转换点算法应用于收割问题。

IF 2.6 4区 工程技术 Q1 Mathematics
Summer Atkins, William W Hager, Maia Martcheva
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引用次数: 0

摘要

在本文中,我们研究了之前分析过的一个空间显式渔业模型的最优捕捞问题。表面上看,这个问题很简单,但如果参数设置到出现奇异弧线的位置,就会出现两个复杂的问题。第一个问题涉及富勒现象(或喋喋不休),在这种现象中,最优控制具有奇异弧线,该弧线不能与砰砰弧线串联,否则会在有限区域内引发无限振荡。1) 在无法用分析方法证明这种现象的情况下,我们如何用数值方法评估问题是否会颤振?第二个问题的重点是最优控制的实现。2) 当最优控制存在难以实施的区域时,我们如何找到既是次优策略又符合实际情况的替代策略?虽然前一个问题并不适用于所有最优捕捞问题,但大多数渔业管理者都应该关注后一个问题。有趣的是,对于这个具体问题,我们回答第一个问题的技术可以回答第二个问题。我们的方法涉及使用扩展版的开关点算法(SPA),该算法可处理对状态具有初始和终端条件的控制问题。在我们的数值实验中,我们获得了收割问题喋喋不休的有力经验证据,并找到了三种开关较少的替代收割策略,这些策略既易于实现,又接近最优。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The switch point algorithm applied to a harvesting problem.

In this paper, we investigate an optimal harvesting problem of a spatially explicit fishery model that was previously analyzed. On the surface, this problem looks innocent, but if parameters are set to where a singular arc occurs, two complex questions arise. The first question pertains to Fuller's phenomenon (or chattering), a phenomenon in which the optimal control possesses a singular arc that cannot be concatenated with the bang-bang arcs without prompting infinite oscillations over a finite region. 1) How do we numerically assess whether or not a problem chatters in cases when we cannot analytically prove such a phenomenon? The second question focuses on implementation of an optimal control. 2) When an optimal control has regions that are difficult to implement, how can we find alternative strategies that are both suboptimal and realistic to use? Although the former question does not apply to all optimal harvesting problems, most fishery managers should be concerned about the latter. Interestingly, for this specific problem, our techniques for answering the first question results in an answer to the the second. Our methods involve using an extended version of the switch point algorithm (SPA), which handles control problems having initial and terminal conditions on the states. In our numerical experiments, we obtain strong empirical evidence that the harvesting problem chatters, and we find three alternative harvesting strategies with fewer switches that are realistic to implement and near optimal.

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来源期刊
Mathematical Biosciences and Engineering
Mathematical Biosciences and Engineering 工程技术-数学跨学科应用
CiteScore
3.90
自引率
7.70%
发文量
586
审稿时长
>12 weeks
期刊介绍: Mathematical Biosciences and Engineering (MBE) is an interdisciplinary Open Access journal promoting cutting-edge research, technology transfer and knowledge translation about complex data and information processing. MBE publishes Research articles (long and original research); Communications (short and novel research); Expository papers; Technology Transfer and Knowledge Translation reports (description of new technologies and products); Announcements and Industrial Progress and News (announcements and even advertisement, including major conferences).
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