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.

翻译：惩罚方法是一种为粒子群优化剂提供处理限制的能力的流行技术,其缺点在于需要针对特定问题设置的惩罚性系数。虽然在文献中可以找到适应性系数,但本文件提出了不同的适应性办法,即系数保持不变。对限制性违反的容忍度进行假的放松,同时仅对超过这种容忍度的违反行为进行惩罚,就会导致伪适应性惩罚。粒子群优化剂在三种容忍放松的一组基准问题中进行测试:无放松;自调初始放松,以确定性减少;自调初始放松,以伪适应性减少。其他作者的成果作为参考框架。