Portability | portable |
---|---|

Stability | experimental |

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]

# Documentation

runEA :: [Genome a] -> FitnessFunc a -> SelectionFunction a -> RecombinationOp a -> MutationOp a -> StdGen -> [[(Genome a, Fitness)]]Source

Runs the evolutionary algorithm with the given start population. This will
produce an infinite list of generations and `take`

or `takeWhile`

should be
used to decide how many generations should be computed. To run a specific
number of generations, use `take`

:

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

type FitnessFunc a = Genome a -> [Genome a] -> FitnessSource

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.

type SelectionFunction a = [(Genome a, Fitness)] -> Rand StdGen [Genome a]Source

A selection function is responsible for selection. It takes pairs of genomes and their fitness and is responsible for returning one or more individuals.

type RecombinationOp a = (Genome a, Genome a) -> Rand StdGen (Genome a, Genome a)Source

A recombination operator takes two *parent* genomes and returns two
*children*.

type MutationOp a = Genome a -> Rand StdGen (Genome a)Source

A mutation operator takes a genome and returns an altered copy of it.

# Example Program

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)

The `numOnes`

function will function as our `FitnessFunc`

and simply returns the number of `1`

's
in the string.

numOnes :: FitnessFunc Char numOnes g _ = (fromIntegral . length . filter (=='1')) g

The `select`

function is our `SelectionFunction`

. It uses sigma-scaled, fitness-proportionate
selection. `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 `p`

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 `p`

.

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'

The `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.
gnuplot (http://www.gnuplot.info/).

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