On the optimal design of river fishways
L. J. Alvarez-Vasquez, J. J. Júdice, A. Martínez, C. Rodríguez, M. E. Vásquez-Méndez and M. A. Vilar
Abstract
A
river fishway is a hydraulic structure enabling fish to overcome stream
obstructions as dams in hydroelectric power plants. The main aim of
this paper is to present an application of mathematical modelling 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 problemis formulatedwithin 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.