diff --git a/learnware/learnware/base.py b/learnware/learnware/base.py
index 4500c71..8578f91 100644
--- a/learnware/learnware/base.py
+++ b/learnware/learnware/base.py
@@ -29,7 +29,7 @@ class Learnware:
         Raises
         ------
         TypeError
-            The type of model must be dict or BaseModel, else raise error
+            The type of model must be str or BaseModel, else raise error
         """
         if isinstance(model, BaseModel):
             return model
@@ -42,7 +42,7 @@ class Learnware:
             model_module = get_module_by_module_path(model_dict["module_path"])
             return getattr(model_module, model_dict["class_name"])()
         else:
-            raise TypeError("model must be BaseModel or dict")
+            raise TypeError("model must be BaseModel or str")
 
     def predict(self, X: np.ndarray) -> np.ndarray:
         return self.model.predict(X)
diff --git a/learnware/market/easy.py b/learnware/market/easy.py
index 8fa78ae..a752081 100644
--- a/learnware/market/easy.py
+++ b/learnware/market/easy.py
@@ -153,7 +153,7 @@ class EasyMarket(BaseMarket):
         # else:
         weight = torch.linalg.inv(K + torch.eye(K.shape[0]).to(user_rkme.device) * 1e-5) @ C
 
-        term1 = user_rkme.eval_Phi(user_rkme)
+        term1 = user_rkme.inner_prod(user_rkme)
         term2 = weight.T @ C
         term3 = weight.T @ K @ weight
         score = float(term1 - 2 * term2 + term3)
@@ -274,7 +274,10 @@ class EasyMarket(BaseMarket):
         for RKME in RKME_list:
             mmd_dist = RKME.dist(user_rkme)
             mmd_dist_list.append(mmd_dist)
-        sorted_dist_list, sorted_learnware_list = (list(t) for t in zip(*sorted(zip(mmd_dist_list, learnware_list))))
+
+        sorted_idx_list = sorted(range(len(learnware_list)), key=lambda k: mmd_dist_list[k])
+        sorted_dist_list = [mmd_dist_list[idx] for idx in sorted_idx_list]
+        sorted_learnware_list = [learnware_list[idx] for idx in sorted_idx_list]
 
         return sorted_dist_list, sorted_learnware_list
 
@@ -304,9 +307,32 @@ class EasyMarket(BaseMarket):
         learnware_list = [self.learnware_list[key] for key in self.learnware_list]
         return learnware_list
     
-    def search_learnware(self, user_info: BaseUserInfo) -> Tuple[Any, List[Learnware]]:
+    def search_learnware(self, user_info: BaseUserInfo, search_num=3) -> Tuple[List[float], List[Learnware], List[Learnware]]:
+        """Search learnwares based on user_info
+
+        Parameters
+        ----------
+        user_info : BaseUserInfo
+            user_info contains semantic_spec and stat_info
+        search_num : int
+            The number of the returned learnwares
+
+        Returns
+        -------
+        Tuple[List[float], List[Learnware], List[float], List[Learnware]]
+            the first is the sorted list of rkme dist
+            the second is the sorted list of Learnware (single) by the rkme dist
+            the third is the list of Learnware (mixture), the size is search_num
+        """
         learnware_list = self._search_by_semantic_spec(user_info)
-        return learnware_list
+
+        if "RKME" not in user_info.stat_info:
+            return None, learnware_list, None
+        else:
+            user_rkme = user_info.stat_info["RKME"]
+            sorted_dist_list, single_learnware_list = self._search_by_rkme_spec_single(learnware_list, user_rkme)
+            weight_list, mixture_learnware_list = self._search_by_rkme_spec_mixture(learnware_list, user_rkme, search_num)
+            return sorted_dist_list, single_learnware_list, mixture_learnware_list
 
     def delete_learnware(self, id: str) -> bool:
         if not id in self.learnware_list: