Wasserstein Evolution : Evolutionary Optimization as Phase Transition

This paper introduces a novel framework linking evolutionary computation to statistical physics by formulating optimization as a statistical phase transition. We propose Wasserstein Evolution (WE), an algorithm based on the Wasserstein gradient flow of a free energy functional, translating the physical competition between exploitative potential gradient forces and explorative entropic forces into an adaptive search mechanism. Theoretical analysis confirms WE's convergence to the Boltzmann distribution, ensuring a principled performance-diversity balance.Experiments compare WE against five established algorithms, including GA, DE, CMA-ES, JADE, and SaDE, on benchmark and physical potential functions. Results demonstrate that WE consistently achieves the lowest free energy and maintains the highest entropy, excelling in both solution quality and diversity preservation. Additional invariance tests using transformed Schwefel 2.22 functions verify that WE possesses translation, scale, and rotation invariance, proving its robustness and intrinsic alignment with the problem's geometry rather than its coordinate representation.Thus, this work delivers not only an effective and robust optimizer but also a new theoretical paradigm for understanding population-based search through statistical physics, viewing convergence as a disorder-to-order phase transition and opening new avenues for designing intelligent optimization methods.