动态规划的正向递推方法

张钊,裴燕玲,张仁宝

中国工程科学 ›› 2005, Vol. 7 ›› Issue (2) : 62 -65.

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中国工程科学 ›› 2005, Vol. 7 ›› Issue (2) : 62 -65.
学术论文

动态规划的正向递推方法

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The Forward Recurrent Method for Dynamic Programming

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摘要

动态规划求最优解是一个反向递推的求解过程,以实例为依据,用正向递推的方法求解动态规划的最优值,并推出动态规划的基本方程和密尔顿-雅可比方程,是对动态规划求最优解方法的探讨。利用动态规划的正向递推方法,在应用中可以大大减少计算量,扩大了它的应用范围。

Abstract

Backward recurrent method is usually adopted in seeking optimal solution by dynamic programming. A forward recurrent method to find optimal solution by dynamic programming is presented on the basis of an instance. The fundamental equation of dynamic programming and Millton-Jacobi's equation are also derived. It's an exploratory study on optimal solution of dynamic programming. An amount of work is reduced in calculating by using forward recurrent method, while applied range of the method is expanded.

关键词

动态规划 / 多级决策 / 泛函 / 最优值

Key words

dynamic programming / multi-level decision / functional equation / optimal solution

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张钊,裴燕玲,张仁宝 动态规划的正向递推方法[J]. 中国工程科学, 2005, 7(2): 62-65 DOI:

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