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Comparing dynamic decision networks to dynamic programming.

机译：将动态决策网络与动态规划进行比较。

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摘要

As the technology used in solving decision problems has advanced, so has the sophistication of methods for solving these problems. Although much research has been devoted to developing methods to assist decision makers analyze decisions, few approaches have been proposed for complex dynamic decision problems. For most of the approaches that have been proposed, the determination of optimal solutions is computationally intractable for problems with just a few decisions and random variables.; The focus of this research is on dynamic decision making. Specifically, two approaches for solving dynamic decisions are investigated: Stochastic Dynamic Programming (DP) and Dynamic Decision Networks (DDNs). Unfortunately, DP becomes intractable for even moderately sized problems. Even though DDNs can efficiently solve much larger problems than DP, their usefulness is questionable because of the limited research performed on them.; The objective of this study is to explore the use of DDNs by addressing how well DDNs approximate DP. DP was selected as the technique to compare to DDNs because it is thought of as the gold standard in decision making optimization. To accomplish this objective, a theoretical approach for comparing the optimal policies of DDNs and DP was developed. Then, this approach was utilized to determine how good DDNs are under different conditions. Computation times were also compared to determine if the time the DDN saves was worth its inaccuracy.; A significant finding of this research concerned how close the expected values of the DDN optimal policies were to those of DP in the cases examined. It was shown that sometimes the DDNs' optimal policies disagreed with the DP optimal policies. However, the expected values of the policies selected by the DDN were always quite close to those of DP.; Although DDNs were exponentially faster than DP, there was a cost for the time savings. An increase in the values of some of the parameters investigated improved the DDN's computational time advantage but reduced its ability to approximate DP optimal policies. The conditions under which the DDN saves the most computation time and provides accurate approximations are fully described.
机译：随着用于解决决策问题的技术的发展，解决这些问题的方法也日趋成熟。尽管已经进行了大量研究以开发用于辅助决策者分析决策的方法，但是针对复杂的动态决策问题却很少提出方法。对于大多数已提出的方法，对于只有几个决策和随机变量的问题，确定最优解在计算上是棘手的。这项研究的重点是动态决策。具体来说，研究了解决动态决策的两种方法：随机动态规划（DP）和动态决策网络（DDN）。不幸的是，即使对于中等大小的问题，DP也变得棘手。尽管DDN可以有效解决比DP大得多的问题，但由于对DDN的研究有限，其实用性值得怀疑。本研究的目的是通过解决DDN与DP的近似程度来探索DDN的使用。选择DP作为与DDN进行比较的技术，因为它被认为是决策优化中的黄金标准。为了实现此目标，开发了一种用于比较DDN和DP最佳策略的理论方法。然后，利用这种方法来确定不同条件下DDN的质量。还对计算时间进行了比较，以确定DDN节省的时间是否值得其准确性。这项研究的重要发现涉及在检查的案例中DDN最佳策略的预期值与DP的预期值有多接近。结果表明，DDN的最佳策略有时与DP最佳策略不一致。但是，DDN选择的策略的期望值始终与DP的期望值非常接近。尽管DDN的速度比DP快几倍，但节省时间却要付出一定的代价。研究的某些参数值的增加改善了DDN的计算时间优势，但降低了其逼近DP最佳策略的能力。充分描述了DDN节省最多计算时间并提供准确近似值的条件。

著录项

  • 作者

    Kobylski, Gerald Charles.;

  • 作者单位

    Stevens Institute of Technology.;

  • 授予单位 Stevens Institute of Technology.;
  • 学科 Operations Research.; Mathematics.; Engineering General.
  • 学位 Ph.D.
  • 年度 2005
  • 页码 285 p.
  • 总页数 285
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 运筹学;数学;工程基础科学;
  • 关键词

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