LibMOON: A Gradient-based MultiObjective OptimizatioN Library in PyTorch

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. A submission to NeurIPS 2024 DB track.

"I raise my cup to invite the moon.
With my shadow we become three from one."
-- Li Bai

Main Contributors

• Xiaoyuan Zhang (Maintainer of Pareto set learning, gradient-based solver)
• Ji Cheng
• Liang Zhao (Maintainer of MOBO)
• Weiduo Liao
• Zhe Zhao
• Xi Lin
• Cheng Gong
• Longcan Chen
• Yingying Yu

Supporters

• Hongzong Li (For the non-local search)

Advisory Board

• Prof. Jingda Deng (Xi'an Jiaotong University) (For advice of High-D hypervolume computation)
• Prof. Yifan Chen (Hong Kong Baptist University) (For advice of OR)
• Prof. Ke Shang (Shenzhen University) (For advice of approximate hypervolume-based methods)
• Prof. Han Zhao (University of Illinois at Urbana-Champaign) (For advice of fariness classification)

Correspondence

The corresponding author is Chair Prof. Qingfu Zhang (FIEEE, City University of Hong Kong).

Contact

• Xiaoyuan Zhang (xzhang2523-c@my.cityu.edu.hk)
• QQ group:
• 

Resources

For more information on methodologies, please visit our GitHub repository. Contributions and stars are welcome!

(1) A standardlized gradient based framework.

Optimization Problem Classes

Problem Class Details

For more information on problem specifics, please refer to the Readme_problem.md file.

Synthetic Problems

Here's a list of synthetic problems along with relevant research papers and project/code links:

Problem	Paper	Project/Code
ZDT	Paper	Project
DTLZ	Paper	Project
MAF	Paper	Project
WFG	Paper	Code
Fi's	Paper	Code
RE	Paper	Code

Multitask Learning Problems

This section details problems related to multitask learning, along with their corresponding papers and project/code references:

Problem	Paper	Project/Code
MO-MNISTs	PMTL	COSMOS
Fairness Classification	COSMOS	COSMOS
Federated Learning	Federal MTL	COSMOS
Synthetic (DST, FTS...)	Envelop	Project
Robotics (MO-MuJoCo...)	PGMORL	Code

Current Supported Solvers

LibMOON includes a variety of solvers tailored for different needs as img below shows. The following solvers are currently:

Gradient-based MOO Solver

• GradAggSolver
• EPOSolver
• MOO-SVGDSolver (*)
• MGDASolver
• PMGDASolver
• PMTLSolver
• HVGradSolver

(*) The original MOO-SVGD code does not include an implementation for Multitask Learning (MTL). Our release of MOO-SVGD is the first open-source code that supports MTL.

Method	Property	#Obj	Support	Published	Complexity
Aggregation fun. based, e.g. Tche,mTche,LS,PBI,...	Pareto solution with aggregations.	Any	Y
COSMOS code	Approximated exact solution.	Any	Y	ICDM 2021	$O(m n K )$
EPO code	Exact solution.	Any	Y	ICML 2020	$O(m^2 n K )$
MOO-SVGD code	A set of diverse Pareto solution.	Any	Y	NeurIPS 2021	$O(m^2 n K^2 )$
MGDA code	Arbitray Pareto solutions. Location affected highly by initialization.	Any	Y	NeurIPS 2018	$O(m^2 n K )$
PMGDA	Pareto solutions satisfying any preference.	Any	Y	Under review	$O(m^2 n K )$
PMTL code	Pareto solutions in sectors.	2. 3 is difficult.	Y	NeurIPS 2019	$O(m^2 n K^2 )$
HVGrad WangHao code	It is a gradient-based HV method.	2/3	Y	CEC 2023	$O(m^2 n K^2 )$

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.

Time complexity of gradient based methods are as follows,

1. Tier 1. GradAggSolver.
2. Tier 2. MGDASolver, EPOSolver, PMTLSolver.
3. Tier 3. GradHVSolver
4. Tier 4. MOOSVGDSolver

Important things to notice: The original code MOO-SVGD does not offer a MTL implement. Our code is the first open source code for MTL MOO-SVGD.

