Evolutionary algorithms (EAs) serve as powerful black-box optimizers inspired by biological evolution. However, most existing EAs predominantly focus on heuristic operators such as crossover and mutation, while usually overlooking underlying physical interpretability such as statistical mechanics and thermosdynamics. This theoretical void limits the principled understanding of algorithmic dynamics, hindering the systematic design of evolutionary search beyond ad-hoc heuristics. To bridge this gap, we first point out that evolutionary optimization can be conceptually reframed as a physical phase transition process. Building on this perspective, we establish the theoretical grounds by modeling the optimization dynamics as a Wasserstein gradient flow of free energy. Consequently, a robust and interpretable solver named Wasserstein Evolution (WE) is proposed. WE mathematically frames the trade-off between exploration and exploitation as a competition between potential gradient forces and entropic forces. This formulation guarantees convergence to the Boltzmann distribution, thereby minimizing free energy and maximizing entropy, which promotes highly diverse solutions. Extensive experiments on complex multimodal and physical potential functions demonstrate that WE achieves superior diversity and stability compared to established baselines.

翻译：进化算法（EAs）作为受生物进化启发的强大黑盒优化器。然而，现有大多数进化算法主要关注交叉和变异等启发式算子，而通常忽视了潜在的物理可解释性，如统计力学和热力学。这一理论空白限制了对算法动态的原理性理解，阻碍了超越临时启发式的进化搜索的系统性设计。为弥合这一差距，我们首先指出，进化优化在概念上可被重新构建为一个物理相变过程。基于这一视角，我们通过将优化动态建模为自由能的Wasserstein梯度流，建立了理论基础。由此，提出了一种稳健且可解释的求解器，命名为Wasserstein Evolution（WE）。WE从数学上将探索与利用之间的权衡表述为势梯度力与熵力之间的竞争。该公式保证了向玻尔兹曼分布的收敛，从而最小化自由能并最大化熵，这促进了高度多样化的解。在复杂多模态和物理势函数上的大量实验表明，与现有基线相比，WE实现了更优的多样性和稳定性。