Recently, several socio-/bio-inspired algorithms have been proposed for solving a variety of problems. Generally, they perform well when applied for solving unconstrained problems; however, their performance degenerates when applied for solving constrained problems. Several types of penalty function approaches have been proposed so far for handling linear and non-linear constraints. Even though the approach is quite easy to understand, the precise choice of penalty parameter is very much important. It may further necessitate significant number of preliminary trials. To overcome this limitation, a new self-adaptive penalty function (SAPF) approach is proposed and incorporated into socio-inspired Cohort Intelligence (CI) algorithm. This approach is referred to as CI–SAPF. Furthermore, CI–SAPF approach is hybridized with Colliding Bodies Optimization (CBO) algorithm referred to as CI–SAPF–CBO algorithm. The performance of the CI–SAPF and CI–SAPF–CBO algorithms is validated by solving discrete and mixed variable problems from truss structure domain, design engineering domain, and several problems of linear and nonlinear in nature. Furthermore, the applicability of the proposed techniques is validated by solving two real-world applications from manufacturing engineering domain. The results obtained from CI–SAPF and CI–SAPF–CBO are promising and computationally efficient when compared with other nature inspired optimization algorithms. A non-parametric Wilcoxon’s rank sum test is performed on the obtained statistical solutions to examine the significance of CI–SAPF–CBO. In addition, the effect of the penalty parameter on pseudo-objective function, penalty function and constrained violations is analyzed and discussed along with the advantages over other algorithms.

近来，已经提出了几种受社会/生物启发的算法来解决各种问题。通常，当用于解决无约束的问题时，它们表现良好。但是，当将它们应用于解决约束问题时，它们的性能会下降。迄今为止，已经提出了几种类型的惩罚函数方法来处理线性和非线性约束。尽管该方法非常容易理解，但惩罚参数的精确选择非常重要。可能还需要进行大量的初步试验。为了克服此限制，提出了一种新的自适应惩罚函数（SAPF）方法，并将其结合到社会启发的同类研究（CI）算法中。这种方法称为CI–SAPF。此外，CI–SAPF方法与称为CI–SAPF–CBO算法的碰撞体优化（CBO）算法混合在一起。CI–SAPF和CI–SAPF–CBO算法的性能通过解决桁架结构领域，设计工程领域以及自然界中的线性和非线性问题的离散变量和混合变量问题而得到验证。此外，通过解决制造工程领域的两个实际应用，验证了所提出技术的适用性。与其他自然启发式优化算法相比，从CI–SAPF和CI–SAPF–CBO获得的结果很有希望且计算效率高。对获得的统计解进行非参数Wilcoxon秩和检验，以检验CI–SAPF–CBO的重要性。此外，