A Mixed Optimal Control Approach for Upstream Fish Migration

Abstract

This paper proposes a simple mathematical model forupstream fish migration along rivers. The model describes the fish migration along a river based on a mixed optimal control approach having swimming velocity, school size, and stopping time of migration as control variables. The optimization problem reduces to a variational inequality. Its explicit "viscosity" solution is presented with the dependence of the fish migration on river environment. To prove uniqueness of the solution to the variational inequality requires a constructive argument not based on the conventional theorems. A novel finite difference scheme for solving the variational inequality is also proposed with its convergence results. An application example of the model discusses the upstream migration of Plecoglossus altivelis (Ayu) in Japan, which evaluates the dependence of the fish migration on the habitat quality and provides recommendations for managing river environment. This is an interdisciplinary research between environmental and mathematical fields.

A simplified stochastic optimization model for logistic dynamics with control-dependent carrying capacity

“…Proposition 2.3 is a consequence of Propositions 2.1 and 2.2. Uniqueness of viscosity solutions to HJB equations is not a trivial issue even for seemingly simple problems [6,67,69].…”

Effects of water currents on fish migration through a Feynman-type path integral approach under $$\sqrt{8/3}$$ Liouville-like quantum gravity surfaces

“…On the other hand, adult fishes move to the spawning area and then return to the feeding ground. During migrations fishes travel a long distance, and furthermore, migrations of some adult fishes such as Plecoglossus altivelis (Ayu), Oncorhynchus masou (Yamame) and Poecilia reticulata (guppy) toward breeding grounds are against the water current (Yoshioka 2017;Yoshioka and Yaegashi 2018;Yoshioka et al 2019) and fish like larger brown trout initiates the downstream migration for spawning (Jonsson and Jonsson 2002). As availability of food at a particular destination is probabilistic, a fish has to use all directions irrespective of water currents.…”

A preface to the special issue of optimization and engineering dedicated to SDEWES 2019 conference

“…Optimized local energy supply for efficient and clean Environment systems has been the topic of study for a growing number of papers that not only analyse the environmental impact of different technologies, but also analyse the economic viability of such technologies (Mikulčić et al 2016). Some of these studies include a multi-objective optimization of a syngas powered internal combustion engine to lower nitrogen oxide emissions (Costa et al 2020), dynamic modelling of the biomass gasification process in a fixed bed reactor (Cerinski et al 2020), nonlinear modelling of transient operating conditions for a gas turbines (Pires et al 2018), numerical modelling of a gas cyclone for particle separation (Mikulčić et al 2014), multi-objective optimization of the municipal solid waste (MSW) management system (Hrabec et al 2018), optimal ventilation system under outdoor air quality conditions (Nam et al 2020), upstream fish migration along rivers (Yoshioka et al 2018), sustainability of bird population management policy using a stochastic differential equation model (Yaegashi et al 2018).…”