A cooperative particle swarm optimizer with stochastic movements for computationally expensive numerical optimization problems

•An improved version of PSO has been proposed, so called extraordinary PSO (EPSO).•Validation of EPSO by computationally expensive benchmark problems reported in CEC’15.•Application of EPSO for optimal solving of benchmark constrained and engineering design problems.•EPSO has been compared with the standard PSO and its other variants.•EPSO offers better quality solutions with respect to other reported optimizers.