View source for Marine population dynamics problem (TACO)

This page contains a model of the [[Marine population dynamics problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. This problem is due to <bibref>Rothschild1997</bibref>. The original model using a collocation formulation can be found in the [http://www.mcs.anl.gov/~more/cops/ COPS library].
Note that you will need to include a generic [[support AMPL files|AMPL/TACO support file]], OptimalControl.mod.
To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.

=== AMPL ===

This is the source file marine_taco.mod
<source lang="AMPL">
# ----------------------------------------------------------------
# Marine population dynamics problem using AMPL and TACO
# (c) Christian Kirches, Sven Leyffer
#
# Source: COPS 3.1 collocation formulation - March 2004
#         Alexander S. Bondarenko - Summer 1998
# ----------------------------------------------------------------
include OptimalControl.mod;

var t;

param ne > 0, integer;               # number of differential equations
param nm > 0, integer;               # number of measurements
				    
param tau {1..nm};                   # times at which observations made
param tf := tau[nm];                 # ODEs defined in [0,tf]

param z {1..nm,1..ne};               # observations
var g {1..ne-1}  >= 0, <= 1;         # growth rates
var m {1..ne} >= 0, <= 1;            # mortality rates
var u {1..ne};

minimize l2error{j in 1..nm}:
	eval ( sum {s in 1..ne} (u[s] - z[j,s])^2, tau[j] );

subject to g_bounds {s in 1..ne-1}: g[s] >= 0;

subject to m_bounds {s in 1..ne}: m[s] >= 0;

subject to de_1:
	diff(u[1],t) = -(m[1]+g[1])*u[1];

subject to de_s {s in 2..ne-1}:
	diff(u[s],t) = g[s-1]*u[s-1] - (m[s]+g[s])*u[s]; 

subject to de_ne:
	diff(u[ne],t) = g[ne-1]*u[ne-1] - m[ne]*u[ne];

data marine_taco.dat;

option solver ...;

solve;

</source>

This is the file marine_taco.dat

<source lang="AMPL">
param ne := 8;
param nm := 21;

# Time measurements

param tau :=
  1    0.0
  2    0.5
  3    1.0
  4    1.5
  5    2.0
  6    2.5
  7    3.0
  8    3.5 
  9    4.0
 10    4.5
 11    5.0
 12    5.5
 13    6.0
 14    6.5
 15    7.0
 16    7.5
 17    8.0
 18    8.5
 19    9.0
 20    9.5
 21   10.0;

# Measurements

param z:
        1       2       3       4       5       6       7       8    := 
  1  20000.0 17000.0 10000.0 15000.0 12000.0  9000.0  7000.0  3000.0
  2  12445.0 15411.0 13040.0 13338.0 13484.0  8426.0  6615.0  4022.0
  3   7705.0 13074.0 14623.0 11976.0 12453.0  9272.0  6891.0  5020.0
  4   4664.0  8579.0 12434.0 12603.0 11738.0  9710.0  6821.0  5722.0
  5   2977.0  7053.0 11219.0 11340.0 13665.0  8534.0  6242.0  5695.0
  6   1769.0  5054.0 10065.0 11232.0 12112.0  9600.0  6647.0  7034.0
  7    943.0  3907.0  9473.0 10334.0 11115.0  8826.0  6842.0  7348.0
  8    581.0  2624.0  7421.0 10297.0 12427.0  8747.0  7199.0  7684.0
  9    355.0  1744.0  5369.0  7748.0 10057.0  8698.0  6542.0  7410.0
 10    223.0  1272.0  4713.0  6869.0  9564.0  8766.0  6810.0  6961.0
 11    137.0   821.0  3451.0  6050.0  8671.0  8291.0  6827.0  7525.0
 12     87.0   577.0  2649.0  5454.0  8430.0  7411.0  6423.0  8388.0
 13     49.0   337.0  2058.0  4115.0  7435.0  7627.0  6268.0  7189.0
 14     32.0   228.0  1440.0  3790.0  6474.0  6658.0  5859.0  7467.0
 15     17.0   168.0  1178.0  3087.0  6524.0  5880.0  5562.0  7144.0
 16     11.0    99.0   919.0  2596.0  5360.0  5762.0  4480.0  7256.0
 17      7.0    65.0   647.0  1873.0  4556.0  5058.0  4944.0  7538.0
 18      4.0    44.0   509.0  1571.0  4009.0  4527.0  4233.0  6649.0
 19      2.0    27.0   345.0  1227.0  3677.0  4229.0  3805.0  6378.0
 20      1.0    20.0   231.0   934.0  3197.0  3695.0  3159.0  6454.0
 21      1.0    12.0   198.0   707.0  2562.0  3163.0  3232.0  5566.0;
</source>

== Other Descriptions ==

Other descriptions of this problem are available in

* Mathematical notation at [[Marine population dynamics problem]]
* [[:Category:AMPL | AMPL]] (using a fixed discretization) at the [http://www.mcs.anl.gov/~more/cops/ COPS library]

== References ==
<biblist />
 
[[Category:AMPL/TACO]]