Parametric Pareto Set Learning (PPSL)

Official implementation of the paper "Parametric Pareto Set Learning: Amortizing Multi-Objective Optimization with Parameters", published in IEEE Transactions on Evolutionary Computation.

🎯 Overview

PPSL addresses the challenge of solving an infinite number of multi-objective optimization problems where optimal solutions must adapt to varying parameters. Unlike traditional methods that generate only finite solution sets, PPSL learns a unified mapping from parameters to the entire Pareto set, enabling real-time inference of optimal solutions for any parameter setting.

Key Features

• 🚀 Amortized Optimization: Shifts computational burden from online solving to offline training
• 🧠 Hypernetwork Architecture: Generates PS model parameters conditioned on input parameters
• ⚡ Low-Rank Adaptation (LoRA): Achieves computational efficiency and scalability
• 🎯 Continuous Pareto Set Learning: Captures the entire Pareto set structure across parameter space
• 🔄 Real-time Inference: Millisecond-level solution generation after training

Applications

1. Dynamic Multiobjective Optimization Problems (DMOPs): Where objectives change over time
2. Multiobjective Optimization with Shared Components: Where design variables must share identical settings for manufacturing efficiency

🛠️ Installation

Prerequisites

• Python ≥ 3.8
• PyTorch ≥ 1.12 (GPU supported; CUDA optional)

Setup

1. Clone the repository:

git clone (available upon acceptance)
cd ppsl

2. Install dependencies:

pip install -r requirements.txt

Required Packages

torch>=1.12.0
numpy>=1.21.0
pymoo>=0.6.0
matplotlib>=3.5.0
scipy>=1.7.0

🚀 Quick Start

Interactive Demo

Explore PPSL through our Jupyter notebook:

jupyter notebook example.ipynb

📁 Repository Structure

ppsl/
├── experiment_dmop.py      # Experiments for Dynamic MOPs
├── experiment_mopsc.py     # Experiments for MOPs with Shared Components
├── trainer.py              # Training methods (fixed/random/black-box)
├── model.py                # Hypernetwork and PS models (LoRA/non-LoRA)
├── example.ipynb           # Interactive demonstration
├── problems/               # Problem definitions
│   ├── problem_dyn.py      # Dynamic MOP benchmarks
│   └── problem_f_re.py     # RE problems
├── results/                # Experimental results
└── requirements.txt        # Package dependencies

🎓 Citation

If you find this work useful, please cite our paper:

@article{ppsl2024,
  title={Parametric Pareto Set Learning: Amortizing Multi-Objective Optimization with Parameters},
  author={Cheng, Ji and Lin, Xi and Xue, Bo and Zhang, Qingfu},
  journal={IEEE Transactions on Evolutionary Computation}, 
  year={2025},
  volume={},
  number={},
  pages={1-1},
}

🙏 Acknowledgments

• Built on PyMOO framework
• Inspired by recent advances in amortized optimization and Pareto set learning