code: def _suggest_gp_model(
      search_space: SearchSpace,
      num_trials: Optional[int] = None,
      optimization_config: Optional[OptimizationConfig] = None,
      use_saasbo: bool = False,
  ) -> Union[None, ModelRegistryBase]:
      """Suggest a model based on the search space. None means we use Sobol.
  
      1. We use Sobol if the number of total iterations in the optimization is
      known in advance and there are fewer distinct points in the search space
      than the known intended number of total iterations.
      2. We use ``BO_MIXED`` if there are fewer ordered parameters in the search space
      than the sum of options for the *unordered* choice parameters, and the number
      of discrete enumerations to be performed by the optimizer is less than
      ``MAX_DISCRETE_ENUMERATIONS_MIXED``, or if there are only choice parameters and
      the number of choice combinations to enumerate is less than
      ``MAX_DISCRETE_ENUMERATIONS_CHOICE_ONLY``. Note that we do not count 2-level choice
      parameters as unordered, since these do not affect the modeling choice.
      3. If there are more ordered parameters in the search space than the sum of options
      for the *unordered* choice parameters, or if there is at least one ordered
      parameter and the number of parameters needed to encode all unordered parameters
      is less than ``MAX_ONE_HOT_ENCODINGS_CONTINUOUS_OPTIMIZATION``, we use BO with
      continuous relaxation.
      * If ``optimization_config`` has multiple objectives, we use ``MOO`` if
      ``use_saasbo is False`` and ``FULLYBAYESIANMOO`` otherwise.
      * Otherwise, we use ``GPEI`` if ``use_saasbo is False`` and ``FULLYBAYESIAN``
      otherwise.
      """
      # Count tunable parameter types.
      num_ordered_parameters = 0
      num_unordered_choices = 0
      num_enumerated_combinations = 1
      num_possible_points = 1
      all_range_parameters_are_discrete = True
      all_parameters_are_enumerated = True
      for parameter in search_space.tunable_parameters.values():
          should_enumerate_param = False
          num_param_discrete_values = None
          if isinstance(parameter, ChoiceParameter):
              should_enumerate_param = True
              num_param_discrete_values = len(parameter.values)
              num_possible_points *= num_param_discrete_values
              if (
                  parameter.is_ordered is False
                  and num_param_discrete_values > 2
              ):
                  num_unordered_choices += num_param_discrete_values
              else:
                  num_ordered_parameters += 1
          elif isinstance(parameter, RangeParameter):
              num_ordered_parameters += 1
              if parameter.parameter_type == ParameterType.FLOAT:
                  all_range_parameters_are_discrete = False
              else:
                  num_param_discrete_values = (
                      int(parameter.upper - parameter.lower) + 1
                  )
                  num_possible_points *= num_param_discrete_values
  
          if should_enumerate_param:
              num_enumerated_combinations *= not_none(
                  num_param_discrete_values
              )
          else:
              all_parameters_are_enumerated = False
  
      # Use Sobol if number of trials is known and sufficient to try all possible points.
      if (
          num_trials is not None
          and all_range_parameters_are_discrete
          and num_possible_points <= num_trials
      ):
          logger.info(
              "Using Sobol since we can enumerate the search space."
          )
          if use_saasbo:
              logger.warning(
                  SAASBO_INCOMPATIBLE_MESSAGE.format("Sobol")
              )
          return None
  
      # Use mixed Bayesian optimization when appropriate. This logic is currently tied to
      # the fact that acquisition function optimization for mixed BayesOpt currently
      # enumerates all combinations of choice parameters.
      # We use continuous relaxation if there are more ordered parameters than there
      # are choices for unordered parameters.
      if (num_ordered_parameters < num_unordered_choices) and (
          num_enumerated_combinations <= MAX_DISCRETE_ENUMERATIONS_MIXED
          or (
              all_parameters_are_enumerated
              and num_enumerated_combinations
              < MAX_DISCRETE_ENUMERATIONS_NO_CONTINUOUS_OPTIMIZATION
          )
      ):
          logger.info(
              "Using Bayesian optimization with a categorical kernel for improved "
              "performance with a large number of unordered categorical parameters."
          )
          if use_saasbo:
              logger.warning(
                  SAASBO_INCOMPATIBLE_MESSAGE.format("`BO_MIXED`")
              )
          return Models.BO_MIXED
  
      if num_ordered_parameters >= num_unordered_choices or (
          num_unordered_choices
          < MAX_ONE_HOT_ENCODINGS_CONTINUOUS_OPTIMIZATION
          and num_ordered_parameters > 0
      ):
          # These use one-hot encoding for unordered choice parameters, resulting in a
          # total of num_unordered_choices OHE parameters.
          # So, we do not want to use them when there are too many unordered choices.
          method = (
              Models.SAASBO if use_saasbo else Models.BOTORCH_MODULAR
          )
          reason = (
              "there are more ordered parameters than there are categories for the "
              "unordered categorical parameters."
              if num_ordered_parameters >= num_unordered_choices
              else "there is at least one ordered parameter and there are fewer than "
              f"{MAX_ONE_HOT_ENCODINGS_CONTINUOUS_OPTIMIZATION} choices for "
              "unordered parameters."
          )
          logger.info(f"Using {method} since {reason}")
          return method
  
      logger.info(
          f"Using Sobol since there are more than {MAX_DISCRETE_ENUMERATIONS_MIXED} "
          "combinations of enumerated parameters. For improved performance, make sure "
          "that all ordered `ChoiceParameter`s are encoded as such (`is_ordered=True`), "
          "and use `RangeParameter`s in place of ordered `ChoiceParameter`s where "
          "possible. Also, consider removing some or all unordered `ChoiceParameter`s."
      )
      if use_saasbo:
          logger.warning(SAASBO_INCOMPATIBLE_MESSAGE.format("Sobol"))
      return None
  
imports: import logging
  import warnings
  from math import ceil
  from typing import Any, cast, Dict, Optional, Type, Union
  import torch
  from ax.core.experiment import Experiment
  from ax.core.optimization_config import OptimizationConfig
  from ax.core.parameter import ChoiceParameter, ParameterType, RangeParameter
  from ax.core.search_space import SearchSpace
  from ax.modelbridge.generation_strategy import GenerationStep, GenerationStrategy
  from ax.modelbridge.registry import MODEL_KEY_TO_MODEL_SETUP, ModelRegistryBase, Models
  from ax.modelbridge.transforms.base import Transform
  from ax.modelbridge.transforms.winsorize import Winsorize
  from ax.models.torch.botorch_modular.model import BoTorchModel
  from ax.models.types import TConfig
  from ax.models.winsorization_config import WinsorizationConfig
  from ax.utils.common.logger import get_logger
  from ax.utils.common.typeutils import not_none
label_desc: Use image node_id 3 for calling a global function with example usage: _suggest_gp_model(search_space, num_trials, optimization_config, use_saasbo) and returns: None, None, Models, method