For calculating constrained optimization problem various socio/bio-inspired algorithms have adopted a penalty function approach to handle linear and nonlinear constraints. In a general sense, the approach is quite easy to understand, but a precise choice of penalty parameter is very much important. It requires a bunch number of primer preliminaries. So as to beat this restriction another self-adaptive penalty function (SAPF) approach will be proposed and incorporated into Particle Swarm Optimization (PSO) algorithm. This approach is referred to as PSO-SAPF. Besides, PSO-SAPF approach will be hybridized with Colliding Bodies Optimization (CBO) referred to as PSO-SAPF-CBO algorithm. The performance of PSO-SAPF and PSO-SAPF-CBO algorithm will be distinctly validated by solving discrete and mixed variable problems from truss structure domain and linear and nonlinear domain. The effect of behavior of penalty parameter, penalty function and constrained violation will be analyzed and discussed with the advantages over other algorithms. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.