code: def test_optimize_without_analytical_gradient_prediction(self):
      expected_optimum_position = [[0, 0]]
      self.mock_optimizer.optimize.return_value = (
          expected_optimum_position
      )
      self.mock_model.analytical_gradient_prediction = False
      self.lcb_mcmc_acquisition = AcquisitionLCB_MCMC(
          self.mock_model, self.space, self.mock_optimizer
      )
  
      optimum_position = self.lcb_mcmc_acquisition.optimize()
  
      self.assertEqual(expected_optimum_position, optimum_position)
  
file_path: GPyOpt/GPyOpt/testing/acquisitions_tests/test_lcb_mcmc_acquisition.py
imports: import unittest
  from mock import Mock
  import numpy
  from GPyOpt.acquisitions import AcquisitionLCB_MCMC
  from GPyOpt.core.task.space import Design_space
label_desc: Use image node_id 5 for calling the TestLCBmcmcAcquisition obj's underlying member method code with example usage: obj.test_optimize_without_analytical_gradient_prediction() without return types