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

Project description

Moon: A Standardized/Flexible Framework for MultiObjective OptimizatioN

Moon

'' 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:

  • MOBO

  • ML pretrained methods.

    • HV net.

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