论文标题
随机优化：Glauber动力学与随机蜂窝自动机
Stochastic optimization: Glauber dynamics versus stochastic cellular automata
论文作者
论文摘要
我们在本文中讨论的主题涉及通过基于（单位点）Glauber动力学和随机细胞自动机（SCA）的模拟退火算法的应用来最小化哈密顿函数。提出了一些严格的结果，以证明对特定类型的SCA的模拟退火的应用是合理的。 After that, we compare the SCA algorithm and its variation, namely the $\varepsilon$-SCA algorithm, studied in this paper with the Glauber dynamics by analyzing their accuracy in obtaining optimal solutions for the max-cut problem on Erdős-Rényi random graphs, the traveling salesman problem (TSP), and the minimization of Gaussian and Bernoulli spin glass哈密顿人。我们观察到，在某些特殊情况下，SCA的性能要比Glauber动力学好，而在所有情况下，$ \ varepsilon $ -SCA的性能最高。
The topic we address in this paper concerns the minimization of a Hamiltonian function for an Ising model through the application of simulated annealing algorithms based on (single-site) Glauber dynamics and stochastic cellular automata (SCA). Some rigorous results are presented in order to justify the application of simulated annealing for a particular kind of SCA. After that, we compare the SCA algorithm and its variation, namely the $\varepsilon$-SCA algorithm, studied in this paper with the Glauber dynamics by analyzing their accuracy in obtaining optimal solutions for the max-cut problem on Erdős-Rényi random graphs, the traveling salesman problem (TSP), and the minimization of Gaussian and Bernoulli spin glass Hamiltonians. We observed that the SCA performed better than the Glauber dynamics in some special cases, while the $\varepsilon$-SCA showed the highest performance in all scenarios.
