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#!/usr/bin/env python
"""Try out the N-queens problem for an arbitrary number of queens.
This program uses Genetic Algorithms to try to solve the N queens
problem, in which you place N different queens on an N by N chess
board such that no two queens will be attacking each other.
We represent queens on the board as a tuple like (1, 2, 3, 4, 5)
which would be 5 queens diaganol across the board.
python <Number of Queens to place>
where <Number of Queens to place> is just a number specifying how many
queens you want to try to calculate this for.
When called as part of the Biopython unit test suite, 5 queens are used.
# standard library
import sys
import random
import time
import unittest
# Biopython
from Bio import Alphabet
# Genetic Algorithm stuff
from Bio.GA.Evolver import GenerationEvolver
from Bio.GA import Organism
from Bio.GA.Mutation.Simple import ConversionMutation
from Bio.GA.Crossover.Point import SinglePointCrossover
from Bio.GA.Selection.RouletteWheel import RouletteWheelSelection
from Bio.GA.Selection.Tournament import TournamentSelection
def main(num_queens):
print "Calculating for %s queens..." % num_queens
num_orgs = 1000
print "Generating an initial population of %s organisms..." % num_orgs
queen_alphabet = QueensAlphabet(num_queens)
start_population = Organism.random_population(queen_alphabet, num_queens,
num_orgs, queens_fitness)
print "Evolving the population and searching for a solution..."
mutator = QueensMutation(mutation_rate = 0.05)
crossover = QueensCrossover(queens_fitness, crossover_prob = .2,
max_crossover_size = 4)
repair = QueensRepair()
# rw_selector = RouletteWheelSelection(mutator, crossover, repair)
t_selector = TournamentSelection(mutator, crossover, repair, 5)
start_time = time.ctime(time.time())
evolver = GenerationEvolver(start_population, t_selector)
evolved_pop = evolver.evolve(queens_solved)
end_time = time.ctime(time.time())
unique_solutions = []
for org in evolved_pop:
if == num_queens:
if org not in unique_solutions:
print "Search started at %s and ended at %s" % (start_time, end_time)
for orgm in unique_solutions:
print "We did it!", org
def display_board(genome):
"""Display a genome in the N-queens problem.
Inspired by the display function in the solution to the N-queens
problem in the Python demo scripts.
print '+-' + '--'*len(genome) + '+'
for row in range(len(genome)):
print '|',
for genome_item in genome:
if genome_item == row:
print 'Q',
print '.',
print '|'
print '+-' + '--'*len(genome) + '+'
def queens_solved(organisms):
"""Determine if we have solved the problem.
We just search through the population for an organism that has a
fitness that is equal to the number of queens in the population.
If so, we have a solution, otherwise we need to keep looking.
for org in organisms:
if == len(org.genome):
return 1
# if we got here we didn't do it
return 0
def queens_fitness(genome):
"""Calculate the fitness of an organization of queens on the chessboard.
o genome -- A MutableSeq object specifying an organism genome.
The number returned is the number of unattacked queens on the board.
fitness = 0
# check each queen on the board
for check_queen_col in range(len(genome)):
is_attacked = 0
# check against all other queens on the board
for other_queen_col in range(len(genome)):
# only check a queen if it isn't exactly the same queen
if check_queen_col != other_queen_col:
# get the row for the two queens we are comparing
check_queen_row = int(genome[check_queen_col])
other_queen_row = int(genome[other_queen_col])
# a queen is attacked if it is in a row with another queen
if check_queen_row == other_queen_row:
is_attacked = 1
# or it is attacked if it is diaganol to another queen
elif (abs(check_queen_row - other_queen_row) ==
abs(check_queen_col - other_queen_col)):
is_attacked = 1
if not(is_attacked):
fitness += 1
return fitness
class QueensAlphabet(Alphabet.Alphabet):
def __init__(self, num_queens):
"""Initialize with the number of queens we are calculating for.
# set up the letters for the alphabet
assert 0 < num_queens <= 9
self.letters = "".join(str(i) for i in range(num_queens))
# --- Problem specific crossover, mutation and repair operations
class QueensRepair:
"""A repair function to help create correct N-Queens solutions.
This attempts to help generate correct solutions by offering some
amount of repair to remove queens that are located in the same rows.
After repair, a sequence should have no queens in the same row.
So, if you start with something infeasible like (1, 2, 2, 3, 3, 4),
after running it through repair you'll get a feasible individual
like (1, 2, 5, 3, 6, 4). This should greatly reduce the number of
individuals that need to be searched through in a population.
def __init__(self, repair_prob = 1):
"""Initialize the repairer.
o repair_prob -- The probability that we'll repair a genome.
By default, we always repair.
self._repair_prob = repair_prob
def _get_duplicates(self, genome):
"""Return all of the letters in the genome that are duplicated.
This checks every letter in the genome (which are the rows of
the chessboard, in this case), and adds them to a list of duplicated
items if there is more than one of them, and then returns this list.
duplicates = []
for item in genome.alphabet.letters:
if genome.count(str(item)) > 1:
return duplicates
def _get_unused(self, genome):
"""Return all of the letters in the genome which are unused.
This checks the letters in the genome (which are th rows on the
chessboard) and returns all items which are not used.
unused = []
for item in genome.alphabet.letters:
if genome.count(str(item)) == 0:
return unused
def repair(self, organism):
"""Repair the specified genome to make it feasible.
o organism -- The Organism object we are going to perform the
repair on.
