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Evolutionary Algorithms in python, queens example

by mat on September 14th, 2009

So a friend of mine introduced me to Evolutionary Algorithms a while back and I got some lecture notes passed onto me explaining the basics and a simple example in pseudo-code.

After a bit of work I’ve written up the queens example as an evolutionary algorithm in python. Here goes:

The queens problem
The following is the quote from wikipedia regarding the problem.

The eight queens puzzle is the problem of putting eight chess queens on an 8×8 chessboard such that none of them is able to capture any other using the standard chess queen’s moves. The queens must be placed in such a way that no two queens would be able to attack each other. Thus, a solution requires that no two queens share the same row, column, or diagonal.

queens problem chess maths python
The above image is one of the many solutions to the problem. Hint: if you are looking for many solutions once you have found one, all of its 4 rotations (if unique) are solutions too.

Check out the wikipedia article for more information

Code
This is the current code with medium amount of comments, I have also provided a heavily commented version for people with less python experience (scroll to bottom).

# -*- coding: utf-8 -*-
##################################################################
##################################################################
# QUEENS EXAMPLE
# - Program Type: Demonstration of Evolutionary alogorithms
# - Authour: Matthew Rollings
# - Date: 14/09/09
##################################################################
##################################################################


# Import randint from the random module
from random import randint

# Creates a array I just use for convenience
board=[1,2,3,4,5,6,7,8]

##################################################################
# FUNCTIONS

# Function to check amount of attacking queens
def check(array):
 
 # Collisions represent number of attacking queens, starts at zero obv.
 collisions=0
 for i in range(1,9):
  if i not in array:
   print "DUPLICATE NUMBER ERROR - KILLING STUPID GENE" # Never happen ;) 
   return 0

 # Total Collisions
 # For each queen in the array
 for i in range(0, 8):
  col=0
  # For every other queen in the array
  for j in range(0, 8):
   # avoids checking self vs self
   if i!=j:
    # if queen i is on a diagonal from queen j, then the
    # difference in magnitude x-cord will equal the difference in 
    # the magnitude of the y-coord
    if abs(board[i]-board[j])==abs(array[j]-array[i]):
     # Sets a variable to tell the next part that a collision was detected
     col=1
  # If a collision was detected add one to collisions
  if col==1:
   collisions+=1
 # Return 8-colllisions, so that 0 is bad (8 attacking queens) and 8 is good (no attacking queens)
 return 8-collisions


# The reproduce function, takes two arguements, the two parents
def reproduce(array1, array2):
 
 # FIRST BABY (mother first then father)
 # Takes first half of mothers gene
 baby=array1[0:4]
 # Can't just add two halves as I will get duplicate numbers
 for i in array2:
  # add fathers genes going in order of numbers left
  if i not in baby:
   baby.append(i)
 # Add a little variation by giving a percentage chance of mutation
 if randint(0,100)>20:
  baby=mutate(baby)
 # Add the baby to the population and add its corresponding fitness
 population.append(baby)
 fitness.append(check(baby))
 
 # SECOND BABY (arrays just swapped around, Father first then mother)
 baby=array2[0:4]
 for i in array1:
  if i not in baby:
   baby.append(i)
 if randint(0,100)>20:
  baby=mutate(baby)
 population.append(baby)
 fitness.append(check(baby)) 
 

# Mutate the array given to the function
def mutate(array1):
 #Chooses two random places (WARNING CAN BE SAME POSITION)
 a=randint(0,7)
 b=randint(0,7)
 # Swaps the two over (temporary var must be used (c))
 c=array1[a]
 array1[a]=array1[b]
 array1[b]=c
 return array1

# Prints the population and corresponding fitness to the screen
# Only used for debugging
def printpop():
 # Prints the group
 for i in range(0, len(population)):
  print population[i],fitness[i]


##################################################################
# VARIABLES 
# The size of the population (how many genes, more = faster convergance but more cpu + memory, fewer = opp.)
popsize=40
# The starting variation of the group because I havn't created a better method
# for starting off. I just add arrays of 1,2,3,4,5,6,7,8 to the population and 
# give them the number of mutations between the following two values to make 
# psudo random starting group
variation=[4,14]  
# How many of the genes to kill each time in percentage, each dead gene will be replaced by a new child :) 
die=0.40 
# Kill limit is calculated from the above percentage
kill_limit=die*popsize



##################################################################
# MAIN

population=[]
fitness=[]
for i in range(0,popsize):
 population.append([1,2,3,4,5,6,7,8])
 a=0
 while a<randint(variation[0],variation[1]):
  a+=1
  population[i]=mutate(population[i])
 fitness.append(check(population[i]))


maxi=0
generations=1

while maxi!=8:
 
 # Picks top # in group to be parents, kills rest
 killed=0
 # starting at the lowest fitness (0 and increasing untill kill limit reached)
 x=0
 while killed<kill_limit:
  for i in range(0,popsize):
   # Try is here to catch any errors
   try:
    if fitness[i]==x:
     # This bit removes the crappy gene from the population and from fitness
     population.pop(i)
     fitness.pop(i)
     # increases the kill counter
     killed+=1
    if killed==kill_limit:
     break
   except:
    break
  # increments fitness
  x+=1
 
 babies=0 
 cpop=len(population)-1 #current population
 while babies<killed:
  # produces two babies from two random parents (should prob give fittest parents preference)
  reproduce(population[randint(0,cpop)],population[randint(0,cpop)])
  babies+=2 

 generations+=1

 # Looks for highest fitness in the group and checks if any have won!
 maxi=0
 for i in range(0,popsize):
  if fitness[i]>maxi:
   maxi=fitness[i]
   if maxi==8:
    print population[i]
    break

print "Took",generations,"generations"

Quick Analysis
I did a very quick analysis keeping the kill off percentage at 0.4 and varying the population size to see the improvement on generations required before a solution is found. I’ve also added a link (scroll to bottom) to the .ods file I used to calculate this (and an excel .xls file for the windows chaps). Below is the graph I calculated for different population sizes and it looks like we would expect, decreasing as the population increases. I only did 10 averages for each point and there were some anomalies, which are to be expected with this method of programming as it essentially relies on random numbers so it is a bit noisey:

eight queens problem python

Links
Note the following might be more desirable to copy and pasting the above as they use tabs rather than spaces.
queens.py – The normal version
queens_commented.py – The heavily commented version.

evolutionary.ods – Analysis in ods format (open office)
evolutionary.xls – Analysis in excel format

If you have any corrections or suggestions please contact me.

7 Comments
  1. JGM permalink

    Heya, tried to grab the commented version from the links at the bottom and they appear busted…

  2. JGM, sorry about that. There was a typo that I copied an pasted for all the links in the syntax of the link. It’s fixed now, and links are working.

    Thanks for pointing it out.

  3. Hm.

    >>> import test.test_generators as ttg
    >>> solutions=ttg.Queens(8).solve()
    >>> solutions.next()
    [0, 4, 7, 5, 2, 6, 1, 3]
    >>> solutions.next()
    [0, 5, 7, 2, 6, 3, 1, 4]

    test.test_generators is a very pleasant read.

  4. Of course there are easier ways to solve the problem but I don’t believe the test_generators method above uses an evolutionary algorithm (I might be wrong as I’ve not got or used this module before) which was the whole purpose of me writing this.

  5. Hi,

    Your code could be written in fewer lines. Try to use techniques like list comprehension and built-in functions.

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