Haskell: Abstracting a Genetic Algorithm

Question

I'm new to the world of Haskell programming and I'm cutting my teeth on a simple genetic algorithm for finding good solutions to the Travelling Salesman problem. I am representing the solutions as permutations on Integers and so I have this type synonym

type Genome = [Int]

The algorithm itself is a set of functions which operate on the solutions:

mutation :: Genome -> Genome
selectParents :: [Genome] -> [Genome] -> [Genome]
crossover :: Genome -> Genome -> (Genome, Genome)
selectSurvivors :: [Genome] -> [Genome] -> [Genome]

I'm not sure how much of my code is relevant to my question so please ask if more details are needed. One thing that might be worth mentioning is that the type signatures above are actually simplified, I am in fact using the State monad to carry around an StdGen so all of these functions actually return stateful computations.

There are several things which I would like to do with this but can't quite get my head around. I want to make it possible to choose different representations for the solutions, it seems to me that this would be a natural place to use a type class, so that Genome would be the type class and [Int] a specific instance of this Genome.

Now, I want to be able to experiment with the implementations, and I want to be able to use the code in other projects. Using a type class like this would require that every new algorithm I create would require me to create another instance of Genome, is this a good way to go about creating a library?

One bonus question, just a thing that's been bothering me, is there any way to create something like a type synonym for a function so that if I'm writing a function which takes functions as arguments I can write the synonym rather than the whole type signature of the function i.e so that something like the following would work.

type someFunc = [Int] -> [Int] -> Int
someOtherFunc :: someFunc -> [Int] -> Int

Right, hopefully that's a lucid enough explanation of the problem, feel like I've missed the really obvious answer but it hasn't jumped out at me. Cheers

Answer 1

Unfortunately, the ideal solution usually depends on your problem domain. This blog post talks about the typeclass approach and the bitwise approach. I personally think a hybrid approach is best if you want flexibility. If there is a good bitwise mapping, you can define it, and the implementation is derived from that, otherwise you can implement the crossover and mutate manually.

ja's method is actually not going to work. Some of your genome functions are going to need random input, which you can get by running in the state monad with a random number generator like this thread

class Genome a where
    fitness :: a -> Int
    breed :: (RandomGen g, MonadState g m) => a -> a -> m a
    mutate :: (RandomGen g, MonadState g m) => a -> m a

Then you have common functions that operate on sets of genomes, regardless of implementation.

selectParents :: (Genome a, RandomGen g, MonadState g m) => [a] -> m [a]
selectSurvivors :: (Genome a, RandomGen g, MonadState g m) => [a] -> m [a]

If you do have a good bit mapping, you can just define fixed functions on BitArrays (notice that each will have to take the fitness function as a parameter)

breed :: (RandomGen g, MonadState g m) => BitArray -> BitArray -> m BitArray
mutate :: (RandomGen g, MonadState g m) => BitArray -> m BitArray
selectParents :: (RandomGen g, MonadState g m) => (BitArray -> Int) -> [BitArray] -> m [BitArray]
selectSurvivors :: (RandomGen g, MonadState g m) => (BitArray -> Int) -> [BitArray] -> m [BitArray]

Answer 2

Yes, using a type class to represent a genome is a good way to go. Something like this:

class Genome a where
   mutation :: a -> a
   selectParents :: [a] -> [a] -> [a]
   crossover :: a -> a -> (a, a)
   selectSurvivors :: [a] -> [a] -> [a]
instance Genome [a] where
   mutation l = l
   selectParents l1 l2 = l1
   crossover g1 g2 = (g1,g2)
   selectSurvivors l1 l2 = l1
data Tree a = Leaf a | Branch [Tree a]   
instance Genome (Tree a) where
   mutation t = t
   selectParents l1 l2 = l1
   crossover g1 g2 = (g1,g2)
   selectSurvivors l1 l2 = l1

As for instancing a new datatype for each algorithm, you can include a few instances in your library, but there's no problem instancing new ones - that's the point !