I want to use MPI for parallel processing the calculation of hamiltonian paths in a graph.
So, I achieved this:
from mpi4py import MPI
import random,time
comm = MPI.COMM_WORLD
my_rank = comm.Get_rank()
p = comm.Get_size()
numOfNodes = 10
numOfProblems = 11
class Graph:
def __init__(self, numOfNodes):
if numOfNodes > 0:
self.numOfNodes = numOfNodes
else:
print("Error")
def calculateMaxPairs(self):
self.maxPairs = self.numOfNodes*(self.numOfNodes - 1)//2
def generatePairs(self):
self.calculateMaxPairs()
self.pairs = []
startRange = self.numOfNodes
endRange = (self.numOfNodes - 10)*3 + 18
numOfPairs = random.randint(startRange, endRange)
while len(self.pairs) != numOfPairs:
try:
startNode = random.randint(1, self.numOfNodes)
endNode = random.randint(1, self.numOfNodes)
if startNode == endNode:
raise ValueError
except ValueError:
pass
else:
pair = (startNode, endNode)
invertedPair = (endNode, startNode)
if pair not in self.pairs and invertedPair not in self.pairs:
self.pairs.append(pair)
self.hamiltonianPath = []
def generatePathLink(self):
self.graphLink = {}
for x in self.pairs:
x = str(x)
splitNode = x.split(', ')
a = int(splitNode[0][1:])
b = int(splitNode[1][:-1])
try:
if b not in self.graphLink[a]:
self.graphLink[a].append(b)
except KeyError:
self.graphLink[a] = []
self.graphLink[a].append(b)
finally:
try:
if a not in self.graphLink[b]:
self.graphLink[b].append(a)
except KeyError:
self.graphLink[b] = []
self.graphLink[b].append(a)
finally:
pass
def findPaths(self, start, end, path = []):
path = path + [start]
if start == end:
return [path]
if start not in self.graphLink:
return []
paths = []
for node in self.graphLink[start]:
if node not in path:
newpaths = self.findPaths(node, end, path)
for newpath in newpaths:
paths.append(newpath)
if (len(newpath) == self.numOfNodes):
self.hamiltonianPath = newpath
raise OverflowError
return paths
def exhaustiveSearch(self):
try:
allPaths = []
for startNode in self.graphLink:
for endNode in self.graphLink:
newPaths = self.findPaths(startNode, endNode)
for path in newPaths:
if (len(path) == self.numOfNodes):
allPaths.append(path)
return allPaths
except OverflowError:
return self.hamiltonianPath
else:
pass
def isHamiltonianPathExist(self):
time_start = time.clock()
self.generatePathLink()
if len(self.graphLink) != self.numOfNodes:
time_elapsed = (time.clock() - time_start)
return [[], time_elapsed]
else:
result = self.exhaustiveSearch()
time_elapsed = (time.clock() - time_start)
if len(result) == 0:
print("There isn't any Hamiltonian Path.")
else:
print("Computing time:", round(time_elapsed, 2), "seconds\n")
return [result, time_elapsed]
comm.send(result, dest=0)
yes = 0
no = 0
total_computing_time = 0
for x in range(1, numOfProblems + 1):
if my_rank !=0:
graph = Graph(numOfNodes)
graph.generatePairs()
output = graph.isHamiltonianPathExist()
else:
for procid in range(1,p):
result = comm.recv(source=procid)
time_elapsed = comm.recv(source=procid, tag=12)
total_computing_time += time_elapsed
if len(result) == 0:
no += 1
else:
yes += 1
print("Have Hamiltonian Path:", yes)
print("Don't Have Hamiltonian Path:", no)
print("Total computing time for %s problems in %s processes: %s s"%(numOfProblems, p, str(round(total_computing_time, 2))))
As you can see in this script, there's two sections.
The first one is where we will generate a Graph and calculate the hamiltonian paths.
The second one is where we tell the script to run this graph generating script in parallel in multiple processors.
The problem here is that it generates the graph and calculate paths in every processor, not dividing the job between them.
Where am I doing wrong?
