基于Metropolis准则的自适应随机搜索算法研究

Research on Adaptive Random Search Algorithm Based on Metropolis Criterion

随机搜索算法是一种原理极其简单的优化方法,利用搜索方向与步长的随机特性,算法能够逐渐向全局最优解靠近,最终达到优化的目的。但正是因为其搜索的随机性,导致了算法优化效率特别低,计算领域极其有限。针对以上问题,提出了自适应最优化的搜索策略,利用当前最优解的位置及其演化路径,不断调整算法优化搜索的方向与步长,提高搜索的效率,同时引入模拟退火算法中的Metropolis接受准则,使改进后的算法不仅能够接受优化解而且能够接受恶化解,提高算法的全局搜索能力。采用MATLAB编程软件,通过对两个经典测试函数的模拟及其与传统随机算法的对比分析,优化计算的结果证明了本文所提算法具有高效的优化计算能力,可以进一步应用于工程领域的优化设计。

Random search algorithm is an extremely simple optimization method, which has a poor effectiveness and limited computing range. To solve these problems, we put forward a search strategy of adaptive optimization, using the location of the current optimal point and the evolutionary path of current iteration to adjust the search direction and step length of algorithm constantly during optimization search, improving the searching efficiency. At the same time we used the rule of Metropolis in the simulated annealing algorithm, to improve the global search ability by both optimal solutions and deteriorative solutions. Then we used the MATLAB to simulate and comparatively analyzed it with traditional random algorithm. The results showed that the proposed algorithm in this paper has efficient optimization computing ability, and can be applied to optimization design in the field of engineering.