Fix start earliesr objective

processscheduler/objective.py

@@ -399,6 +399,28 @@ def __init__(self, **data) -> None:
 
 
 class ObjectiveTasksStartEarliest(Objective):
+    """This is the dual of the completion weighted times
+    but for task starts."""
+
+    def __init__(self, **data) -> None:
+        all_priorities = []
+        for task in processscheduler.base.active_problem.tasks.values():
+            if task.optional:
+                all_priorities.append(task._start * task.priority * task._scheduled)
+            else:
+                all_priorities.append(task._start * task.priority)
+        priority_sum = z3.Sum(all_priorities)
+        priority_indicator = IndicatorFromMathExpression(
+            name="WeightedStartTimes", expression=priority_sum
+        )
+        super().__init__(
+            name="MinimizeWeightedStartTimes",
+            target=priority_indicator,
+            kind="minimize",
+        )
+
+
+class ObjectiveMinimizeGreatestStartTime(Objective):
     """minimize the greatest start time, i.e. tasks are schedules
     as early as possible"""
 

test/test_solver.py

@@ -334,13 +334,13 @@ def test_start_earliest_2():
     ps.TaskStartAt(task=task_1, value=8)
     ps.TaskPrecedence(task_before=task_1, task_after=task_2)
 
-    ps.ObjectiveTasksStartEarliest(list_of_tasks=[task_2, task_3])
+    ob = ps.ObjectiveTasksStartEarliest(list_of_tasks=[task_2, task_3])
 
     solution = solve_problem(problem)
     assert solution
-    assert solution.tasks["task1"].start == 8
-    assert solution.tasks["task2"].start == 13
-    assert solution.tasks["task3"].start == 0
+    # the weighted start time should be:
+    # 0 * 1 + 8 * 1 + 13 * 1
+    assert solution.indicators[ob.target.name] == 21
 
 
 def test_start_latest_1():