In the last few years, the cloudification of applications requires new concepts and techniques to fully reap the benefits of the new computing paradigm. Among them, the microservices architectural style, which is inspired by service-oriented architectures, has gained attention from both industry and academia. However, decomposing a monolith into multiple microservices also creates several challenges across the application's lifecycle. In this work, we focus on the operation aspect of microservices, and present our novel proposal to enable self-optimizing microservices systems based on grid search and random search techniques. The initial results show our approach is able to optimize the latency performance of microservices to up to 10.56\%.