So I am making genetic algorithms where the fittest chromosome is the one that is all ones [1,1,1,1...]. I coded the whole thing below while debugging I found that crossover, mutation, generate_population works and I went through the code for my other functions and they all make sense. But whenever I run it I find that after the second or third generation all my other generations are the same. so my questions are that why is that happening because I went through my code and every new generation should have a different and "fitter" population and there should be variety among each population. Any help would be really appreciated. result image
import random
def generate_population(size):
population = []
for i in range(size):
individual = []
for g in range(64):
x = random.randrange(0,2)
individual.append(x)
population.append(individual)
return population
def fitnessFunc(individual):
fit = 0
for i in individual:
if i == 1:
fit += 1
else:
fit = fit
return fit
def choice_by_roulette(sorted_population, fitness_sum):
offset = 0
normalized_fitness_sum = fitness_sum
lowest_fitness = fitnessFunc(sorted_population[0])
if lowest_fitness < 0:
offset = lowest_fitness
normalized_fitness_sum += offset * len(sorted_population)
draw = random.uniform(0, 1)
accumulated = 0
for individual in sorted_population:
fitness = fitnessFunc(individual)+offset
probability = fitness / normalized_fitness_sum
accumulated += probability
if draw <= accumulated:
return individual
def sort_population_by_fitness(population):
return sorted(population, key=fitnessFunc)
def crossover(individual_a, individual_b):
for i in range(64):
pop = random.randint(1,2)
if pop == 1:
individual_a[i] = individual_b[i]
else:
individual_a = individual_a
return individual_a
def mutate(individual):
rand = random.randrange(0,10)
if rand == 5:
if individual[rand]==1:
individual[rand]=0
else:
individual[rand]=1
return individual
def make_next_generation(previous_population):
next_generation = []
sorted_by_fitness_population = sort_population_by_fitness(previous_population)
population_size = len(previous_population)
fitness_sum = sum(fitnessFunc(individual) for individual in population)
for i in range(population_size):
choice = choice_by_roulette(sorted_by_fitness_population, fitness_sum)
schoice = choice_by_roulette(sorted_by_fitness_population, fitness_sum)
if choice != None:
first_choice = choice
if schoice != None:
second_choice = schoice
individual = crossover(first_choice, second_choice)
individual = mutate(individual)
next_generation.append(individual)
return next_generation
population = generate_population(size=10)
generations = 1000
i = 1
while True:
print(f" GENERATION {i}")
for individual in population:
print(individual, fitnessFunc(individual))
if i == generations:
break
i += 1
population = make_next_generation(population)
best_individual = sort_population_by_fitness(population)[-1]
print(" FINAL RESULT")
print(best_individual, fitnessFunc(best_individual))
I found three major problems. Will try to break it down, but since I'm not completely sure what intended result is, it's hard to say for sure how it should be done.
Problem 1: Crossover function mutates parent generation "in place" while creating next generation. That means ~ 25 % of one parents genes will mutate towards other parents gene set.
Problem 2: make_next_generation() does not make sure two different individuals are sent to crossover. That will sometimes result in individuals passing over unchanged to the next generation.
Problem 3: mutate(individual) only affects one gene out of 64. (Guessing not on purpose)
import random
def generate_individual():
# Use list comprehensions
return [random.randrange(0,2) for g in range(64)]
def generate_population(size):
# Same result, only less code
return [generate_individual() for i in range(size)]
def fitnessFunc(individual):
# Yes, this line does the same work.
return sum(individual)
# fit = 0
# for i in individual:
# if i == 1:
# fit += 1
# The following two lines did nothing
# else:
# fit = fit
# return fit
There is a real problem in choice_by_roulette(). Don't know how it's supposed to work, though. Commented below.
def choice_by_roulette(sorted_population, fitness_sum):
offset = 0
normalized_fitness_sum = fitness_sum
lowest_fitness = fitnessFunc(sorted_population[0])
# Lower than 0? fitnessFunc() will never return that.
# Could it be lowest_fitness > 0?
if lowest_fitness < 0:
offset = lowest_fitness
normalized_fitness_sum += offset * len(sorted_population)
draw = random.random()
accumulated = 0
for individual in sorted_population:
fitness = fitnessFunc(individual)+offset
probability = fitness / normalized_fitness_sum
accumulated += probability
if draw <= accumulated:
return individual
def sort_population_by_fitness(population):
return sorted(population, key=fitnessFunc)
Crossover should not mutate old individuals(?). Since the same individuals may get picked more than once, they will have mutated ~ 50 % towards another individual within the same generation. This is probably your biggest issue.
