The Set Covering Problem (SCP) is an important combinatorial optimization problem that finds application in a large variety of practical areas, particularly in airline crew scheduling or vehicle routing and facility placement problems. To solve de SCP we employ the Spotted Hyena Optimizer (SHO), which is a metaheuristic inspired by the natural behavior of the spotted hyenas. In this work, in order to improve the performance of our proposed approach we use Autonomous Search (AS), a case of adaptive systems that allows modifications of internals components on the run. We illustrate interesting experimental results where the proposed approach is able to obtain global optimums for a set of well-known set covering problem instances.