code: def test_get_pareto_front_trials_nd() -> None:
      study = create_study(
          directions=["minimize", "maximize", "minimize"]
      )
      assert {
          _trial_to_values(t)
          for t in _get_pareto_front_trials_nd(
              study.trials, study.directions
          )
      } == set()
  
      study.optimize(lambda t: [2, 2, 2], n_trials=1)
      assert {
          _trial_to_values(t)
          for t in _get_pareto_front_trials_nd(
              study.trials, study.directions
          )
      } == {(2, 2, 2)}
  
      study.optimize(lambda t: [1, 1, 1], n_trials=1)
      assert {
          _trial_to_values(t)
          for t in _get_pareto_front_trials_nd(
              study.trials, study.directions
          )
      } == {
          (1, 1, 1),
          (2, 2, 2),
      }
  
      study.optimize(lambda t: [3, 1, 3], n_trials=1)
      assert {
          _trial_to_values(t)
          for t in _get_pareto_front_trials_nd(
              study.trials, study.directions
          )
      } == {
          (1, 1, 1),
          (2, 2, 2),
      }
  
      study.optimize(lambda t: [3, 2, 3], n_trials=1)
      assert {
          _trial_to_values(t)
          for t in _get_pareto_front_trials_nd(
              study.trials, study.directions
          )
      } == {
          (1, 1, 1),
          (2, 2, 2),
      }
  
      study.optimize(lambda t: [1, 3, 1], n_trials=1)
      assert {
          _trial_to_values(t)
          for t in _get_pareto_front_trials_nd(
              study.trials, study.directions
          )
      } == {(1, 3, 1)}
      assert (
          len(
              _get_pareto_front_trials_nd(
                  study.trials, study.directions
              )
          )
          == 1
      )
  
      study.optimize(
          lambda t: [1, 3, 1], n_trials=1
      )  # The trial result is the same as the above one.
      assert {
          _trial_to_values(t)
          for t in _get_pareto_front_trials_nd(
              study.trials, study.directions
          )
      } == {(1, 3, 1)}
      assert (
          len(
              _get_pareto_front_trials_nd(
                  study.trials, study.directions
              )
          )
          == 2
      )
  
file_path: optuna/tests/test_multi_objective.py
imports: from typing import Tuple
  from optuna import create_study
  from optuna.study._multi_objective import _get_pareto_front_trials_2d
  from optuna.study._multi_objective import _get_pareto_front_trials_nd
  from optuna.trial import FrozenTrial
label_desc: Use image node_id 3 for calling a global function with example usage: test_get_pareto_front_trials_nd() without return types