In this contribution, a new optimization strategy called Self-Adaptive Big Bang-Big Crunch (SA-BB-BC) algorithm is proposed. This methodology consists on the association between the operators of the Big Bang-Big Crunch (BB-BC) algorithm, two strategies to update the population size and a parameter for controlling the influence of particle positions and the best particle in the system. The proposed methodology is applied to three classical engineering systems design. The obtained results demonstrate that SA-BB-BC is an interesting optimization strategy when compared with the canonical BB-BC algorithm, BB-BC-r algorithm and other well-established algorithms. It is important to mention that the proposed algorithm can avoid premature convergence, reducing the number of evaluations of the objective function, but maintaining the accuracy of the solutions.