# Moo

```
------------------------------------------------
< Moo. Breeding Genetic Algorithms with Haskell. >
------------------------------------------------
\ ^__^
\ (oo)\_______
(__)\ )\/\
||----w |
|| ||
```

## Features

```
| | Binary GA | Continuous GA |
|-----------------------+----------------------+--------------------------|
|Encoding | binary bit-string | sequence of real values |
| | Gray bit-string | |
|-----------------------+----------------------+--------------------------|
|Initialization | random uniform |
| | constrained random uniform |
| | arbitrary custom |
|-----------------------+-------------------------------------------------|
|Objective | minimization and maximiation |
| | optional scaling |
| | optional ranking |
| | optional niching (fitness sharing) |
|-----------------------+-------------------------------------------------|
|Selection | roulette |
| | stochastic universal sampling |
| | tournament |
| | optional elitism |
| | optionally constrained |
| | custom non-adaptive ^ |
|-----------------------+-------------------------------------------------|
|Crossover | one-point |
| | two-point |
| | uniform |
| | custom non-adaptive ^ |
| +----------------------+--------------------------|
| | | BLX-α (blend) |
| | | SBX (simulated binary) |
| | | UNDX (unimodal normally |
| | | distributed) |
|-----------------------+----------------------+--------------------------|
|Mutation | point | Gaussian |
| | asymmetric | |
| | constant frequency | |
| +----------------------+--------------------------|
| | custom non-adaptive ^ |
|-----------------------+-------------------------------------------------|
|Replacement | generational with elitism |
| | steady state |
|-----------------------+-------------------------------------------------|
|Stop | number of generations |
|condition | values of objective function |
| | stall of objective function |
| | custom or interactive (`loopIO`) |
| | time limit (`loopIO`) |
| | compound conditions (`And`, `Or`) |
|-----------------------+-------------------------------------------------|
|Logging | pure periodic (any monoid) |
| | periodic with `IO` |
|-----------------------+-------------------------------------------------|
|Constrainted | constrained initialization |
|optimization | constrained selection |
| | death penalty |
|-----------------------+-------------------------------------------------|
|Multiobjective | NSGA-II |
|optimization | constrained NSGA-II |
```

`^`

non-adaptive: any function which doesn't depend on generation number

There are other possible encodings which are possible to represent
with list-like genomes (`type Genome a = [a]`

):

- permutation encodings (
`a`

being an integer, or other `Enum`

type)
- tree encodings (
`a`

being a subtree type)
- hybrid encodings (
`a`

being a sum type)

## Contributing

There are many ways you can help developing the library:

I'm not a native speaker of English. If you are, please proof-read
and correct the comments and the documentation.

Moo is designed with possibility of implementing custom genetic
operators in mind. If you write new operators (`SelectionOp`

,
`CrossoverOp`

, `MutationOp`

) or replacement strategies
(`StepGA`

), consider contributing them to the library.
In the comments please give a reference to an academic
work which introduces or studies the method. Explain when or why
it should be used. Provide tests and examples if possible.

Implementing some methods (like adaptive genetic algorithms) will
require to change some library types. Please discuss your approach
first.

Contribute examples. Solutions of known problems with known optima
and interesting properties. Try to avoid examples which are too
contrived.

## An example

Minimizing Beale's function (optimal value f(3, 0.5) = 0):

```
import Moo.GeneticAlgorithm.Continuous
beale :: [Double] -> Double
beale [x, y] = (1.5 - x + x*y)**2 + (2.25 - x + x*y*y)**2 + (2.625 - x + x*y*y*y)**2
popsize = 101
elitesize = 1
tolerance = 1e-6
selection = tournamentSelect Minimizing 2 (popsize - elitesize)
crossover = unimodalCrossoverRP
mutation = gaussianMutate 0.25 0.1
step = nextGeneration Minimizing beale selection elitesize crossover mutation
stop = IfObjective (\values -> (minimum values) < tolerance)
initialize = getRandomGenomes popsize [(-4.5, 4.5), (-4.5, 4.5)]
main = do
population <- runGA initialize (loop stop step)
print (head . bestFirst Minimizing $ population)
```

For more examples, see examples/ folder.