A simple genetic algorithm in Clojure December 26, 2012

Interested in Clojure and genetic algorithms? You're in the right place. Let's implement a simple genetic algorithm (GA) in Clojure.

Generic algorithms

DNA

Genetic algorithms are a way to evolve an algorithm over time in a survival-of-the-fittest fashion. The idea is to incorporate key aspects of biological evolution such as selection, mutation, and cross-over (breeding). Genetic algorithms are good for avoiding local optimas in finely tuned solutions while also not throwing away every bit of a solution when adjusting the search space.

Clojure

Clojure is a modern LISP that runs on the JVM. I chose Clojure for this task mostly because I'm interested in learning the language but also because it seems very natural to me to model a genetic algorithm in terms of things Clojure is good at. Those things being functional transforms and lazy infinite sequences.

Robby the Robot

We'll base our GA on Melanie Mitchell's (MM) Robby the Robot described in her excellent book on Complexity Theory: Complexity, a Guided Tour.

Robby's world

Robby lives in a two-dimensional, rectangular world divided into squares. Each square may be clean or dirty. Robby's job is to clean these squares, not run into walls and not waste time trying to clean squares that aren't dirty. Robby's fitness is determined by the actions he takes.

Fitness
  • Clean dirty square: 10 points
  • Run into wall: -5 points
  • Clean a clean square: -1 point

Robby's DNA

MM doesn't go in detail about the code she wrote to implement Robby the Robot, but she does talk about the underlying data structures she used. She does this so that the reader can understand how crossover) (i.e. breeding) works in a genetic algorithm.

Robby's DNA comprises 243 genes which represent each possible state of his world and which action he'll take in each of those states. His world is only composed of what he can see and he can only see the immediately adjacent squares in the cardinal directions and the square he is currently occupying. MM implementation used an array of ints to represent this. Each index represented a state and the integer in that position of the array represented the action. The possible actions are

Robby's actions

  • Clean
  • Move north
  • Move south
  • Move east
  • Move west
  • Move in a random direction (Yes, Robby has free will!)
  • Stop

MM describes how she implemented crossover in terms of this datastructure. When given two parents to breed she simply picks a random index within their DNA (from 0 to 242) and takes up to that index from the first parent and everything after that index from the second parent. The result is a new child.

Datastructure overview

An execution of this program will consists of many instances of two datastructures: rooms and agents.

Room

A room is a randomly generated vector of vectors where each cell can either be :dirty or :clean. Rooms are square and coordinates map to vector indicies. A 4x4 room may look like this

[[:clean :clean :dirty :clean] [:dirty :dirty :clean :clean] [:clean :clean :clean :clean] [:dirty :clean :dirty :clean]]

Agent

An agent is a vector of actions (or you could say an association of integer to action). An agent may look like this

[:north :south :east :north :stop :stop :clean :west :random :east :random :east :west :random :stop :clean etc...]

Scoring an agent against a room means putting the agent at position (0,0) in the room, determining which action the agent would take given the state of the agent at that position in the room, taking that action, and repeating 199 more times. Remember that when an agent takes an action it may change position, change its state (i.e. cleaning a dirty square) or may do nothing (by bumping into a wall, stopping or cleaning a clean square).

Wait a minute...

We're clearly missing something. How does our program know what a given gene in an agent's genome does? For example, when our agent is on a dirty square and surrounded by clean squares which index into its genome do we examine to discover which action it should take?

At this point we could decide to change the agent datastructure to be a mapping of state to action. However, I decided to keep it this way for two reasons.

  • It's easier (and probably faster?) to perform crossover during breeding with a vector than a map.
  • This more closely mimicks the datastructures that MM used.

So let's talk about how we specify which state each gene in Robby's DNA represents.

Going from a state to an action

First we need a way to determine a state given an agent, room and position. A simple map of each direction and whether it's clean, dirty, or a wall should do:

A state is a map of direction to contents.

Now we need to associate states like that with indices into Robby's genome.

Robby's genome has 243 entries in it, thus writing the mapping by hand is out of the question. We need a way to map a given state (e.g. north:clean south:clean west:dirty east:clean current:dirty) to a an action using a given agent's genome. With the datastructues we have this means writing another map of state to gene index.

If we're not going to write this map by hand then what do we do? Well we can start by generating an array of every possible state using Clojure's for function.

With that we can generate every possible state in one vector and then use Clojure's handy zipmap function to create a resulting map of state to integer.

The end result looked like this

Now we can determine an agent's state from the agent, room and position within that room. Then go from a state to an index into an agent's genome to determine which action the agent will take.

That's enough for now, next time we'll talk about crossover, mutation and using infinite sequences to represent things like generations and and agent's lifetime in a room.

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