Abstract
A river fishway is a hydraulic structure enabling fish to overcome stream obstructions such as dams in hydroelectric power plants. The main aim of this paper is to present an application of mathematical modeling and optimal control theory to an ecological engineering problem related to preserve and enhance natural stocks of fish migrating between saltwater and freshwater. Particularly, we improve the optimal shape design of a fishway. This problem is formulated within the framework of the optimal control of partial differential equations, approximated by a discrete optimization problem, and solved by using both a gradient method (a Spectral Projected-Gradient algorithm) and a derivative-free method (the Nelder-Mead algorithm). Finally, numerical results are compared and analyzed for a standard real-world situation.
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