Performance debugging in production is a fundamental activity in modern service-based systems. The diagnosis of performance issues is often time-consuming, since it requires thorough inspection of large volumes of traces and performance indices. In this paper we present DeLag, a novel automated search-based approach for diagnosing performance issues in service-based systems. DeLag identifies subsets of requests that show, in the combination of their Remote Procedure Call execution times, symptoms of potentially relevant performance issues. We call such symptoms Latency Degradation Patterns. DeLag simultaneously searches for multiple latency degradation patterns while optimizing precision, recall and latency dissimilarity. Experimentation on 700 datasets of requests generated from two microservice-based systems shows that our approach provides better and more stable effectiveness than three state-of-the-art approaches and general purpose machine learning clustering algorithms. DeLag is more effective than all baseline techniques in at least one case study (with p $\leq$ 0.05 and non-negligible effect size). Moreover, DeLag outperforms in terms of efficiency the second and the third most effective baseline techniques on the largest datasets used in our evaluation (up to 22%).