code: def optimize_acqf_homotopy(
      acq_function: AcquisitionFunction,
      bounds: Tensor,
      q: int,
      homotopy: Homotopy,
      num_restarts: int,
      raw_samples: Optional[int] = None,
      fixed_features: Optional[Dict[int, float]] = None,
      options: Optional[Dict[str, Union[bool, float, int, str]]] = None,
      final_options: Optional[
          Dict[str, Union[bool, float, int, str]]
      ] = None,
      batch_initial_conditions: Optional[Tensor] = None,
      post_processing_func: Optional[Callable[[Tensor], Tensor]] = None,
      prune_tolerance: float = 1e-4,
  ) -> Tuple[Tensor, Tensor]:
      r"""Generate a set of candidates via multi-start optimization.
  
      Args:
          acq_function: An AcquisitionFunction.
          bounds: A `2 x d` tensor of lower and upper bounds for each column of `X`.
          q: The number of candidates.
          homotopy: Homotopy object that will make the necessary modifications to the
              problem when calling `step()`.
          num_restarts: The number of starting points for multistart acquisition
              function optimization.
          raw_samples: The number of samples for initialization. This is required
              if `batch_initial_conditions` is not specified.
          fixed_features: A map `{feature_index: value}` for features that
              should be fixed to a particular value during generation.
          options: Options for candidate generation.
          final_options: Options for candidate generation in the last homotopy step.
          batch_initial_conditions: A tensor to specify the initial conditions. Set
              this if you do not want to use default initialization strategy.
          post_processing_func: Post processing function (such as roundingor clamping)
              that is applied before choosing the final candidate.
      """
      candidate_list, acq_value_list = [], []
      if q > 1:
          base_X_pending = acq_function.X_pending
  
      for _ in range(q):
          candidates = batch_initial_conditions
          homotopy.restart()
  
          while not homotopy.should_stop:
              candidates, acq_values = optimize_acqf(
                  q=1,
                  acq_function=acq_function,
                  bounds=bounds,
                  num_restarts=num_restarts,
                  batch_initial_conditions=candidates,
                  raw_samples=raw_samples,
                  fixed_features=fixed_features,
                  return_best_only=False,
                  options=options,
              )
              homotopy.step()
  
              # Prune candidates
              candidates = prune_candidates(
                  candidates=candidates.squeeze(1),
                  acq_values=acq_values,
                  prune_tolerance=prune_tolerance,
              ).unsqueeze(1)
  
          # Optimize one more time with the final options
          candidates, acq_values = optimize_acqf(
              q=1,
              acq_function=acq_function,
              bounds=bounds,
              num_restarts=num_restarts,
              batch_initial_conditions=candidates,
              return_best_only=False,
              options=final_options,
          )
  
          # Post-process the candidates and grab the best candidate
          if post_processing_func is not None:
              candidates = post_processing_func(candidates)
              acq_values = acq_function(candidates)
          best = torch.argmax(acq_values.view(-1), dim=0)
          candidate, acq_value = candidates[best], acq_values[best]
  
          # Keep the new candidate and update the pending points
          candidate_list.append(candidate)
          acq_value_list.append(acq_value)
          selected_candidates = torch.cat(candidate_list, dim=-2)
          if q > 1:
              acq_function.set_X_pending(
                  torch.cat(
                      [base_X_pending, selected_candidates], dim=-2
                  )
                  if base_X_pending is not None
                  else selected_candidates
              )
  
      if q > 1:  # Reset acq_function to previous X_pending state
          acq_function.set_X_pending(base_X_pending)
      homotopy.reset()  # Reset the homotopy parameters
  
      return selected_candidates, torch.stack(acq_value_list)
  
file_path: botorch/botorch/optim/optimize_homotopy.py
imports: from typing import Callable, Dict, Optional, Tuple, Union
  import torch
  from botorch.acquisition import AcquisitionFunction
  from botorch.optim.homotopy import Homotopy
  from botorch.optim.optimize import optimize_acqf
  from torch import Tensor
label_desc: Use image node_id 2 for calling a global function with example usage: optimize_acqf_homotopy(acq_function, bounds, q, homotopy, num_restarts, raw_samples, fixed_features, options, final_options, batch_initial_conditions, post_processing_func, prune_tolerance) and returns: selected_candidates,  torch