code: def test_optimize_l0_homotopy(
      self,
      mock_homotopy: Mock,
      mock_get_batch_initial_conditions: Mock,
  ) -> None:
      tkwargs: Dict[str, Any] = {"dtype": torch.double}
      acquisition = self.get_acquisition_function(
          fixed_features=self.fixed_features,
          options={
              "penalty": "L0_norm",
              "target_point": self.target_point,
          },
      )
      # overwrite acqf to validate homotopy
      model = GenericDeterministicModel(f=lambda x: 5 - (x - p) ** 2)
      acqf = PosteriorMean(model=model)
      acquisition.acqf = acqf
  
      p = Parameter(-2 * torch.ones(1, **tkwargs))
      hp = HomotopyParameter(
          parameter=p,
          schedule=LinearHomotopySchedule(start=4, end=0, num_steps=5),
      )
      mock_homotopy.return_value = Homotopy(homotopy_parameters=[hp])
  
      search_space_digest = SearchSpaceDigest(
          feature_names=["a"],
          bounds=[(-10.0, 5.0)],
      )
      candidate, acqf_val = acquisition._optimize_with_homotopy(
          n=1,
          search_space_digest=search_space_digest,
          optimizer_options={
              "num_restarts": 2,
              "sequential": True,
              "raw_samples": 16,
          },
      )
      self.assertEqual(candidate, torch.zeros(1, **tkwargs))
      self.assertEqual(acqf_val, 5 * torch.ones(1, **tkwargs))
  
imports: from __future__ import annotations
  import dataclasses
  import functools
  from typing import Any, Dict, Optional, Union
  from unittest import mock
  from unittest.mock import Mock
  import torch
  from ax.core.search_space import SearchSpaceDigest
  from ax.models.torch.botorch_modular.acquisition import Acquisition
  from ax.models.torch.botorch_modular.sebo import L1_norm_func, SEBOAcquisition
  from ax.models.torch.botorch_modular.surrogate import Surrogate
  from ax.models.torch_base import TorchOptConfig
  from ax.utils.common.constants import Keys
  from ax.utils.common.testutils import TestCase
  from ax.utils.common.typeutils import not_none
  from ax.utils.testing.mock import fast_botorch_optimize
  from botorch.acquisition import PosteriorMean
  from botorch.acquisition.monte_carlo import qNoisyExpectedImprovement
  from botorch.acquisition.multi_objective.monte_carlo import qNoisyExpectedHypervolumeImprovement
  from botorch.acquisition.penalized import L0Approximation
  from botorch.models.deterministic import GenericDeterministicModel
  from botorch.models.gp_regression import SingleTaskGP
  from botorch.models.model import ModelList
  from botorch.optim import Homotopy, HomotopyParameter, LinearHomotopySchedule
  from botorch.utils.datasets import SupervisedDataset
  from torch.nn import Parameter
label_desc: Use image node_id 5 for calling the TestSebo obj's underlying member method code with example usage: obj.test_optimize_l0_homotopy(mock_homotopy, mock_get_batch_initial_conditions) without return types