A Theoretical Analysis of Analogy-Based Evolutionary Transfer Optimization

2025-03-27

AI Summary

Evolutionary Transfer Optimization (ETO) has long suffered from a theory–practice gap, particularly lacking rigorous theoretical foundations for the core mechanism of “similarity-driven knowledge transfer.” Method: This paper establishes the first formal theoretical framework for analogy-driven ETO, systematically mapping analogical reasoning sub-processes to ETO’s three fundamental challenges—source task selection, knowledge mapping, and target adaptation. It introduces two key theorems: unconditional non-negativity and conditional positive performance gain, rigorously proving that analogical transfer guarantees no performance degradation and ensures strict improvement under similarity conditions. Building upon the No Free Lunch theorem, it further characterizes the conditional superiority of analogy-driven ETO. Contribution/Results: The work provides the first verifiable theoretical guarantees and actionable design principles for similarity-driven ETO algorithms, bridging foundational theory and practical algorithmic development.

Technology Category

• Cognitive Modeling & Cognitive Systems: Analogy
• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Evolutionary transfer optimization (ETO) has been gaining popularity in research over the years due to its outstanding knowledge transfer ability to address various challenges in optimization. However, a pressing issue in this field is that the invention of new ETO algorithms has far outpaced the development of fundamental theories needed to clearly understand the key factors contributing to the success of these algorithms for effective generalization. In response to this challenge, this study aims to establish theoretical foundations for analogy-based ETO, specifically to support various algorithms that frequently reference a key concept known as similarity. First, we introduce analogical reasoning and link its subprocesses to three key issues in ETO. Then, we develop theories for analogy-based knowledge transfer, rooted in the principles that underlie the subprocesses. Afterwards, we present two theorems related to the performance gain of analogy-based knowledge transfer, namely unconditionally nonnegative performance gain and conditionally positive performance gain, to theoretically demonstrate the effectiveness of various analogy-based ETO methods. Last but not least, we offer a novel insight into analogy-based ETO that interprets its conditional superiority over traditional evolutionary optimization through the lens of the no free lunch theorem for optimization.

Problem

• Establish theoretical foundations for analogy-based ETO
• Link analogical reasoning to key issues in ETO
• Demonstrate performance gain of analogy-based knowledge transfer

Innovation

• Establishes theoretical foundations for analogy-based ETO
• Develops theories for analogy-based knowledge transfer
• Presents theorems on performance gain in ETO