def crossover(individual_a, individual_b):
for i in range(64):
pop = random.randint(1,2)
if pop == 1:
individual_a[i] = individual_b[i]
else:
individual_a = individual_a
return individual_a
My suggestion:
def crossover(individual_a, individual_b):
return [random.choice(genes) for genes in zip(individual_a, individual_b)]
Here you don't need to return anything. You're literally mutating individual in place. Also, only gene 5 can mutate, but maybe that's supposed to be?
def mutate(individual):
rand = random.randrange(0,10)
if rand == 5:
individual[rand] = 1 - individual[rand] # Toggle: 1-0=1, 1-1=0
# if individual[rand]==1:
# individual[rand]=0
# else:
# individual[rand]=1
def make_next_generation(previous_population):
next_generation = []
sorted_by_fitness_population = sort_population_by_fitness(previous_population)
population_size = len(previous_population)
fitness_sum = sum(fitnessFunc(individual) for individual in population)
for i in range(population_size):
choice = choice_by_roulette(sorted_by_fitness_population, fitness_sum)
schoice = choice_by_roulette(sorted_by_fitness_population, fitness_sum)
# This code will not work. first_choice will be user without being declared below if any of there are None.
# if choice != None:
# first_choice = choice
# if schoice != None:
# second_choice = schoice
# choice and schoice will sometimes be the same individual. That will definitely diminish the genetic diversity.
while choice == schoice:
schoice = choice_by_roulette(sorted_by_fitness_population, fitness_sum)
individual = crossover(choice, schoice)
mutate(individual)
next_generation.append(individual)
return next_generation
population = generate_population(size=10)
generations = 1000
for i in range(1, generations+1):
print(f" GENERATION {i}")
for individual in population:
print(individual, fitnessFunc(individual))
population = make_next_generation(population)
best_individual = sort_population_by_fitness(population)[-1]
print(" FINAL RESULT")
print(best_individual, fitnessFunc(best_individual))
I am currently working on my Python game, in ika, which uses python 2.5
I decided to use A* pathfinding for the AI. However, I find it too slow for my needs (3-4 enemies can lag the game, but I would like to supply up to 4-5 without problems). I know, that such complex search like A* is not mean to be scripted in python, but I am pretty sure, that my pathfinder is also implemented in the wrong way.
My question is: How can I speed up this algorithm?
I wrote my own binary heap, and there are some try: except: lines inside some functions. Those lines can create large overhead? Are there better methods maintaining the open list?
I supplied the algorithm with graphics interface, for testing purposes (when the pathfinder finishes searching, it will write the number of iterations and seconds it takes to find the path, inside the ika.txt file. Also, Pressing A will do a complete search, and S does that step by step.)
Graphical version:
http://data.hu/get/6084681/A_star.rar
Also, here is a pastebin version:
http://pastebin.com/9N8ybX5F
Here is the main code I use for pathfinding:
import ika
import time
class Node:
def __init__(self,x,y,parent=None,g=0,h=0):
self.x = x
self.y = y
self.parent = parent
self.g = g
self.h = h
def cost(self):
return self.g + self.h
def equal(self,node):
if self.x == node.x and self.y == node.y:
return True
else:
return False
class Emerald_Pathfinder:
def __init__(self):
pass
def setup(self,start,goal):
self.start = start
self.goal = goal
self.openlist = [None,start] # Implemented as binary heap
self.closedlist = {} # Implemented as hash
self.onopenlist = {} # Hash, for searching the openlist
self.found = False
self.current = None
self.iterations = 0
def lowest_cost(self):
pass
def add_nodes(self,current):
nodes = []
x = current.x
y = current.y
self.add_node(x+1,y,current,10,nodes)
self.add_node(x-1,y,current,10,nodes)
self.add_node(x,y+1,current,10,nodes)
self.add_node(x,y-1,current,10,nodes)
# Dont cut across corners
up = map.is_obstacle((x,y-1),x,y-1)
down = map.is_obstacle((x,y+1),x,y+1)
left = map.is_obstacle((x-1,y),x-1,y)
right = map.is_obstacle((x+1,y),x+1,y)
if right == False and down == False:
self.add_node(x+1,y+1,current,14,nodes)
if left == False and up == False:
self.add_node(x-1,y-1,current,14,nodes)
if right == False and up == False:
self.add_node(x+1,y-1,current,14,nodes)
if left == False and down == False:
self.add_node(x-1,y+1,current,14,nodes)
return nodes
def heuristic(self,x1,y1,x2,y2):
return (abs(x1-x2)+abs(y1-y2))*10
def add_node(self,x,y,parent,cost,list):
# If not obstructed
if map.is_obstacle((x,y),x,y) == False:
g = parent.g + cost
h = self.heuristic(x,y,self.goal.x,self.goal.y)
node = Node(x,y,parent,g,h)
list.append(node)
def ignore(self,node,current):
# If its on the closed list, or open list, ignore
try:
if self.closedlist[(node.x,node.y)] == True:
return True
except:
pass
# If the node is on the openlist, do the following
try:
# If its on the open list
if self.onopenlist[(node.x,node.y)] != None:
# Get the id number of the item on the real open list
index = self.openlist.index(self.onopenlist[(node.x,node.y)])
