input-output-hk / moo

Genetic algorithm library for Haskell. Binary and continuous (real-coded) GAs. 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, tournament, and stochastic universal sampling (SUS); with optional niching, ranking, 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.

Moo

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< Moo. Breeding Genetic Algorithms with Haskell. >
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Installation

Installation from Hackage

Hackage is a Haskell community's package archive. This is where the latest versions of packages are published first. To install Moo from Hackage use Cabal-Install:

• install Haskell Platform or GHC and Cabal-Install
• run cabal update
• run cabal install moo

Installation with Stack

Stackage is a stable package archive. Stackage builds are supposed to be reproducible. Stackage also provides Long Term Support releases. To build Moo with Stackage dependencies, use the stack tool:

• install stack
• if necessary, install GHC: run stack setup
• run: stack update
• in the project source directory run: stack build
• to run tests: stack test

Build Status

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.