We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large, complex, and constrained spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as optimization heuristics for state space traversal and the theoretical convergence properties of Markov Chain Monte Carlo algorithms for sampling from unknown distributions. Local optimality information that is identified via a directed search by our optimization heuristic is used to adaptively update a Markov chain in a promising direction within the framework of a Multiple-Try Metropolis Markov Chain model that incorporates a generalized Metropolis-Hastings ratio. We further expand the reach of our EMCMC algorithm by harnessing the computational power afforded by massively parallel computing architecture through the integration of a parallel EA framework that guides Markov chains running in parallel.

我们开发了一种进化马尔可夫链蒙特卡洛（EMCMC）算法，用于对位于大型，复杂且受约束的空间状态空间内的空间分区进行采样。我们的算法结合了进化算法（EAs）作为状态空间遍历的优化启发式算法的优势以及马尔可夫链蒙特卡洛算法的理论收敛性，可从未知分布中进行采样。通过我们的优化启发式方法通过定向搜索确定的局部最优性信息，可在包含广义Metropolis-Hastings比的多次尝试Metropolis Markov Chain模型的框架内，以有希望的方向自适应地更新Markov Chain。