全局优化的并行交互式随机逼近退火算法
Parallel and Interacting Stochastic Approximation Annealing algorithms for global optimisation
摘要：
提出了并行交互式随机逼近退火（PISAA）算法，该算法是一种全局优化的随机模拟方法，利用群体蒙特卡罗思想对随机逼近退火（SAA）算法进行了扩展和改进.标准的SAA算法保证收敛到全局最小值时，平方根冷却时间表是使用，但其性能的效率取决于其自我调整机制。由于SAA的机制是基于仅从单个链获得的信息，因此在复杂的优化问题中可能会出现收敛缓慢的问题。所提出的算法涉及模拟的SAA链，相互作用的方式，确保显着改善的自我调整机制和更好地探索采样空间的人口。该算法的核心思想是（i）从整个马尔可夫链群体中回收信息，以设计更准确/稳定的自调整机制，以及（ii）结合更先进的建议，如交叉操作，用于探索采样空间。PISAA在收敛性方面表现出显著的改进。PISAA可以在并行计算环境中实现。我们证明了所提出的算法具有挑战性的应用，包括贝叶斯网络学习和蛋白质折叠的良好性能。我们的数值比较表明，PISAA优于模拟退火，随机逼近退火，退火进化随机逼近蒙特卡罗，特别是在高维或崎岖的情况下。
英文摘要：
We present the parallel and interacting stochastic approximation annealing (PISAA) algorithm, a stochastic simulation procedure for global optimisation, that extends and improves the stochastic approximation annealing (SAA) by using population Monte Carlo ideas. The standard SAA algorithm guarantees convergence to the global minimum when a square-root cooling schedule is used; however the efficiency of its performance depends crucially on its self-adjusting mechanism. Because its mechanism is based on information obtained from only a single chain, SAA may present slow convergence in complex optimisation problems. The proposed algorithm involves simulating a population of SAA chains that interact each other in a manner that ensures significant improvement of the self-adjusting mechanism and better exploration of the sampling space. Central to the proposed algorithm are the ideas of (i) recycling information from the whole population of Markov chains to design a more accurate/stable self-adjusting mechanism and (ii) incorporating more advanced proposals, such as crossover operations, for the exploration of the sampling space. PISAA presents a significantly improved performance in terms of convergence. PISAA can be implemented in parallel computing environments if available. We demonstrate the good performance of the proposed algorithm on challenging applications including Bayesian network learning and protein folding. Our numerical comparisons suggest that PISAA outperforms the simulated annealing, stochastic approximation annealing, and annealing evolutionary stochastic approximation Monte Carlo especially in high dimensional or rugged scenarios.
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