# If one of the coordinates equal, its not diagonal.
if node.x == current.x or node.y == current.y:
cost = 10
else:
cost = 14
# Check, is this items G cost is higher, than the current G + cost
if self.openlist[index].g > (current.g + cost):
# If so, then, make the list items parent, the current node.
self.openlist[index].g = current.g + cost
self.openlist[index].parent = current
# Now resort the binary heap, in the right order.
self.resort_binary_heap(index)
# And ignore the node
return True
except:
pass
return False
def resort_binary_heap(self,index):
m = index
while m > 1:
if self.openlist[m/2].cost() > self.openlist[m].cost():
temp = self.openlist[m/2]
self.openlist[m/2] = self.openlist[m]
self.openlist[m] = temp
m = m / 2
else:
break
def heap_add(self,node):
self.openlist.append(node)
# Add item to the onopenlist.
self.onopenlist[(node.x,node.y)] = node
m = len(self.openlist)-1
while m > 1:
if self.openlist[m/2].cost() > self.openlist[m].cost():
temp = self.openlist[m/2]
self.openlist[m/2] = self.openlist[m]
self.openlist[m] = temp
m = m / 2
else:
break
def heap_remove(self):
if len(self.openlist) == 1:
return
first = self.openlist[1]
# Remove the first item from the onopenlist
self.onopenlist[(self.openlist[1].x,self.openlist[1].y)] = None
last = self.openlist.pop(len(self.openlist)-1)
if len(self.openlist) == 1:
return last
else:
self.openlist[1] = last
v = 1
while True:
u = v
# If there is two children
if (2*u)+1 < len(self.openlist):
if self.openlist[2*u].cost() <= self.openlist[u].cost():
v = 2*u
if self.openlist[(2*u)+1].cost() <= self.openlist[v].cost():
v = (2*u)+1
# If there is only one children
elif 2*u < len(self.openlist):
if self.openlist[2*u].cost() <= self.openlist[u].cost():
v = 2*u
# If at least one child is smaller, than parent, swap them
if u != v:
temp = self.openlist[u]
self.openlist[u] = self.openlist[v]
self.openlist[v] = temp
else:
break
return first
def iterate(self):
# If the open list is empty, exit the game
if len(self.openlist) == 1:
ika.Exit("no path found")
# Expand iteration by one
self.iterations += 1
# Make the current node the lowest cost
self.current = self.heap_remove()
# Add it to the closed list
self.closedlist[(self.current.x,self.current.y)] = True
# Are we there yet?
if self.current.equal(self.goal) == True:
# Target reached
self.goal = self.current
self.found = True
print self.iterations
else:
# Add the adjacent nodes, and check them
nodes_around = self.add_nodes(self.current)
for na in nodes_around:
if self.ignore(na,self.current) == False:
self.heap_add(na)
def iterateloop(self):
time1 = time.clock()
while 1:
# If the open list is empty, exit the game
if len(self.openlist) == 1:
ika.Exit("no path found")
# Expand iteration by one
self.iterations += 1
# Make the current node the lowest cost
self.current = self.heap_remove()
