Many-Objective and Iteration Evaluation

[faranak1991]

[faranak1991]

Hello everyone,

I have been using the following commands to minimize the 5-objective problem using both NSGA3 (and NSGA2). I am tracking the best value of each function over iterations. However, I have noticed that the best value of objective does not seem to consider all previous generations when comparing. I expected the best value of each objective to show a downward trend. It shows that the best value after some generations appears to restart. Here's an example:

Generation 1: Best_F: [0.00023328 0.00086596 0.00054079 0.01242588 0.01710647]
Generation 2: Best_F: [0.00023328 0.00086596 0.00054079 0.0146338 0.00846329]
Generation 3: Best_F: [0.00020456 0.00086524 0.00192541 0.01354562 0.00846329]
Generation 4: Best_F: [0.00042178 0.00084673 0.00321917 0.0097553 0.00483079]
Generation 5: Best_F: [0.00042178. 0.00084673 0.00279974 0.0097553 0.00483079]
Generation 6: Best_F: [0.0002391 0.00084328 0.00075635 0.0097553 0.00810061]
Generation 7: Best_F: [0.00022657 0.00088079 0.00051862 0.0097553 0.01031505]
Generation 8: Best_F: [0.00022779 0.00081578 0.00037185 0.01208127 0.01104479]

Is this behavior normal? I would appreciate it if someone could help figure this out. Any assistance would be greatly appreciated.

a part of my code:
class myProblem(Problem):
def init(self):
super().init(n_var=22, n_obj=5, n_constr=0, xl=lower_bounds, xu=upper_bounds)
def _evaluate(self, X, out, *args, **kwargs):
n_samples = X.shape[0]
f1 = np.empty((n_samples, 1))
f2 = np.empty((n_samples, 1))
f3 = np.empty((n_samples, 1))
f4 = np.empty((n_samples, 1))
f5 = np.empty((n_samples, 1))
for i in range(n_samples):
x = X[i, :] # Extract the i-th individual's parameters
objectives = objective_function(x)
# Assign the computed objectives to fi
f1[i, 0] = objectives[0] # objectives[0] is delta1
f2[i, 0] = objectives[1] # objectives[1] is delta2
f3[i, 0] = objectives[2] # objectives[2] is delta3
f4[i, 0] = objectives[3] # objectives[3] is delta4
f5[i, 0] = objectives[4] # objectives[4] is delta5
out["F"] = np.column_stack((f1, f2, f3, f4, f5))

class MyOutput(Output):
def init(self):
super().init()
self.F_mean = Column("F_mean", width=13)
self.F_std = Column("F_std", width=13)
self.best_F = Column("Best_F", width=13)
self.columns += [self.F_mean, self.F_std, self.best_F] # Include the new column
def update(self, algorithm):
super().update(algorithm)
F_values = algorithm.pop.get("F") # containing the objective function values for each solution in the population
self.F_mean.set(np.mean(F_values))
self.F_std.set(np.std(F_values))
# Calculate the best F value
best_F_value = np.min(F_values, axis=0)
self.best_F.set(best_F_value)

      # Write the data to the output file
    with open('output.txt', 'a') as output_file:
        #output_file.write(f"F_mean: {np.mean(F_values)}\n")
        output_file.write(f"Best_F: {best_F_value}\n")
        output_file.write("-" * 30 + '\n')

[blankjul]

your code is not easy to follow. but are you basically talking about the ideal point in your population?

[faranak1991]

Yes.