============
Introduction
============

``LibMOON`` is a multiobjective optimization framework that spans from single-objective optimization to multiobjective
optimization. It aims to enhance the understanding of optimization problems and facilitate fair comparisons between MOO
algorithms.


Supported Benchmark Datasets
============================

+------------------------------------------------------------------------------------------------------------------------------------+--------------------+---------------------------------------------------------+
| Datasets                                                                                                                           | Problems           | Project/Code                                            |
+====================================================================================================================================+====================+=========================================================+
| `ZDT <https://ieeexplore.ieee.org/document/996017>`_                                                                               | Synthetic          | `Project <https://pymoo.org/problems/multi/zdt.html>`_  |
+------------------------------------------------------------------------------------------------------------------------------------+                    |                                                         |
| `DTLZ <https://ieeexplore.ieee.org/document/996017>`_                                                                              |                    |                                                         |
+------------------------------------------------------------------------------------------------------------------------------------+                    |                                                         |
| `MAF <https://link.springer.com/article/10.1007/s40747-017-0039-7>`_                                                               |                    |                                                         |
+------------------------------------------------------------------------------------------------------------------------------------+                    +---------------------------------------------------------+
| `WFG <https://ieeexplore.ieee.org/document/996017>`_                                                                               |                    | `Code <https://github.com/ryojitanabe/reproblems>`_     |
+------------------------------------------------------------------------------------------------------------------------------------+                    |                                                         |
| `Fi's <https://ieeexplore.ieee.org/document/996017>`_                                                                              |                    |                                                         |
+------------------------------------------------------------------------------------------------------------------------------------+                    |                                                         |
| `RE <https://arxiv.org/abs/2009.12867>`_                                                                                           |                    |                                                         |
+------------------------------------------------------------------------------------------------------------------------------------+--------------------+---------------------------------------------------------+
| `MO-MNISTs <https://proceedings.neurips.cc/paper_files/paper/2019/file/685bfde03eb646c27ed565881917c71c-Paper.pdf>`_               | Multitask Learning | `COSMOS <https://github.com/ruchtem/cosmos>`_           |
+------------------------------------------------------------------------------------------------------------------------------------+                    |                                                         |
| `Fairness Classification <https://arxiv.org/pdf/2103.13392>`_                                                                      |                    |                                                         |
+------------------------------------------------------------------------------------------------------------------------------------+                    |                                                         |
| `Federated Learning <https://proceedings.neurips.cc/paper_files/paper/2023/file/7cb2c2a8d35576c00078b6591ec26a7d-Paper.pdf>`_      |                    |                                                         |
+------------------------------------------------------------------------------------------------------------------------------------+                    +---------------------------------------------------------+
| `Synthetic (DST, FTS...) <https://proceedings.neurips.cc/paper_files/paper/2019/file/4a46fbfca3f1465a27b210f4bdfe6ab3-Paper.pdf>`_ |                    |`Project <https://github.com/sample-repo/envelop-code>`_ |
+------------------------------------------------------------------------------------------------------------------------------------+                    +---------------------------------------------------------+
| `Robotics (MO-MuJoCo...) <https://proceedings.mlr.press/v119/xu20h/xu20h.pdf>`_                                                    |                    |  `Code <https://github.com/mit-gfx/PGMORL>`_            |
+------------------------------------------------------------------------------------------------------------------------------------+--------------------+---------------------------------------------------------+
| `Real-world Multi-objective Optimization Problem Suite <https://arxiv.org/pdf/2009.12867>`_                                        |    Real World      |  `Project <https://github.com/ryojitanabe/reproblems>`_ |
+------------------------------------------------------------------------------------------------------------------------------------+--------------------+---------------------------------------------------------+


Supported Algorithms
====================

``LibMOON`` supports the following algorithms:

