Anomaly detection on time-series metrics is essential for reliable microservice systems. The growing variety of time series anomaly detection (TSAD) algorithms, however, makes model selection and hyperparameter tuning a challenging task. While AutoML methods have been applied to automate this process, they typically optimize only for accuracy, overlooking latency and resource consumption. We present MOTSAD, a multi-objective optimization framework that combines a meta-feature-based warm start with a TSAD-specific evolutionary algorithm to jointly improve detection performance and efficiency. Experiments demonstrate that MOTSAD boosts F1-score by up to 21%, reduces inference latency by 8.4%, and outperforms multi-objective baselines by 3% in terms of the evaluation metric, showing its effectiveness for practical deployments.