In this Kernel, we modify the DE algorithm codes developed previously here. The modified DE Algorithm now can be used by taking multi-objective functions into account.
Steps taken are as follow:
- The main objective function (fobj) and side objective function are defined.
- The DE Algorithm written by Pablo R. Mier is modified and includes the new function called generate candidate.
- The generate candidate function takes the main objective function (fobj) and side objective function and the boundaries into account to generates candidates.
- The generate candidate function considered the side objective function along with maximum and minimum limitations to filter the candidates (See this following line in the generates function).
if side_obj_1_fitness[0] < 1000 and side_obj_1_fitness[0] > 900: - Evaluate the side objective function and filter those candidates that are not satisfied the side_objective function.
- Here we use side objective function and we want to make sure that the DE performs evolution on those candidates that are between 900 and 1000 values generated by side objective function.
def generate_candidate(fobj, side_obj_1, bounds):
cond = True
while cond == True:
dimensions = len(bounds)
pop = np.random.rand(1, dimensions)
min_b, max_b = np.asarray(bounds).T
diff = np.fabs(min_b - max_b)
pop_denorm = min_b + pop * diff
# calculate the fitness using fitness function and save it into the fitness parameter
fitness = np.asarray([fobj(ind) for ind in pop_denorm])
# calculate the side objective function and save it into the side object_1 parameter
side_obj_1_fitness = np.asarray([side_obj_1(ind) for ind in pop_denorm])
#evaluate the side objective function and filter those candidates
#that are not satisfied the side_objective function.
# Here we use side objective function and we want to make sure that the DE performs evolution on those candidates
# that is between 900 and 1000 values generated by side objective function.
if side_obj_1_fitness[0] < 1000 and side_obj_1_fitness[0] > 900:
cond = False
# print('candidate = ', pop_denorm)
# print('fitness = ', fitness[0]), print('side_obj_1_fitness = ', side_obj_1_fitness[0])
return pop[0], pop_denorm[0] - The De Algorithm modified to evaluate the new candidate's fitness taking both main and side objective functions into account.
Check out the line in the main code (
DE_Algorithm_Multi_Objective_Function\codes\Differential Evolution Algorithm Modified.ipynb).
fitness = np.asarray([fobj(ind) for ind in pop_denorm])
#Sub_Objective function are evaluated at the following.
side_obj_1_fitness = np.asarray([side_obj_1(ind) for ind in pop_denorm])- A new function (gene_trial_in_range) is defined which generates the trial candidates in predetermined ranges as follows.
def gene_trial_in_range(popsize, j, mut, dimensions, crossp, pop, min_b, diff):
cond = True
while cond == True:
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
cond = False
return trial_denorm, trial- You may run the program for a population of 5 and see the output along with their fitness after 4 iterations. Check out the results (res) as follow). The first array includes the 5 best candidates after 4 iterations. the second array includes each candidate's fitness (using a main-objective function) after 4 iterations.
(array([[9.71347573],
[9.69980814],
[9.72554979],
[9.69181503],
[9.67379587]]),
array([47.1758054 , 47.04313899, 47.29315934, 46.96563926, 46.79116331]),
4)