The Lotka Volterra fishing problem is a Mixed Integer Optimal Control Problem (MIOCP). It finds a fishing strategy over 12 years to equilibrate the predator-prey fish to a sustainable steady-state value. The Lotka Volterra equations for a predator-prey system have an additional term to introduce fishing by man with constants. The differential states x0 and x1 are the biomass of prey and predator, respectively. The third differential state is the integral of the squared error to drive both the predictor and prey biomass values to 1.0. The decision to send out the fishing fleet at time t is the manipulated variable w(t). The time window is from 0 to 12.
The Lotka Volterra fishing problem seeks an optimal fishing strategy over a fixed time horizon to bring both predator and prey fish to a desired steady state. The manipulated variable is the fishing by man. The manipulated variable is either continuous or a discrete value with no fishing (0) or full fishing (1).
The mathematical equations are Ordinary Differential Equations (ODEs). The optimal binary manipulated variable chatters on and off, making the Lotka Volterra fishing problem an interesting benchmark of mixed-integer optimal control solvers.
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