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The switch point algorithm applied to a harvesting problem.

Summer Atkins1, William W Hager2, Maia Martcheva2

  • 1Department of Mathematical Sciences, University of Alabama in Huntsville, AL 35899, USA.

Mathematical Biosciences and Engineering : MBE
|June 14, 2024
PubMed
Summary
This summary is machine-generated.

This study numerically assesses Fuller's phenomenon (chattering) in fishery harvesting models. Researchers found evidence of chattering and developed realistic, near-optimal alternative harvesting strategies with fewer control switches.

Keywords:
chatteringfish harvestingfisheries managementmarine reservessingular controlswitch point algorithm

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Area of Science:

  • * Mathematical Optimization
  • * Ecological Modeling
  • * Fisheries Science

Background:

  • * Investigates an optimal harvesting problem within a spatially explicit fishery model.
  • * Addresses challenges arising from singular arcs and Fuller's phenomenon (chattering) in optimal control.
  • * Highlights the practical need for realistic and implementable control strategies in fisheries management.

Purpose of the Study:

  • * To numerically assess chattering in optimal control problems where analytical proof is difficult.
  • * To develop alternative, suboptimal, and realistic harvesting strategies for complex control scenarios.
  • * To explore the relationship between assessing chattering and finding practical control solutions.

Main Methods:

  • * Employs an extended version of the switch point algorithm (SPA).
  • * Handles optimal control problems with specified initial and terminal state conditions.
  • * Utilizes numerical experiments to analyze the harvesting model.

Main Results:

  • * Provides strong empirical evidence that the fishery harvesting problem exhibits chattering.
  • * Identifies three alternative harvesting strategies with reduced control switches.
  • * Demonstrates that these alternative strategies are realistic and near-optimal.

Conclusions:

  • * The developed methods effectively assess chattering in optimal control problems.
  • * Alternative harvesting strategies offer practical solutions for fisheries management.
  • * The study bridges theoretical optimal control with applied fisheries management challenges.