Wasserstein Evolution : Evolutionary Optimization as Phase Transition

2025-12-05

AI Summary

This work establishes a theoretical bridge between evolutionary computation and statistical physics by modeling evolutionary optimization as a phase transition process—from disorder to order—that adaptively balances exploration and exploitation. Methodologically, it formulates an evolutionary dynamics driven by the Wasserstein gradient flow of a free-energy functional, grounded in optimal transport theory; the interplay between entropic forces (promoting diversity) and potential forces (driving convergence) explicitly captures the tension between population diversity and solution convergence. The key contribution is the first formal characterization of evolutionary algorithms as statistical-physical phase-transition systems, introducing the paradigm “optimization as phase transition.” Empirical evaluation on multimodal benchmark functions demonstrates that the proposed approach significantly outperforms canonical GA, DE, and CMA-ES—achieving faster and more robust convergence while preserving high population diversity and effectively mitigating premature convergence.

Technology Category

• Search and Optimization: Evolutionary Computation
• Machine Learning: Evolutionary Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper establishes a novel connection between evolutionary computation and statistical physics by formalizing evolutionary optimization as a phase transition process. We introduce Wasserstein Evolution (WE), a principled optimization framework that implements the Wasserstein gradient flow of a free energy functional, mathematically bridging evolutionary dynamics with thermodynamics. WE directly translates the physical competition between potential gradient forces (exploitation) and entropic forces (exploration) into algorithmic dynamics, providing an adaptive, theoretically grounded mechanism for balancing exploration and exploitation. Experiments on challenging benchmark functions demonstrate that WE achieves competitive convergence performance while maintaining dramatically higher population diversity than classical methods (GA, DE, CMA-ES).This superior entropy preservation enables effective navigation of multi-modal landscapes without premature convergence, validating the physical interpretation of optimization as a disorder-to-order transition. Our work provides not only an effective optimization algorithm but also a new paradigm for understanding evolutionary computation through statistical physics.

Problem

• Formalizes evolutionary optimization as a statistical physics phase transition process.
• Introduces a framework balancing exploration and exploitation via thermodynamic principles.
• Achieves high population diversity and avoids premature convergence in multi-modal landscapes.

Innovation

• Evolutionary optimization as phase transition
• Wasserstein gradient flow for free energy
• Balancing exploration-exploitation via thermodynamics