Marine population dynamics problem (TACO) - Revision history

JonasSchulze: Text replacement - "\(.*)\<\/bibref\>" to ""

2015-12-30T20:32:09Z

Text replacement - "\<bibref\>(.*)\<\/bibref\>" to "<bib id="$1" />"

← Older revision		Revision as of 20:32, 30 December 2015
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	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].		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 <bib id="Rothschild1997" />. 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.		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.		To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.

JonasSchulze: Text replacement - "" to ""

2015-12-30T20:28:25Z

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	== References ==		== References ==
	<~~bibreferences~~/>		<biblist />

	[[Category:AMPL/TACO]]		[[Category:AMPL/TACO]]

Ckirches: /* AMPL */

2011-09-29T20:55:25Z

AMPL

← Older revision		Revision as of 20:55, 29 September 2011
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	diff(u[ne],t) = g[ne-1]u[ne-1] - m[ne]u[ne];		diff(u[ne],t) = g[ne-1]u[ne-1] - m[ne]u[ne];

	data ~~cops_marine~~.dat;		data marine_taco.dat;

	option solver ...;		option solver ...;
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	</source>		</source>

	This is the file ~~cops_marine~~.dat		This is the file marine_taco.dat

	<source lang="AMPL">		<source lang="AMPL">

Ckirches: Reference for marine pop problem (TACO)

2011-09-29T20:54:16Z

Reference for marine pop problem (TACO)

← Older revision		Revision as of 20:54, 29 September 2011
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	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. The original model using a collocation formulation can be found in the [http://www.mcs.anl.gov/~more/cops/ COPS library].		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.		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.		To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.
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	param z {1..nm,1..ne}; # observations		param z {1..nm,1..ne}; # observations
	var g {1..ne-1} >= 0, <= 1; # growth rates		var g {1..ne-1} >= 0, <= 1; # growth rates
	var m {1..ne} >= 0, <= 1; # mortality rates		var m {1..ne} >= 0, <= 1; # mortality rates
	var u {1..ne};		var u {1..ne};

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

			== References ==
			<bibreferences/>

	[[Category:AMPL/TACO]]		[[Category:AMPL/TACO]]

Ckirches: Marine population dynamics problem (TACO)

2011-09-29T19:08:16Z

Marine population dynamics problem (TACO)

New page

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. 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 cops_marine.dat;

option solver ...;

solve;

</source>

This is the file cops_marine.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]

[[Category:AMPL/TACO]]