.. _mobo-setting:

MOBO Setting
============

In the multi-objective Bayesian optimization (MOBO) setting, the true objective functions are available but expensive to evaluate.
Because the evaluation budget is typically small, collecting a large diffusion training dataset directly is infeasible.
To address this limitation, ``moospread`` adopts the data-augmentation strategy of
`CDM-PSL <https://ojs.aaai.org/index.php/AAAI/article/view/34913>`_.
This approach produces a sufficiently large training dataset for the diffusion model while respecting the evaluation-budget constraints.

In this example, we use the Branin–Currin problem, which is a bi-objective benchmark task.

.. code-block:: python

   import numpy as np
   import torch

   # Import the SPREAD solver
   from moospread import SPREAD

   # Import a test problem
   from moospread.tasks import BraninCurrin

   # Define the problem
   problem = BraninCurrin()


When initializing the SPREAD solver, the parameter ``mode`` must be set to ``"bayesian"``.
Setting ``timesteps`` to a relatively small value (e.g., ``25``) is important to reduce computational cost and accelerate optimization.

You may use a custom surrogate model architecture by specifying ``surrogate_model`` and its corresponding training function via ``train_func_surrogate``.
By default, ``moospread`` uses Gaussian processes as surrogate models.

.. code-block:: python

   # Initialize the SPREAD solver
   solver = SPREAD(
       problem,
       num_blocks=2,
       timesteps=25,
       num_epochs=1000,
       train_tol=100,
       mode="bayesian",
       model_dir="./model_dir/",
       seed=2026,
       verbose=True
   )


To solve the problem, specify:

- the number of initial samples using ``n_init_mobo``,
- the number of MOBO iterations using ``n_steps_mobo``,
- the batch size selected at each step using ``batch_select_mobo``, and
- the number of generations using ``spread_num_samp_mobo``.

As shown in the experiments reported in the paper, using an auxiliary operator to escape local minima is beneficial.
This can be enabled by setting ``use_escape_local_mobo=True``.

In the MOBO setting, we recommend the following parameter choices:

- For bi-objective problems:

  - ``rho_scale_gamma = 0.9``
  - ``eta_init = 0.9``
  - ``lr_inner = 0.9``

- For problems with more than two objectives:

  - ``rho_scale_gamma = 0.01 / 0.0001``
  - ``eta_init = 0.9``
  - ``lr_inner = 0.9 / 5e-4``

If intermediate Pareto fronts are not required, set ``iterative_plot=False``.

.. code-block:: python

   # Solve the problem
   result_Xy, hv_all_value = solver.solve(
       rho_scale_gamma=0.9,
       eta_init=0.9,
       lr_inner=0.9,
       iterative_plot=True,
       plot_period=10,
       max_backtracks=25,
       save_results=True,
       samples_store_path="./samples_dir/",
       images_store_path="./images_dir/",
       n_init_mobo=100,
       use_escape_local_mobo=True,
       n_steps_mobo=20,
       spread_num_samp_mobo=25,
       batch_select_mobo=5
   )

Since ``iterative_plot`` is enabled in this example, we can visualize the generative process using the images saved in ``images_store_path`` (see :ref:`visualization`).

Here, the generated points are plotted after each MOBO step (1, 2, …, 20). Therefore, we need to set ``reverse=False``.

.. code-block:: python

   solver.create_video(
       image_folder="images_dir/BraninCurrin_bayesian",
       output_video="videos_dir/BraninCurrin_bayesian.mp4",
       total_duration_s=20.0,
       first_transition_s=2.0,
       fps=30,
       reverse=False
   )


.. list-table::
   :widths: 50 50
   :align: center

   * - .. figure:: _static/BraninCurrin_n5_bayesian.gif
          :width: 300px

          Generative process

     - .. figure:: _static/spread_BraninCurrin_T=25_N=5_t=20_seed=2026_bayesian.jpg
          :width: 300px

          Final generated Pareto front

If we set ``hypervolume=True`` and provide  
``hv_all_value_file="samples_dir/spread_BraninCurrin_T25_K20_FE100_seed=2026_bayesian_hv_results.pkl"``,  
we can visualize the evolution of the hypervolume.

.. list-table::
   :widths: 50 50
   :align: center

   * - .. figure:: _static/BraninCurrin_n5_bayesian_hv.gif
          :width: 300px

     - .. figure:: _static/spread_hv_BraninCurrin_T=25_t=21_seed=2026_bayesian.jpg
          :width: 300px