Small and efficient implementation of the Differential Evolution algorithm using the rand/1/bin schema

differential_evolution.py

import numpy as np

def de(fobj, bounds, mut=0.8, crossp=0.7, popsize=20, its=1000):
    dimensions = len(bounds)
    pop = np.random.rand(popsize, dimensions)
    min_b, max_b = np.asarray(bounds).T
    diff = np.fabs(min_b - max_b)
    pop_denorm = min_b + pop * diff
    fitness = np.asarray([fobj(ind) for ind in pop_denorm])
    best_idx = np.argmin(fitness)
    best = pop_denorm[best_idx]
    for i in range(its):
        for j in range(popsize):
            idxs = [idx for idx in range(popsize) if idx != j]
            a, b, c = pop[np.random.choice(idxs, 3, replace = False)]
            mutant = np.clip(a + mut * (b - c), 0, 1)
            cross_points = np.random.rand(dimensions) < crossp
            if not np.any(cross_points):
                cross_points[np.random.randint(0, dimensions)] = True
            trial = np.where(cross_points, mutant, pop[j])
            trial_denorm = min_b + trial * diff
            f = fobj(trial_denorm)
            if f < fitness[j]:
                fitness[j] = f
                pop[j] = trial
                if f < fitness[best_idx]:
                    best_idx = j
                    best = trial_denorm
        yield best, fitness[best_idx]

Hi Pablomier

I got some problems when following your post here: https://pablormier.github.io/2017/09/05/a-tutorial-on-differential-evolution-with-python/

Issue # 1:
I ran:

from yabox.problems import problem
problem(lambda x: sum(x**2)/len(x), bounds=[(-5, 5)] * 2).plot3d()

ImportError: cannot import name 'problem'

I found that there is no problem class in your yabox.problems but BaseProblem instead. How can your code work? Even though I replaced it with BaseProblem but there is another error.

Issue #2
I ran:

result = list(de(lambda x: x**2 / len(x), bounds=[(-100, 100)] * 32))

IndexError: index 251 is out of bounds for axis 0 with size 20

It seems that "pop_denorm" is 2D array but "best_idx" which is returned from np.argmin(fitness) is work for 1D array and out of size
pop_denorm[best_idx] is not right, is not it? pop_denorm is a 2D array but you used it as 1D array (pop_denorm[best_idx]).

Can you show me how to fix it in your code?

Thanks

Hi Pablo

Why one of these two functions work but the other cannot? It seems that you write this function wrongly since it does not sum x^2 as the formula.

list(de(lambda x: x**2 / len(x), bounds=[(-100, 100)] * 32))
-> fail to run

list(de(lambda x: sum(x**2) / len(x), bounds=[(-100, 100)] * 32))
-> good to run

Thanks

Viet

Hi,

You have to provide an objective function to optimize, which returns a number. x ** 2 / len(x) in you case is a 32 vector, but sum(x**2)/len(x) is a number.

Cheers,
P

Hi Pablo

Thank you for your response. So you mean if any objective function = f(x) returns a vector/matrix/array will not work. Is it right? In this case, I have to select which dimension of a vector/matric/array such as f [i, j, k] to return?

How about the issue "ImportError: cannot import name 'problem'"? What's wrong?

Thanks

Viet

Yes you are right, you need to assign values to your vectors that you can compare. If your goal is to maximize or minimize other kind of funcion, you would need multiobjective optimization.

The import problems you are having I guess is for not using Yabox?:

pip install yabox

Then in python:

from yabox import problems

It should work.

Cheers

hi Pablo, how I fit the follow function in your code? fobj = lambda x: sum(((1-x) ^2)+ 100*(((x+1) - x^2)^2)/len(x-1)
all the bounds i put give me a SyntaxError: invalid syntax

Python does not use the ^ operator, but ** instead: (1-x)**2 + 100...

Hi Pablo, I have the same problem: cannot import name 'problem' from 'yabox.problems'

I installed yabox in my machine and doesn't work.

Hi how should I change the code to get best/1/bin