
SelectionFunction. It uses sigma-scaled, fitness-proportionate
sigmaScale is defined in
SimpleEA.Utils. By first taking the four
best genomes (by using the
elite function) we get elitism, making sure that
maximum fitness never decreases.
select :: SelectionFunction Char select gs = select' (take 4 $ elite gs) where scaled = zip (map fst gs) (sigmaScale (map snd gs)) select' gs' = if length gs' >= length gs then return gs' else do p1 <- fitPropSelect scaled p2 <- fitPropSelect scaled let newPop = p1:p2:gs' select' newPop
Crossover consists of finding a crossover point along the length of the genomes
and swapping what comes after between the two genomes. The parameter
determines the likelihood of crossover taking place.
crossOver :: Double -> RecombinationOp Char crossOver p (g1,g2) = do t <- getRandomR (0.0, 1.0) if t < p then do r <- getRandomR (0, length g1-1) return (take r g1 ++ drop r g2, take r g2 ++ drop r g1) else return (g1,g2)
Mutation flips a random bit along the length of the genome with probability
mutate :: Double -> MutationOp Char mutate p g = do t <- getRandomR (0.0, 1.0) if t < p then do r <- getRandomR (0, length g-1) return (take r g ++ flipBit (g !! r) : drop (r+1) g) else return g where flipBit '0' = '1' flipBit '1' = '0'
main function creates a list of 100 random genomes (bit-strings) of length
20 and then runs the EA for 100 generations (101 generations including the
random starting population). Average and maximum fitness values and standard
deviation is then calculated for each generation and written to a file if a file
name was provided as a parameter. This data can then be plotted with, e.g.
main = do args <- getArgs g <- newStdGen let (g1,g2) = split g let p = take 100 $ randomGenomes 20 '0' '1' g1 let gs = take 101 $ runEA p numOnes select (crossOver 0.75) (mutate 0.01) g2 let fs = avgFitnesses gs let ms = maxFitnesses gs let ds = stdDeviations gs mapM_ print $ zip5 gs [1..] fs ms ds unless (null args) $ writeFile (head args) $ getPlottingData gs