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	Synthetic	Project
DTLZ
MAF
WFG		Code
Fi’s
RE
MO-MNISTs	Multitask Learning	COSMOS
Fairness Classification
Federated Learning
Synthetic (DST, FTS…)		Project
Robotics (MO-MuJoCo…)		Code
Real-world Multi-objective Optimization Problem Suite	Real World	Project

Supported Algorithms

LibMOON supports the following algorithms:

Method	Property	#Obj	Support	Venues	Complexity	Arguments
EPO	Exact solution.	Any	Yes	ICML 2020	\(O(m^2 n K)\)	`EPOSolver`
HVGrad	It is a gradient-based HV method.	2/3	Yes	CEC2023	\(O(m^2 n K^2)\)	`HVGradSolver`
MGDA-UB	Arbitray Pareto solutions. Location affected highly by initialization.	Any	Yes	NeurIPS 2018	\(O(m^2 n K)\)	`MGDAUBSolver`
MOO-SVGD	A set of diverse Pareto solution.	Any	Yes	NeurIPS 2021	\(O(m^2 n K^2)\)	`MOO-SVGDSolver`
PMGDA	Pareto solutions satisfying any preference.	Any	Yes	TETCI	\(O(m^2 n K)\)	`PMGDASolver`
PMTL	Pareto solutions in sectors.	3 is difficult.	Yes	NeurIPS 2019	\(O(m^2 n K^2)\)	`PMTLSolver`
Agg-LS	Pareto solution with aggregations.	Any	Yes	Any	\(O(m n K )\)	`GradAggSolver`
Agg-Tche	Pareto solution with aggregations.	Any	Yes	Any	\(O(m n K )\)	`GradAggSolver`
Agg-mTche	Pareto solution with aggregations.	Any	Yes	Any	\(O(m n K )\)	`GradAggSolver`
Agg-PBI	Pareto solution with aggregations.	Any	Yes	Any	\(O(m n K )\)	`GradAggSolver`
Agg-COSMOS	Approximated exact solution.	Any	Yes	ICDM 2021	\(O(m n K )\)	`GradAggSolver`
Agg-SmoothTche	Pareto solution with aggregations.	Any	Yes	Any	\(O(m n K )\)	`GradAggSolver`

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

Method	Problems	Property	Arguments
EPO-based PSL	Pareto set learning Solvers	Exact solutions	`Agg-based PSL`
Aggregation-based PSL		Minimal aggregation function solutions	`Agg-based PSL`
PMGDA-based PSL		Specific solutions	`PMGDA-based PSL`
Evolutionary PSL		Mitigate local minima by ES	`Evolutionary-based PSL`
LoRA PSL		Light model structure	`LoRA-based psl`
Tch-LCB	MultiObjective Bayesian Optimization Solvers		`PSLMOBOSolver`
DirHV-EI			`PSLDirHVEISolver`
DirHV-EGO			`DirHVEGOSolver`

Citation

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

@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 (Maintainer of Pareto set learning, gradient-based solver)
Liang Zhao (Maintainer of MOBO)
Yingying Yu (Software design)
Xi Lin (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 (FIEEE, City University of Hong Kong, Corresponding)
Prof. Han Zhao (University of Illinois at Urbana-Champaign)
Prof. Yifan Chen (Hong Kong Baptist University)
Prof. Ke Shang (Shenzhen University)
Prof. Genghui Li (Shenzhen University)
Prof. Zhenkun Wang (Southern University of Science and Technology)
Prof. Tao Qin (Microsoft Research)