A Multifactorial Optimization Framework Based on Adaptive Intertask Coordinate System.

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Machine Learning

Background:

• Population-based search algorithms' effectiveness depends on their coordinate systems.
• Existing multifactorial optimization (MFO) algorithms use fixed coordinate systems, limiting efficient intertask knowledge transfer across diverse function landscapes.

Purpose of the Study:

• To propose a novel intertask knowledge transfer strategy for MFOs using an active coordinate system.
• To enhance the efficiency of knowledge transfer between different optimization tasks.

Main Methods:

• An active coordinate system is established on a common subspace of two search spaces.
• Geodesic flow is introduced to find an intermediate subspace.
• A low-dimension intermediate subspace is sampled, and its corresponding coordinate system is derived.
• Intertask trial generation involves projecting individuals onto this low-dimension subspace.

Main Results:

• The active coordinate system identifies common modalities within subspaces.
• Projection onto the low-dimension subspace reveals invariant features of function landscapes.
• The method is intrinsically regularized by focusing on major eigenvectors, reducing noise from redundant dimensions.
• Experimental results demonstrate promising performance of the proposed strategy.

Conclusions:

• The proposed active coordinate system and intertask knowledge transfer strategy significantly improve MFO performance.
• This approach effectively handles function landscapes with varying modalities, rotations, and dimensions.
• The method offers a robust solution for efficient cross-task learning in optimization.