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Nature Inspired Computation and Applications Laboratory School of Computer Science and Technology University of Science and Technology of China Pattern Recognition Lecture 7 Stochastic Methods Apr.16,2011
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Nature Inspired Computation and Applications Laboratory 主要内容 随机方法简介 模拟退火算法 演化方法 遗传算法 遗传规划 演化规划 演化策略
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Nature Inspired Computation and Applications Laboratory 随机方法简介 为什么需要随机算法? 之前讲到的方法大都是首先假设一个单参数或多参数的模型, 根据训练样本来估计参数取值(学习问题转化为了优化问 题)。 当优化问题极为复杂时,既不存在解析解,又无法用传统的 优化 方法加以解决,则只能求助于随机(优化)算法。
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Nature Inspired Computation and Applications Laboratory 随机方法简介 二次型问题: 给定多个变量 ,每个变量的数值都取 1 或者 -1 确定 N 的合适取值,使得下面的代价函数(能量函 数)最小: 二次型优化问题通常很难得到最优解 直接求解:是 NP 难问题 穷举搜索:不现实 “贪心”搜索:容易陷入局部能量极小处或者不收敛 N i s i , , 1 , i s N j i j i ij s s w E 1 , 2 1
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Nature Inspired Computation and Applications Laboratory 随机方法简介 解决办法:寻找其他搜索方法 搜索算法 盲目搜索:搜索过程中获取的中间信息不用以改进控 制策略, eg :深度 / 广度优先、代价优先 …… 启发式搜索:使用搜索过程获得的信息改进控制策略, eg :爬山法、模拟退火算法 ……
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Nature Inspired Computation and Applications Laboratory 模拟退火算法 起源 —— 物理退火: 过程:加热;等温;降温。 退火操作相当有效。
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Nature Inspired Computation and Applications Laboratory 模拟退火算法 系统位于一个特定构型 具有能量 的概 率: 其中分子部分称为 Boltzmann 因子, Z(T) 一个归一化常数,即“配分函数”: E ) ( ) ( / T Z e P T E T E e T Z / ) (
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Nature Inspired Computation and Applications Laboratory 模拟退火算法 Boltzmann 因子的指数项来源: 随着能量的上升,允许构型的数目以指数减少
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This note was uploaded on 06/16/2011 for the course CS 1256 taught by Professor Tangke during the Spring '10 term at USTC.