Run components in the correct order

haystack/core/pipeline/base.py

@@ -946,36 +946,71 @@ def _find_next_runnable_component(
         :returns: The name and the instance of the next Component that can be run
         """
 
-        def is_runnable(name, comp):
-            # Check that at least one connection provides a value to the component
-            # This ensures that components with only default inputs do not run
-            # unless a value is passed to them
-            at_least_one_conn = False
-            for input_socket in comp.__haystack_input__._sockets_dict.values():  # type: ignore
-                if input_socket.name not in components_inputs.get(name, {}) and input_socket.is_mandatory:
-                    return False
-
-            for sender, receiver, edge_data in self.graph.edges(data=True):
-                if receiver != name:
-                    continue
-                receiver_socket = edge_data["to_socket"].name
-
-                if receiver_socket in components_inputs.get(name, {}):
-                    at_least_one_conn = True
-            return at_least_one_conn
+        def count_inputs(name, comp):
+            # Count the number of inputs that are provided
+            # Returns None if a mandatory input is missing, an integer otherwise
+            # This can ensure that components with only default inputs are not run
+            num_inputs = 0
+            for input_socket in comp.__haystack_input__._sockets_dict.values():
+                if (
+                    input_socket.name not in components_inputs.get(name, {})
+                    and input_socket.is_mandatory
+                    and not input_socket.is_variadic
+                ):
+                    return None
+                if input_socket.name in components_inputs.get(name, {}):
+                    num_inputs += 1
+            return num_inputs
 
-        waiting_queue = [(name, comp, _is_lazy_variadic(comp), is_runnable(name, comp)) for name, comp in waiting_queue]
+        waiting_queue = [
+            (name, comp, _is_lazy_variadic(comp), count_inputs(name, comp)) for name, comp in waiting_queue
+        ]
 
-        first_runnable = next(((name, comp) for (name, comp, _, runnable) in waiting_queue if runnable), None)
+        first_runnable = next(
+            (
+                (name, comp)
+                for (name, comp, lazy_variadic, num_inputs) in waiting_queue
+                if not lazy_variadic and num_inputs is not None and num_inputs > 0
+            ),
+            None,
+        )
         if first_runnable:
             return first_runnable
 
         first_lazy_variadic = next(
-            ((name, comp) for (name, comp, lazy_variadic, _) in waiting_queue if lazy_variadic), None
+            (
+                (name, comp)
+                for (name, comp, lazy_variadic, num_inputs) in waiting_queue
+                if lazy_variadic and num_inputs is not None and num_inputs > 0
+            ),
+            None,
         )
         if first_lazy_variadic:
             return first_lazy_variadic
 
+        # Return components that get no input at all but have default arguments
+        first_default_lazy_variadic = next(
+            (
+                (name, comp)
+                for (name, comp, lazy_variadic, num_inputs) in waiting_queue
+                if lazy_variadic and num_inputs is not None
+            ),
+            None,
+        )
+        if first_default_lazy_variadic:
+            return first_default_lazy_variadic
+
+        first_default = next(
+            (
+                (name, comp)
+                for (name, comp, lazy_variadic, num_inputs) in waiting_queue
+                if not lazy_variadic and num_inputs is not None
+            ),
+            None,
+        )
+        if first_default:
+            return first_default
+
         return None
 
     def _find_next_runnable_lazy_variadic_or_default_component(