# check if we should repair or not
repair_chance = random.random()
if repair_chance <= self._repair_prob:
while 1:
# get the duplicated items we need to work on
duplicated_items = self._get_duplicates(organism.genome)
if len(duplicated_items) == 0:
# take the first duplicated element, and convert it to
# a row that is not already taken
duplicated_pos = organism.genome.index(duplicated_items[0])
free_rows = self._get_unused(organism.genome)
assert len(free_rows) > 0, "Unexpected lack of empty rows"
new_item = random.choice(free_rows)
organism.genome[duplicated_pos] = new_item
return organism
class QueensCrossover:
"""Crossover operation to help in solving the N-Queens problem.
This tries to perform smarter crossovers by picking out regions of
the genome that have high fitness.
It scans through both genomes in the crossover with a window half the
size of the genome, and finds the region with the highest fitness in
both genomes. It then recombines these high fitness windows to form
the new genome that is returned.
def __init__(self, fitness_func, crossover_prob = .1,
max_crossover_size = 4):
"""Initialize to do N-Queens optimized crossover.
o fitness_func -- A function that can calculate the fitness of
a genome.
o crossover_prob -- The probability of having a crossover
between two passed in organisms.
o max_crossover_size -- The maximum crossover size of the 'best' region
to search for.
self._crossover_prob = crossover_prob
self._fitness_calc = fitness_func
self._max_crossover_size = max_crossover_size
def do_crossover(self, org_1, org_2):
"""Perform a crossover between two organisms.
new_org_1 = org_1.copy()
new_org_2 = org_2.copy()
# determine if we have a crossover
crossover_chance = random.random()
if crossover_chance <= self._crossover_prob:
# find the region of highest probability in both orgs
best_1, rest_1 = self._find_best_region(new_org_1.genome,
make_best_larger = 1)
best_2, rest_2 = self._find_best_region(new_org_2.genome,
make_best_larger = 0)
assert len(best_1) + len(best_2) == len(rest_1) + len(rest_2), \
"Did not preserve genome length!"
new_org_1.genome = best_1 + best_2
new_org_2.genome = rest_1 + rest_2
return new_org_1, new_org_2
def _find_best_region(self, genome, make_best_larger = 1):
"""Find the best region in the given genome.
o genome -- A MutableSeq object specifying the genome of an organism
o make_best_larger -- A flag to determine whether the best region
we should search for should be the larger region of the split
caused by crossover or the smaller region. This makes it easy
to split two genomes, recombine them, and get a solution that
makes sense.
o Two MutableSeq objects. They are both half of the size of the passed
genome. The first is the highest fitness region of the genome and the
second is the rest of the genome.
first_region = max(len(genome) / 2, self._max_crossover_size)
second_region = len(genome) - first_region
if make_best_larger:
region_size = max(first_region, second_region)
region_size = min(first_region, second_region)
# loop through all of the segments and find the best fitness segment
# represent best_fitness as a three tuple with the coordinates of
# the start and end as the first two elements, and the fitness of
# the region as the last element. Start with a value that
# will overridden right away
best_fitness = [0, 0, -1]
for start_index in range(len(genome) - region_size):
region_fitness = \
self._fitness_calc(genome[start_index: start_index + region_size])
if region_fitness > best_fitness[2]:
best_fitness = [start_index, start_index + region_size,
# get the two regions and return 'em
best_region = genome[best_fitness[0]:best_fitness[1]]
rest_region = genome[0:best_fitness[0]] + genome[best_fitness[1]:]
return best_region, rest_region
class QueensMutation:
"""Mutation operation to help in the N-Queens problem.
This performs mutation, but instead of randomly mutating a single
item to any other, it tries to mutate it to a row that is not already
taken at some other position in the genome. This thus tries to
generate more 'correct' mutations that will help achieve the solution.
def __init__(self, mutation_rate = 0.001):
"""Inititialize a mutator.
o mutation_rate -- The change of a mutation happening at any
position in the genome.
self._mutation_rate = mutation_rate
def mutate(self, organism):
"""Mutate the genome trying to put in 'helpful' mutations.
new_org = organism.copy()
gene_choices = list(new_org.genome.alphabet.letters)
# potentially mutate any gene in the genome
for gene_index in range(len(new_org.genome)):
mutation_chance = random.random()
# if we have a mutation
if mutation_chance <= self._mutation_rate:
# find only choices that are not already taken elsewhere
# in the genome
gene_choices = list(new_org.genome.alphabet.letters)
for gene in new_org.genome:
if gene in gene_choices:
# if there are no choices left, we are stuck going for random
if len(gene_choices) == 0:
gene_choices = list(new_org.genome.alphabet.letters)
# get a new letter with the left-over choices
new_letter = random.choice(gene_choices)
new_org.genome[gene_index] = new_letter
return new_org
num_queens = 5
#Class defined for use via
class QueensTest(unittest.TestCase):
def test_queens(self):
"""Place five queens with a GA"""
if __name__ == "__main__":
if len(sys.argv) == 1:
#Run with defaults, for use as a unit test
elif len(sys.argv) == 2:
num_queens = int(sys.argv[1])
print "Usage:"
print "python <Number of Queens to place>\n"
print "where <Number of Queens to place> is an optional parameter"
print "specifying how many queens you want to try to calculate"
print "this for. The default number of queens to place is 5."
print "Range 1 to 9 is supported."
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