If we want to be more precise, this type of optimization is called simulated annealing (population = 1, no cross-over, just mutations):
"At each step, the SA heuristic considers some neighbour s' of the current state s, and probabilistically decides between moving the system to state s' or staying in state s. The probabilities are chosen so that the system ultimately tends to move to states of lower energy. Typically this step is repeated until the system reaches a state that is good enough for the application, or until a given computation budget has been exhausted."
Unfortunately, it's not even that! Simulated annealing needs a cooling heuristic, which makes the algorithm smarter as it gets closer to the optimum. What this is is some combination of hill climbing and random state space search. Not sure if it has a name.
Want evidence? Look at the iteration counts. With SA, you'd see the differences between the successive pictures be roughly constant or even decrease (I can't prove it, but I've implemented it, and you usually end up choosing a cooling heuristic that roughly matches the human intuition for "closeness").
As it is, the algorithm that's implemented finds it exponentially harder to get close to optimum. You start off with a gap of 100 iterations between optima, and you end up at 300,000.
Which is exactly why I think this is even more amazing -- it's just about the dumbest algorithm you can think of, and it still manages to vectorize an arbitrary raster image. If an actual GA or SA version were built, it could have some real potential. (See my comment below.)
I just did this because I got inspired. What does it count as, genetic programming?
It uses naive mutation and crossover(don't know if they qualfiy as real crossover and mutation) and a simple fitness function.
It is fairly pointless since all it does is find a list with ones but it does so in just around 400 generations while random guessing takes forever.
from __future__ import division
import matplotlib.mlab as M
import matplotlib.pyplot as plt
import random as R
def crossover(a, b):
new = []
for x,y in zip(a,b):
if R.random() > 0.5:
new.append(x)
else:
new.append(y)
return new
def mutate(xs):
xs[int(R.uniform(0, len(xs)))] = int(R.uniform(1, 10))
return xs
def fitness(xs, goal):
summa = 0
for x,y in zip(xs, goal):
summa += abs(x-y)
return summa, xs, True if summa == 0 else False
def nFittest(xs, goal, n=2):
fittest = sorted(fitness(x, goal) for x in xs)[:n]
if fittest[0][2] :
return fittest[0]
elif fittest[1][2]:
return fittest[1]
else:
return fittest
def init(fields, n):
return [[int(R.uniform(1,10)) for x in xrange(fields)] for y in xrange(n)]
def newGen(a,b,n):
next = [crossover(a,b) for x in xrange(n)]
mutated = []
for x in next:
if R.random() > 0.9: mutated.append(mutate(x))
else: mutated.append(x)
return mutated
def run(printing=True):
n = 0
first = init(15, 10)
while n < 1000000:
n += 1
next = nFittest(first, [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], 2)
if type(next) == tuple: break
first = newGen(next[0][1],next[1][1], 10)
if printing:
print "Nbr of generations: ", n
print next
return n, next
def plot():
trials = [run(False)[0] for x in range(100)]
print "Done trials"
averages = [sum(trials[:x]) / len(trials[:x])\
for x in xrange(1,len(trials)+1)]
print "Done averages"
plt.plot([x for x in xrange(len(averages))], averages, 'ro')
plt.axis([1, 100, 0, 1000])
plt.show()
def test():
goal = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
c=0
while 1:
c += 1
x = [int(R.uniform(1,10)) for y in range(15)]
if sum(x) == 15: break
if c % 10000 == 0: print c
print x
Good GA, but for genetic programming, you need to come up with a program representation and then evolve something in that space that spits out a solution. V. simple in lisp, given the code/data are the same thing. You could try the same thing with python's string eval, but it'll be trickier to define the lexemes and what qualifies as a feasible program.
Crossing over at one point is not as effective as an even crossover, since it is actually equivalent to an even crossover with one static and one dynamic point. Thus, building blocks in the middle are more likely to be disrupted than building blocks on the ends.
That being said, his approach is also a viable GA operator. It is called a uniform crossover. But really, to qualify as a GA, his solution only needs some kind of variation, mutation, and selection.
Although part of the reason I picked that username is that a lot of my work involves statistics/probability, so it's not entirely a coincidence that I should be posting about this.
Comments
If we want to be more precise, this type of optimization is called simulated annealing (population = 1, no cross-over, just mutations):
"At each step, the SA heuristic considers some neighbour s' of the current state s, and probabilistically decides between moving the system to state s' or staying in state s. The probabilities are chosen so that the system ultimately tends to move to states of lower energy. Typically this step is repeated until the system reaches a state that is good enough for the application, or until a given computation budget has been exhausted."
http://en.wikipedia.org/wiki/Simulated_annealing
Unfortunately, it's not even that! Simulated annealing needs a cooling heuristic, which makes the algorithm smarter as it gets closer to the optimum. What this is is some combination of hill climbing and random state space search. Not sure if it has a name.
Want evidence? Look at the iteration counts. With SA, you'd see the differences between the successive pictures be roughly constant or even decrease (I can't prove it, but I've implemented it, and you usually end up choosing a cooling heuristic that roughly matches the human intuition for "closeness").
As it is, the algorithm that's implemented finds it exponentially harder to get close to optimum. You start off with a gap of 100 iterations between optima, and you end up at 300,000.
Which is exactly why I think this is even more amazing -- it's just about the dumbest algorithm you can think of, and it still manages to vectorize an arbitrary raster image. If an actual GA or SA version were built, it could have some real potential. (See my comment below.)
I just did this because I got inspired. What does it count as, genetic programming? It uses naive mutation and crossover(don't know if they qualfiy as real crossover and mutation) and a simple fitness function. It is fairly pointless since all it does is find a list with ones but it does so in just around 400 generations while random guessing takes forever.
Good GA, but for genetic programming, you need to come up with a program representation and then evolve something in that space that spits out a solution. V. simple in lisp, given the code/data are the same thing. You could try the same thing with python's string eval, but it'll be trickier to define the lexemes and what qualifies as a feasible program.
Here's Koza's material from his Stanford class: http://www.genetic-programming.com/coursemainpage.html
Dude, pastebin? :-)
Yeah, I guess this is GA alright. Your crossover is not right -- it should "cross over" at one point, not flip flop at each location :-)
[Edit] And there's a lot of in-breeding going on! You want to keep 10-20 sequences from each generation, not just 2.
Crossing over at one point is not as effective as an even crossover, since it is actually equivalent to an even crossover with one static and one dynamic point. Thus, building blocks in the middle are more likely to be disrupted than building blocks on the ends.
That being said, his approach is also a viable GA operator. It is called a uniform crossover. But really, to qualify as a GA, his solution only needs some kind of variation, mutation, and selection.
Ah yes, you are right. I also didn't realize it's not even genetic programming as DNA seems to be just polygon data, not polygon-drawing programs.
BTW your comment was eponysterical :)
http://mssv.net/wiki.cgi?Eponysterical
Ha ha.
Although part of the reason I picked that username is that a lot of my work involves statistics/probability, so it's not entirely a coincidence that I should be posting about this.
Since it has a neighborhood function, i.e. doesn't select from the global population, I'd say it's a form of tabu search.