libmoon 0.0.1

Moon: A small step of MOO, a big step for the human

Moon: A Standardized/Flexible Framework for MultiObjective OptimizatioN

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

Moon: is a multiobjective optimization framework, from single-objective optimization to multiobjective optimization, towards a better understanding of optimization problems.

Do not release.

Main contributors: Xiaoyuan Zhang, Ji Cheng, Liao Zhang, Weiduo Liao, Xi Lin.

Corresponding to: Prof. Qingfu Zhang.

Advised by: Prof. Yifan Chen, Prof. Zhichao Lu, Prof. Ke Shang, Prof. Tao Qin.

This project has four important parts:

(1) A standardlized gradient based framework.

• Problem class. For more problem details, please also check the Readme_problem.md file. (1) For synthetic problems,

• Problem	Paper	Project/Code
  ZDT	paper	project
  DTLZ	[paper]	project
  MAF	paper	[project]
  WFG code	Real world problems.	Y
  Fi's code	Real world problems.	Y
  RE	paper	code

(2) For multitask learning problems,

Problem	Paper	Project/Code
MO-MNISTs	PMTL	COSMOS
Fairness Classification	COSMOS	COSMOS
Federated Learning

(3) For MORL problems,

Problem	Paper	Project/Code
Synthetic (DST FTS...)	Envelop	code
Robotics (MO-MuJoCo...)	PGMORL	code

• Gradient-based Solver.

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

  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.

  For running time consideration, . -1 T1.

  MOO-SVGD is the slowest one.

  EPO, MOO-SVGD, PMTL,

  Current support: GradAggSolver, MGDASolver, EPOSolver, MOOSVGDSolver, GradHVSolver, PMTLSolver.

  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.

• PSL solvers

  • EPO-based
  • Agg-based
  • Hypernetwork-based
  • ConditionalNet-based
  • Simple PSL model

• MOEA/D Current supported:

  • Vanilla MOEA/D

  • Will be released soon:

  • MOEA/D AWA.

  • MOEA/D neural AWA.

• MOBO

• ML pretrained methods.

  • HV net.