Gradients¶

If the problem is implemented using autograd then the gradients through automatic differentiation are available out of the box. Let us consider the following problem definition for a simple quadratic function without any constraints:

[1]:

import numpy as np

import pymoo.gradient.toolbox as anp
from pymoo.core.problem import Problem
from pymoo.gradient.automatic import AutomaticDifferentiation


class MyProblem(Problem):

    def __init__(self):
        super().__init__(n_var=10, n_obj=1, xl=-5, xu=5)

    def _evaluate(self, x, out, *args, **kwargs):
        out["F"] = anp.sum(anp.power(x, 2), axis=1)

problem = AutomaticDifferentiation(MyProblem())

The gradients can be retrieved by appending F to the return_values_of parameter:

[2]:

X = np.array([np.arange(10)]).astype(float)
F, dF = problem.evaluate(X, return_values_of=["F", "dF"])

The resulting gradients are stored in dF and the shape is (n_rows, n_objective, n_vars):

[3]:

print(X, F)
print(dF.shape)
print(dF)

[[0. 1. 2. 3. 4. 5. 6. 7. 8. 9.]] [[285.]]
(1, 1, 10)
[[[ 0.  2.  4.  6.  8. 10. 12. 14. 16. 18.]]]

Analogously, the gradient of constraints can be retrieved by appending dG.