\(\epsilon\)-Constraint Handling¶

Instead of directly redefining the problem, one can also redefine an algorithm that changes its conclusion, whether a solution is feasible given the constraint violation over time. One common way is to allow an \(\epsilon\) amount of infeasibility to still consider a solution as feasible. Now, one can decrease the \(\epsilon\) over time and thus finally fall back to a feasibility first algorithm. The \(\epsilon\) has reached zero depending on perc_eps_until. For example, if perc_eps_until=0.5 then after 50% of the run has been completed \(\epsilon=0\).

Info

This constraint handling method has been added recently and is still experimental. Please let us know if it has or has not worked for your problem.

Such a method can be especially useful for equality constraints which are difficult to satisfy. See the example below:

[2]:

from pymoo.algorithms.soo.nonconvex.de import DE
from pymoo.constraints.eps import AdaptiveEpsilonConstraintHandling
from pymoo.optimize import minimize
from pymoo.problems.single import G1

problem = ConstrainedProblemWithEquality()

algorithm = AdaptiveEpsilonConstraintHandling(DE(), perc_eps_until=0.5)

res = minimize(problem,
               algorithm,
               ('n_gen', 200),
               seed=1,
               verbose=False)

print("Best solution found: \nX = %s\nF = %s\nCV = %s" % (res.X, res.F, res.CV))

Best solution found:
X = [0.25000315 0.74999705]
F = [1.0000002]
CV = [0.]