Pareto optimization with small data by learning across common objective spaces.

Area of Science:

• Optimization
• Machine Learning
• Computational Science

Background:

• Multi-objective optimization faces challenges in covering the Pareto front (PF) due to exponential scaling with dimensionality.
• Expensive optimization domains limit available evaluation data, hindering accurate PF representation.
• Pareto estimation (PE) uses inverse machine learning but suffers from small training datasets.

Purpose of the Study:

• To address the small data challenge in Pareto estimation (PE) for multi-objective optimization.
• To propose and evaluate a novel multi-source inverse transfer learning method for PE.
• To enhance the accuracy and efficiency of approximating the Pareto set in decision space.

Main Methods:

• Developed a multi-source inverse transfer learning framework for Pareto estimation (PE).
• Leveraged experiential source tasks to augment PE in target optimization tasks.
• Utilized common objective spaces to enable information transfer between heterogeneous source-target pairs.

Main Results:

• Demonstrated significant gains in predictive accuracy for inverse models.
• Showcased improved Pareto front (PF) approximation capacity in Pareto set learning.
• Validated the approach on benchmark functions and high-fidelity composite materials manufacturing simulations.

Conclusions:

• Multi-source inverse transfer learning effectively alleviates small data challenges in Pareto estimation (PE).
• The proposed method enhances the predictive accuracy and PF approximation capabilities.
• Enables feasible, accurate inverse models for on-demand human-machine interaction in multi-objective decision-making.