diff --git a/flaml/automl/automl.py b/flaml/automl/automl.py
index d2d9f98956..47a82a5b2a 100644
--- a/flaml/automl/automl.py
+++ b/flaml/automl/automl.py
@@ -2521,8 +2521,8 @@ def _search(self):
         self._warn_threshold = 10
         self._selected = None
         self.modelcount = 0
-        if self._max_iter < 2 and self.estimator_list and self._state.retrain_final:
-            # when max_iter is 1, no need to search
+        if self._max_iter < 1 and self.estimator_list and self._state.retrain_final:
+            # when max_iter is 1, search is also necessary for test. Besides, it won't take a lot of time.
             self.modelcount = self._max_iter
             self._max_iter = 0
             self._best_estimator = estimator = self.estimator_list[0]
diff --git a/flaml/fabric/mlflow.py b/flaml/fabric/mlflow.py
index 4cfb0e2cd2..e0ad4e870b 100644
--- a/flaml/fabric/mlflow.py
+++ b/flaml/fabric/mlflow.py
@@ -504,16 +504,22 @@ def log_automl(self, automl):
             self.adopt_children(automl)
 
         if self.manual_log:
-            best_mlflow_run_id = self.manual_run_ids[automl._best_iteration]
+            if len(self.manual_run_ids) == 0:
+                best_mlflow_run_id = self.parent_run_id or mlflow.active_run().info.run_id
+            else:
+                best_mlflow_run_id = self.manual_run_ids[automl._best_iteration]
             best_run_name = self.mlflow_client.get_run(best_mlflow_run_id).info.run_name
             automl.best_run_id = best_mlflow_run_id
             automl.best_run_name = best_run_name
             self.mlflow_client.set_tag(best_mlflow_run_id, "flaml.best_run", True)
             self.best_run_id = best_mlflow_run_id
             if self.parent_run_id is not None:
-                conf = automl._config_history[automl._best_iteration][1].copy()
-                if "ml" in conf.keys():
-                    conf = conf["ml"]
+                conf = {}
+                if automl._best_iteration in automl._config_history:###
+                    conf = automl._config_history[automl._best_iteration][1].copy()
+                    if "ml" in conf.keys():
+                        conf = conf["ml"]
+
 
                 mlflow.log_params(conf)
                 mlflow.log_param("best_learner", automl._best_estimator)