# The moo package

Moo library provides building blocks to build custom
genetic algorithms in Haskell. They can be used to
find solutions to optimization and search problems.

Variants supported out of the box: binary (using
bit-strings) and continuous (real-coded).
Potentially supported variants: permutation,
tree, hybrid encodings (require customizations).

Binary GAs: binary and Gray encoding; point mutation;
one-point, two-point, and uniform crossover.
Continuous GAs: Gaussian mutation; BLX-α, UNDX, and
SBX crossover.
Selection operators: roulette, and tournament;
with optional niching and scaling.
Replacement strategies: generational with elitism
and steady state.
Constrained optimization: random constrained
initialization, death penalty, constrained
selection without a penalty function.
Multi-objective optimization: NSGA-II
and constrained NSGA-II.

[

Skip to ReadMe]

## Properties

Version | **1.0** |
---|

Change log | None available |
---|

Dependencies | array, base (==4.*), gray-code (>=0.2.1), mersenne-random-pure64, monad-mersenne-random, mtl (>=2), random (>=0.1), random-shuffle (>=0.0.2), time [details] |
---|

License | BSD3 |
---|

Author | Sergey Astanin <s.astanin@gmail.com> |
---|

Maintainer | Sergey Astanin <s.astanin@gmail.com> |
---|

Stability | experimental |
---|

Category | AI, Algorithms, Optimisation, Optimization |
---|

Home page | http://www.github.com/astanin/moo/ |
---|

Source repository | head: git clone git://github.com/astanin/moo.git |
---|

Uploaded | Tue May 21 16:34:03 UTC 2013 by SergeyAstanin |
---|

Downloads | 403 total (8 in last 30 days) |
---|

Votes | |
---|

Status | Docs uploaded by user Build status unknown [no reports yet] |
---|

## Modules

[Index]

## Downloads

#### Maintainers' corner

For package maintainers and hackage trustees

## Readme for moo-1.0

# 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.