实际水电管理问题的两种近似随机动态规划方法

IF 4.5 3区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Luckny Zephyr, Bernard F. Lamond, Kenjy Demeester, Marco Latraverse
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引用次数: 0

摘要

我们提出了一种近似的随机动态规划方法,用于现实世界的水电管理问题,其中必须在一年的规划范围内(三天时间步长)从水库中释放水以产生电力,为铝冶炼厂提供动力。在每个时期,决策都受到放水量限制和四个水库水位等因素的制约。该方法是对我们之前关于简单近似随机动态规划的工作的回顾,其中所谓的成本或价值函数是在选择作为简单顶点的网格点上近似的。后者是通过首先将水库水位空间划分为简单图,然后迭代细分现有的简单图,直到达到所需的近似误差或达到固定数量的网格点来构建的。对于每个单纯形,近似误差由上界和下界之差给出。该方案需要将创建的简单项列表存储在内存中。在每次迭代中,搜索列表以找到近似误差最大的现有单纯形。这可能非常耗时,因为现有的简单程序的数量可能非常大。在新的提议中,我们通过将原始的简单方案与蒙特卡罗模拟相结合,避免了创建一长串简单方案,类似于强化学习中的探索策略。基于操作指标和数据包络分析的超效率概念,我们将新方法与其祖先和由工业合作伙伴开发和使用的内部软件包进行基准测试。基于蒙特卡罗简化的方案(新方法)在所有考虑的指标上都优于前一种方法。此外,我们比较了两种方法在不同网格尺寸下的计算效率。蒙特卡罗简单方法的平均CPU时间(超过15个重复)在简单方法的78%到98%之间变化。当网格大小增加到3000点以上时,简单方法变得难以处理,与蒙特卡罗版本相反,这证实了后者的优势。最后,为了进一步证明蒙特卡罗简化方法,我们通过复制原始系统的每个组件来创建一个人工系统。与新提议相反,在简单方法下,这个问题只适用于相对中等大小的网格(最多1500个点),在蒙特卡罗方法下,平均CPU时间变化在简单方法的2%到5%之间。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Two simplex-based approximate stochastic dynamic programming schemes for a real hydropower management problem

Two simplex-based approximate stochastic dynamic programming schemes for a real hydropower management problem

We present an approximate stochastic dynamic programming methodology for a real-world hydropower management problem, in which water must be released from reservoirs to produce electricity to power aluminum smelters over a planning horizon of a year (three-day time step). In each period, decisions are constrained by limits on the releases and the level of the four reservoirs, among others. The approach is a revisit of our previous work on simplicial approximate stochastic dynamic programming, in which the so-called cost-to-go or value functions are approximated over grid points chosen as vertices of simplices. The latter are constructed by first partitioning the reservoir level space into simplices and then iteratively subdividing existing simplices until a desired approximation error or a fixed number of grid points is reached. For each simplex, the approximation error is given by the difference between an upper and a lower bound. This scheme requires storing the list of created simplices in memory. In each iteration, the list is searched to find the existing simplex with the highest approximation error. This may be time-consuming as the number of existing simplices may be very large. In the new proposal, we avoid creating a long list of simplices by combining the original simplicial scheme with Monte Carlo simulation, similar to an exploration strategy in reinforcement learning. We benchmark the new method against its ancestor and an internal software package developed and used by an industrial partner, based on operational metrics and the concept of super-efficiency in data envelopment analysis. The Monte Carlo simplex-based scheme (the new method) outperforms the former method on all metrics considered. In addition, we compare the computational efficiency of both methods for different grid sizes. The average CPU time (over 15 replications) of the Monte Carlo simplicial approach varies between 78% and 98% of that of the simplicial method. As the grid sizes increase above 3,000 points, the simplicial method becomes intractable, in contrast to the Monte Carlo version, which confirms the advantage of the latter. Lastly, to further justify the Monte Carlo simplicial method, we create an artificial system by duplicating each component of the original system. In contrast to the new proposal, under the simplicial approach, the problem is tractable only for relatively modest size grids (up to 1,500 points), for which the average CPU time under the Monte Carlo approach varies between 2% and 5% of that of its simplicial counterpart.

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来源期刊
Annals of Operations Research
Annals of Operations Research 管理科学-运筹学与管理科学
CiteScore
7.90
自引率
16.70%
发文量
596
审稿时长
8.4 months
期刊介绍: The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications. In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
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