# Add it to the closed list
self.closedlist[(self.current.x,self.current.y)] = True
# Are we there yet?
if self.current.equal(self.goal) == True:
# Target reached
self.goal = self.current
self.found = True
print "Number of iterations"
print self.iterations
break
else:
# Add the adjacent nodes, and check them
nodes_around = self.add_nodes(self.current)
for na in nodes_around:
if self.ignore(na,self.current) == False:
self.heap_add(na)
time2 = time.clock()
time3 = time2-time1
print "Seconds to find path:"
print time3
class Map:
def __init__(self):
self.map_size_x = 20
self.map_size_y = 15
self.obstructed = {} # Library, containing x,y couples
self.start = [2*40,3*40]
self.unit = [16*40,8*40]
def is_obstacle(self,couple,x,y):
if (x >= self.map_size_x or x < 0) or (y >= self.map_size_y or y < 0):
return True
try:
if self.obstructed[(couple)] != None:
return True
except:
return False
def render_screen():
# Draw the Character
ika.Video.DrawRect(map.start[0],map.start[1],map.start[0]+40,map.start[1]+40,ika.RGB(40,200,10),1)
# Draw walls
for x in range(0,map.map_size_x):
for y in range(0,map.map_size_y):
if map.is_obstacle((x,y),x,y) == True:
ika.Video.DrawRect(x*40,y*40,(x*40)+40,(y*40)+40,ika.RGB(168,44,0),1)
# Draw openlist items
for node in path.openlist:
if node == None:
continue
x = node.x
y = node.y
ika.Video.DrawRect(x*40,y*40,(x*40)+40,(y*40)+40,ika.RGB(100,100,100,50),1)
# Draw closedlist items
for x in range(0,map.map_size_x):
for y in range(0,map.map_size_y):
try:
if path.closedlist[(x,y)] == True:
ika.Video.DrawRect(x*40,y*40,(x*40)+20,(y*40)+20,ika.RGB(0,0,255))
except:
pass
# Draw the current square
try:
ika.Video.DrawRect(path.current.x*40,path.current.y*40,(path.current.x*40)+40,(path.current.y*40)+40,ika.RGB(128,128,128), 1)
except:
pass
ika.Video.DrawRect(mouse_x.Position(),mouse_y.Position(),mouse_x.Position()+8,mouse_y.Position()+8,ika.RGB(128,128,128), 1)
# Draw the path, if reached
if path.found == True:
node = path.goal
while node.parent:
ika.Video.DrawRect(node.x*40,node.y*40,(node.x*40)+40,(node.y*40)+40,ika.RGB(40,200,200),1)
node = node.parent
# Draw the Target
ika.Video.DrawRect(map.unit[0],map.unit[1],map.unit[0]+40,map.unit[1]+40,ika.RGB(128,40,200),1)
def mainloop():
while 1:
render_screen()
if mouse_middle.Pressed():
# Iterate pathfinder
if path.found == False:
path.iterateloop()
elif mouse_right.Pressed():
# Iterate pathfinder by one
if path.found == False:
path.iterate()
elif ika.Input.keyboard["A"].Pressed():
# Iterate pathfinder
if path.found == False:
path.iterateloop()
elif ika.Input.keyboard["S"].Pressed():
# Iterate pathfinder by one
if path.found == False:
path.iterate()
elif mouse_left.Position():
# Add a square to the map, to be obstructed
if path.iterations == 0:
x = mouse_x.Position()
y = mouse_y.Position()
map.obstructed[(int(x/40),int(y/40))] = True
# Mouse preview
x = mouse_x.Position()
y = mouse_y.Position()
mx = int(x/40)*40
my = int(y/40)*40
ika.Video.DrawRect(mx,my,mx+40,my+40,ika.RGB(150,150,150,70),1)
ika.Video.ShowPage()
ika.Input.Update()
map = Map()
path = Emerald_Pathfinder()
path.setup(Node(map.start[0]/40,map.start[1]/40),Node(map.unit[0]/40,map.unit[1]/40))
mouse_middle = ika.Input.mouse.middle
mouse_right = ika.Input.mouse.right
mouse_left = ika.Input.mouse.left
mouse_x = ika.Input.mouse.x
mouse_y = ika.Input.mouse.y
# Initialize loop
mainloop()
I appreciate any help!
(sorry for any spelling mistakes, English is not my native language)
I think a proper implementation in python will be fast enough for your purposes. But the boost library has an astar implementation and python bindings. https://github.com/erwinvaneijk/bgl-python