Pareto set learning(PSL) Solvers

LibMOON supports various models of PSL solvers, categorized as follows:

• EPO-based PSL
• Agg-based PSL
• PMGDA-based PSL
• Evolutionary-based PSL

MultiObjective Bayesian Optimization (MOBO) Solvers

• PSL-MONO
• PSL-DirHV-EI
• DirHV-EGO

ML Pretrained Methods

• HV Net, a model for handling high-volume data, available here.

Installation

Libmoon is available on PyPI. You can install it using pip:

pip install libmoon==0.1.11

• Example1: Finding a size-K (K=5) Pareto solutions with four lines of code.

from libmoon.solver.gradient.methods import EPOSolver
from libmoon.util_global.initialization import synthetic_init
from libmoon.util_global.weight_factor import uniform_pref
from libmoon.util_global import get_problem

problem = get_problem(problem_name='ZDT1')
prefs = uniform_pref(n_prob=5, n_obj=problem.n_obj, clip_eps=1e-2)
solver = EPOSolver(problem, step_size=1e-2, n_iter=1000, tol=1e-2)
res = solver.solve(x=synthetic_init(problem, prefs), prefs=prefs)

• Example2: PSL in a problem with three lines of solving problem and two lines of evaluating the results.

from libmoon.solver.psl.core_psl import AggPSLSolver
from libmoon.util_global import get_problem
from libmoon.util_global.weight_factor import uniform_pref
from torch import Tensor

problem = get_problem(problem_name='ZDT1')
# agg list [ ’ls ’, ’tche ’, ’mtche ’, ’pbi ’, ... ]
prefs = uniform_pref(n_prob=100, n_obj=problem.n_obj, clip_eps=1e-2)
solver = AggPSLSolver(problem, agg='ls')
model = solver.solve()
eval_y = problem.evaluate(model(Tensor(prefs).cuda()))

=======

LibMOON: A Gradient-based MultiObjective OptimizatioN Library in PyTorch

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. A submission to NeurIPS 2024 DB track.

"I raise my cup to invite the moon.
With my shadow we become three from one."
-- Li Bai

Main Contributors

• Xiaoyuan Zhang (Maintainer of Pareto set learning, gradient-based solver)
• Ji Cheng
• Liao Zhao (Maintainer of MOBO)
• Weiduo Liao
• Zhe Zhao
• Xi Lin
• Cheng Gong
• Longcan Chen
• YingYing Yu

Advisory Board

• Prof. Jingda Deng (Xi'an Jiaotong University) (For advice of High-D hypervolume computation)
• Prof. Yifan Chen (Hong Kong Baptist University) (For advice of OR)
• Prof. Ke Shang (Shenzhen University) (For advice of approximate hypervolume-based methods)
• Prof. Han Zhao (University of Illinois at Urbana-Champaign) (For advice of fariness classification)

Correspondence

The corresponding author is Chair Prof. Qingfu Zhang (FIEEE, City University of Hong Kong).

Contact

• Xiaoyuan Zhang (xzhang2523-c@my.cityu.edu.hk)
• QQ group:
• 

Resources

For more information on methodologies, please visit our GitHub repository. Contributions and stars are welcome!

(1) A standardlized gradient based framework.

Optimization Problem Classes

Problem Class Details

For more information on problem specifics, please refer to the Readme_problem.md file.

Synthetic Problems

Here's a list of synthetic problems along with relevant research papers and project/code links:

Problem	Paper	Project/Code
ZDT	Paper	Project
DTLZ	Paper	Project
MAF	Paper	Project
WFG	Paper	Code
Fi's	Paper	Code
RE	Paper	Code

Multitask Learning Problems

This section details problems related to multitask learning, along with their corresponding papers and project/code references:

Problem	Paper	Project/Code
MO-MNISTs	PMTL	COSMOS
Fairness Classification	COSMOS	COSMOS
Federated Learning	Federal MTL	COSMOS
Synthetic (DST, FTS...)	Envelop	Project
Robotics (MO-MuJoCo...)	PGMORL	Code

Current Supported Solvers

LibMOON includes a variety of solvers tailored for different needs as img below shows. The following solvers are currently:

Gradient-based MOO Solver

• GradAggSolver
• EPOSolver
• MOO-SVGDSolver (*)
• MGDASolver
• PMGDASolver
• PMTLSolver
• HVGradSolver

(*) The original MOO-SVGD code does not include an implementation for Multitask Learning (MTL). Our release of MOO-SVGD is the first open-source code that supports MTL.