+-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------+---------------------+------------+-------------+---------------------+-------------------+
| Method                                                                                                            | Property                                                               | #Obj                |Support     |Venues       |Complexity           |Arguments          |
+===================================================================================================================+========================================================================+=====================+============+=============+=====================+===================+
|`EPO <https://proceedings.mlr.press/v119/mahapatra20a/mahapatra20a.pdf>`_                                          | Exact solution.                                                        | Any                 |Yes         |ICML 2020    |:math:`O(m^2 n K)`   |``EPOSolver``      |
+-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------+---------------------+------------+-------------+---------------------+-------------------+
|`HVGrad <https://arxiv.org/abs/2102.04523>`_                                                                       | It is a gradient-based HV method.                                      | 2/3                 |Yes         |CEC2023      |:math:`O(m^2 n K^2)` |``HVGradSolver``   |
+-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------+---------------------+------------+-------------+---------------------+-------------------+
|`MGDA-UB <https://proceedings.neurips.cc/paper/2018/file/432aca3a1e345e339f35a30c8f65edce-Paper.pdf>`_             | Arbitray Pareto solutions. Location affected highly by initialization. | Any                 |Yes         |NeurIPS 2018 |:math:`O(m^2 n K)`   |``MGDAUBSolver``   |
+-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------+---------------------+------------+-------------+---------------------+-------------------+
|`MOO-SVGD <https://openreview.net/pdf?id=S2-j0ZegyrE>`_                                                            | A set of diverse Pareto solution.                                      | Any                 |Yes         |NeurIPS 2021 |:math:`O(m^2 n K^2)` |``MOO-SVGDSolver`` |
+-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------+---------------------+------------+-------------+---------------------+-------------------+
|`PMGDA <https://arxiv.org/abs/2402.09492>`_                                                                        | Pareto solutions satisfying any preference.                            | Any                 |Yes         |TETCI        |:math:`O(m^2 n K)`   |``PMGDASolver``    |
+-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------+---------------------+------------+-------------+---------------------+-------------------+
|`PMTL <https://proceedings.neurips.cc/paper_files/paper/2019/file/685bfde03eb646c27ed565881917c71c-Paper.pdf>`_    | Pareto solutions in sectors.                                           | 2. 3 is difficult.  |Yes         |NeurIPS 2019 |:math:`O(m^2 n K^2)` |``PMTLSolver``     |
+-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------+---------------------+------------+-------------+---------------------+-------------------+
|`Agg-LS <https://bayanbox.ir/view/2515773690068372592/Kaisa-Miettinen-Nonlinear-Multiobjective-Optimization.pdf>`_ | Pareto solution with aggregations.                                     | Any                 |Yes         |Any          |:math:`O(m n K )`    |``GradAggSolver``  |
+-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------+---------------------+------------+-------------+---------------------+-------------------+
| `Agg-Tche <https://ieeexplore.ieee.org/document/4358754>`_                                                        | Pareto solution with aggregations.                                     | Any                 |Yes         |Any          |:math:`O(m n K )`    |``GradAggSolver``  |
+-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------+---------------------+------------+-------------+---------------------+-------------------+
| `Agg-mTche <https://ieeexplore.ieee.org/document/7927726>`_                                                       | Pareto solution with aggregations.                                     | Any                 |Yes         |Any          |:math:`O(m n K )`    |``GradAggSolver``  |
+-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------+---------------------+------------+-------------+---------------------+-------------------+
| `Agg-PBI <https://ieeexplore.ieee.org/document/4358754>`_                                                         | Pareto solution with aggregations.                                     | Any                 |Yes         |Any          |:math:`O(m n K )`    |``GradAggSolver``  |
+-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------+---------------------+------------+-------------+---------------------+-------------------+
|`Agg-COSMOS <https://arxiv.org/pdf/2103.13392>`_                                                                   | Approximated exact solution.                                           | Any                 |Yes         |ICDM 2021    |:math:`O(m n K )`    | ``GradAggSolver`` |
+-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------+---------------------+------------+-------------+---------------------+-------------------+
| `Agg-SmoothTche <https://openreview.net/forum?id=m4dO5L6eCp>`_                                                    | Pareto solution with aggregations.                                     | Any                 |Yes         |Any          |:math:`O(m n K )`    |``GradAggSolver``  |
+-------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------+---------------------+------------+-------------+---------------------+-------------------+


Here, :math:`m` is the number of objectives, :math:`K` is the number of samples, and :math:`n` is the number of decision variables.
For neural network based methods, :math:`n` is the number of parameters; hence :math:`n` is very large (>10000), :math:`K` is also large (
e.g., 20-50), while :math:`m` is small (2.g., 2-4).
As a result, :math:`m^2` is not a big problem. :math:`n^2` is a big problem. :math:`K^2` is a big problem.


