  The penalization method is a popular technique to provide particle swarm
optimizers with the ability to handle constraints. The downside is the need of
penalization coefficients whose settings are problem-specific. While adaptive
coefficients can be found in the literature, a different adaptive scheme is
proposed in this paper, where coefficients are kept constant. A pseudo-adaptive
relaxation of the tolerances for constraint violations while penalizing only
violations beyond such tolerances results in a pseudo-adaptive penalization. A
particle swarm optimizer is tested on a suite of benchmark problems for three
types of tolerance relaxation: no relaxation; self-tuned initial relaxation
with deterministic decrease; and self-tuned initial relaxation with
pseudo-adaptive decrease. Other authors' results are offered as frames of
reference.
