Cohort intelligence with self-adaptive penalty function approach hybridized with colliding bodies optimization algorithm for discrete and mixed variable constrained problems

Abstract

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.