View source for Lotka Volterra fishing problem (JuMP)

This is an implementation of the [[Lotka Volterra fishing problem]] using JuMP.
The problem was discretized and the ODEs are solved using the explicit Euler method.
Although not necessary in JuMP the code was divided into three parts (following AMPL) - model file, data file and run file. The run file calls the other files and performs additional tasks such as printing results.

The control function <math> u(t) </math> was relaxed to the domain <math> [0,1] </math>.

Model file ("lotka_mod.jl"):
<source lang="AMPL">
#JuMP implementation of Lotka-Volterra fishing example using collocation
#mod file

#declaring the model
m = Model()

#defining variables
@defVar(m, x[ii=1:n_x, tt=1:N])
@defVar(m, L_control <= u[tt=1:N] <= U_control)

#set objective function
@setObjective(m, Min, x[3,N])

#setting constraints
#starting values
@addConstraint(m, starting_value[ii=1:n_x], x[ii,1] == x_start[ii])

#ODE - solved with explicit euler method (i.e. x_k+1 = x_k + stepsize * f(x_k, t_k))
@addConstraint(m, ODE[ii=1:n_x, tt=1:N-1],  x[ii,tt+1] - x[ii,tt] - step_size * ode_rhs(x[:,tt], u[tt])[ii]  == 0)
</source>

Data file ("lotka_dat.jl"):
<source lang="AMPL">
#JuMP implementation of Lotka-Volterra fishing example using collocation
#dat file

#general parameters
c0 = 0.4;
c1 = 0.2;

#number of states
n_x = 3;

##discretization
#number of shooting intervals / discretization points
N = 300;
#starting / end time
t_start = 0;
t_end = 12;
#time discretization
time = linspace(t_start,t_end, N+1);
step_size = (t_end - t_start)/N;

#starting value
x_start = [0.5, 0.7, 0];

#bounds for control
L_control = 0
U_control = 1;


##right hand side of ODE
function ode_rhs(state, control)
#give in form f1, f2, f3,...
 state[1] - state[1] * state[2] - c0 * state[1] * control,
-state[2] + state[1] * state[2] - c1 * state[2] * control,
(state[1]-1) * (state[1]-1) + (state[2]-1) * (state[2]-1)
end
</source>

Run file ("lotka_run.jl"):
<source lang="AMPL">
#JuMP implementation of Lotka-Volterra fishing example using collocation
#run file

using JuMP;
using Ipopt;


println("----------------------------------------------------")
println("Time used for data")
@time include("lotka_dat.jl")
println("----------------------------------------------------")
println("Time used for modeling")
@time include("lotka_mod.jl")
println("----------------------------------------------------")
println("Time used for solving")
@time solve(m);

println("----------------------------------------------------")
println("----------------------------------------------------")


println("Optimal objective value is: ", getObjectiveValue(m))
println("Optimal Solution is: \n", getValue(x), getValue(u))
</source>

[[Category: Julia/JuMP]]