+-----------------------------------------------------------------------+---------------------------------------------+---------------------------------------+---------------------------+
|Method                                                                 |Problems	                              | Property                              |Arguments                  |
+=======================================================================+=============================================+=======================================+===========================+
| `EPO-based PSL <https://arxiv.org/abs/2010.04104>`_                   |Pareto set learning Solvers                  |Exact solutions                        |``EPO-based PSL``          |
+-----------------------------------------------------------------------+                                             +---------------------------------------+---------------------------|
| `Aggregation-based PSL <https://arxiv.org/abs/2010.04104>`_           |                                             |Minimal aggregation function solutions |``Agg-based PSL``          |
+-----------------------------------------------------------------------+                                             +---------------------------------------+---------------------------+
| `PMGDA-based PSL <https://arxiv.org/abs/2402.09492>`_                 |                                             | Specific solutions                    |``PMGDA-based PSL``        |
+-----------------------------------------------------------------------+                                             +---------------------------------------+---------------------------+
| `Evolutionary PSL <https://arxiv.org/html/2310.20426v3>`_             |                                             |  Mitigate local minima by ES          |``Evolutionary-based PSL`` |
+-----------------------------------------------------------------------+                                             +---------------------------------------+---------------------------+
| `LoRA PSL <https://www.arxiv.org/abs/2407.20734>`_                    |                                             | Light model structure                 |``LoRA-based psl``         |
+-----------------------------------------------------------------------+---------------------------------------------+---------------------------------------+---------------------------+
| `Tch-LCB <https://ieeexplore.ieee.org/document/7969460>`_             |MultiObjective Bayesian Optimization Solvers |                                       |``PSLMOBOSolver``          |
+-----------------------------------------------------------------------+                                             +---------------------------------------+---------------------------+
| `DirHV-EI <https://ieeexplore.ieee.org/abstract/document/10093980/>`_ |                                             |                                       |``PSLDirHVEISolver``       |
+-----------------------------------------------------------------------+                                             +---------------------------------------+---------------------------+
| `DirHV-EGO <https://ieeexplore.ieee.org/document/4358754>`_           |                                             |                                       |``DirHVEGOSolver``         |
+-----------------------------------------------------------------------+---------------------------------------------+---------------------------------------+---------------------------+


Citation
========

If you find ``LibMOON`` useful for your research or development, please cite the following:


.. code-block:: python

    @article{xzhang2024libmoon,
      title={LibMOON: A Gradient-based MultiObjective OptimizatioN Library in PyTorch},
      author={Xiaoyuan Zhang and Liang Zhao and Yingying Yu and Xi Lin and Zhenkun Wang and Yifan Chen and Han Zhao and Qingfu Zhang},
      journal={arXiv preprint arXiv:2409.02969},
      year={2024},
      url={https://arxiv.org/abs/2409.02969}
    }


Contributors
============
``LibMOON`` is developed by the following contributors:

- `Xiaoyuan Zhang <https://scholar.google.com/citations?user=KQj18L8AAAAJ&hl=zh-TW>`_  (Maintainer of Pareto set learning, gradient-based solver)
- `Liang Zhao <https://liazhao5.github.io/>`_  (Maintainer of MOBO)
- `Yingying Yu <https://scholar.google.com/citations?user=nw6-_5wAAAAJ&hl=en>`_  (Software design)
- `Xi Lin <https://xi-l.github.io/>`_  (Software design)

Contact Us
==========

- If you have any question or suggestion, please feel free to contact us by raising an issue or sending an email
  to ``xzhang2523-c@my.cityu.edu.hk``.



Advisory Board
==============

- Prof. `Qingfu Zhang <https://www.cs.cityu.edu.hk/~qzhan7/index.html>`_ (FIEEE, City University of Hong Kong, **Corresponding**)
- Prof. `Han Zhao <https://hanzhaoml.github.io/>`_ (University of Illinois at Urbana-Champaign)
- Prof. `Yifan Chen <https://ychen-stat-ml.github.io/>`_ (Hong Kong Baptist University)
- Prof. `Ke Shang <https://scholar.google.com.hk/citations?user=jFUXL1AAAAAJ&hl=zh-CN>`_ (Shenzhen University)
- Prof. `Genghui Li <https://scholar.google.com/citations?user=3WixDRMAAAAJ&hl=zh-CN>`_ (Shenzhen University)
- Prof. `Zhenkun Wang <https://faculty.sustech.edu.cn/?tagid=wangzk3&iscss=1&snapid=1&orderby=date&go=1&lang=en>`_ (Southern University of Science and Technology)
- Prof. `Tao Qin <https://scholar.google.com/citations?user=Bl4SRU0AAAAJ&hl=zh-CN>`_ (Microsoft Research)