Marine population dynamics problem

Marine population dynamics problem
Algebraic states:	$n_s$
Continuous control values:	$2n_s$
Path constraints:	$4n_s$

The Marine population dynamics problem estimates growth and mortality rates of a marine species at each stage (for example ages or development stage) given the population as a function of time.( Problem taken from the COPS library)

Mathematical formulation

The problem is given by

$\begin{array}{llcl}\underset{g,m}{\min }& \sum _{j=1}^{n_s}& & ||y({\tau }_j;g,m)-z_j|{|}^2\\ \text{s.t.}& {\dot{y}}_j& =& g_{j-1}{y}_{j-1}-(m_j+g_j)y_j\mathrm{\forall }j\in 1,...,n_s,\\ & g_j,m_j& \in & [0,1].\end{array}$

where $g_j$ and $m_j$ are the growth and mortality rates at stage $j$ respectively and the initial conditions are unknown. The error between computed and observed data is minimized.

Parameters

There are $n_s$ stages and $n_m$ timepoints at which the error is minimized.

Source Code

Model descriptions are available in

• AMPL/TACO code at Marine population dynamics problem (TACO)