Method	Property	#Obj	Support	Published	Complexity
Aggregation fun. based, e.g. Tche,mTche,LS,PBI,...	Pareto solution with aggregations.	Any	Y
COSMOS code	Approximated exact solution.	Any	Y	ICDM 2021	$O(m n K )$
EPO code	Exact solution.	Any	Y	ICML 2020	$O(m^2 n K )$
MOO-SVGD code	A set of diverse Pareto solution.	Any	Y	NeurIPS 2021	$O(m^2 n K^2 )$
MGDA code	Arbitray Pareto solutions. Location affected highly by initialization.	Any	Y	NeurIPS 2018	$O(m^2 n K )$
PMGDA	Pareto solutions satisfying any preference.	Any	Y	Under review	$O(m^2 n K )$
PMTL code	Pareto solutions in sectors.	2. 3 is difficult.	Y	NeurIPS 2019	$O(m^2 n K^2 )$
HVGrad WangHao code	It is a gradient-based HV method.	2/3	Y	CEC 2023	$O(m^2 n K^2 )$

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.

Time complexity of gradient based methods are as follows,

1. Tier 1. GradAggSolver.
2. Tier 2. MGDASolver, EPOSolver, PMTLSolver.
3. Tier 3. GradHVSolver
4. Tier 4. MOOSVGDSolver

Important things to notice: The original code MOO-SVGD does not offer a MTL implement. Our code is the first open source code for MTL MOO-SVGD.

Pareto set learning(PSL) Solvers

LibMOON supports various models of PSL solvers, categorized as follows:

• EPO-based PSL
• Agg-based PSL
• PMGDA-based PSL
• Evolutionary-based PSL

MultiObjective Bayesian Optimization (MOBO) Solvers

• PSL-MONO
• PSL-DirHV-EI
• DirHV-EGO

ML Pretrained Methods

• HV Net, a model for handling high-volume data, available here.

Installation

Libmoon is available on PyPI. You can install it using pip:

pip install libmoon==0.1.11

• Example1: Finding a size-K (K=5) Pareto solutions with four lines of code.

from libmoon.solver.gradient.methods import EPOSolver
from libmoon.util_global.initialization import synthetic_init
from libmoon.util_global.weight_factor import uniform_pref
from libmoon.util_global import get_problem

problem = get_problem(problem_name='ZDT1')
prefs = uniform_pref(n_prob=5, n_obj=problem.n_obj, clip_eps=1e-2)
solver = EPOSolver(problem, step_size=1e-2, n_iter=1000, tol=1e-2)
res = solver.solve(x=synthetic_init(problem, prefs), prefs=prefs)

• Example2: PSL in a problem with three lines of solving problem and two lines of evaluating the results.

from libmoon.solver.psl.core_psl import AggPSLSolver
from libmoon.util_global import get_problem
from libmoon.util_global.weight_factor import uniform_pref
from torch import Tensor

problem = get_problem(problem_name='ZDT1')
# agg list [ ’ls ’, ’tche ’, ’mtche ’, ’pbi ’, ... ]
prefs = uniform_pref(n_prob=100, n_obj=problem.n_obj, clip_eps=1e-2)
solver = AggPSLSolver(problem, agg='ls')
model = solver.solve()
eval_y = problem.evaluate(model(Tensor(prefs).cuda()))

If you find our code useful, please cite our paper:

@software{libmoon_2024,
  author = {Zhang, Xiaoyuan and Zhao, Liang and Yu, Yingying and Lin, Xi and Chen, Yifan and Zhao, Han and Zhang, Qingfu},
  title = {{LibMOON: A Gradient-based MultiObjective
OptimizatioN Library in PyTorch}},
  url = {https://github.com/xzhang2523/libmoon},
  version = {2.0.4},
  year = {2024}
}