Lotka Volterra fishing problem (AMPL) - Revision history

SebastianSager: cosmetics

2009-07-31T10:16:54Z

cosmetics

← Older revision		Revision as of 10:16, 31 July 2009
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	== Results ==		== Results ==

			=== Bonmin ===
	The solution calculated by Bonmin (subversion revision number 1453, default settings, 3 GHz, Linux 2.6.28-13-generic, with ASL(20081205)) has an objective function value of <MATH>\Phi= 1.34434</MATH>, while the optimum of the relaxation is <MATH>\Phi=1.3423368</MATH>. Bonmin needs 35301 iterations and 2741 nodes (4899.97 seconds). Strong branching is done 81 times (1859 iterations), with 0 fathomed nodes and 0 fixed variables. The intervals on the equidistant grid on which <MATH>w(t) = 1</MATH> holds, counting from 0 to 99, are 20-32, 34, 36, 38, 40, 44, 53.		The solution calculated by Bonmin (subversion revision number 1453, default settings, 3 GHz, Linux 2.6.28-13-generic, with ASL(20081205)) has an objective function value of <MATH>\Phi= 1.34434</MATH>, while the optimum of the relaxation is <MATH>\Phi=1.3423368</MATH>. Bonmin needs 35301 iterations and 2741 nodes (4899.97 seconds). Strong branching is done 81 times (1859 iterations), with 0 fathomed nodes and 0 fixed variables. The intervals on the equidistant grid on which <MATH>w(t) = 1</MATH> holds, counting from 0 to 99, are 20-32, 34, 36, 38, 40, 44, 53.

	A ~~faster~~ solution obtained by Knitro version 6.0 under NEOS server environment ~~and~~ tested by Henry Kar Ming Chan. The standard defaults ~~are~~ used except the strong branching strategies and the integrality gap tolerances without parallel features. Final objective value is 1.34521362. Number of nodes processed is 508 and number of subproblems solved is 671. Total program CPU time is 2823.85 seconds with time spent in evaluations for 684.37 seconds. The intervals on the equidistant grid on which <MATH>w(t) = 1</MATH> holds, counting from 0 to 99, are 20-32, 34, 36-37, 42, 44, 52.		=== Knitro ===
			A solution obtained by Knitro version 6.0 under NEOS server environment was tested by [[User:Henry_Chan \| Henry Kar Ming Chan]]. The standard defaults were used except the strong branching strategies and the integrality gap tolerances without parallel features. Final objective value is 1.34521362. Number of nodes processed is 508 and number of subproblems solved is 671. Total program CPU time is 2823.85 seconds with time spent in evaluations for 684.37 seconds. The intervals on the equidistant grid on which <MATH>w(t) = 1</MATH> holds, counting from 0 to 99, are 20-32, 34, 36-37, 42, 44, 52.

	[[Category:AMPL]]		[[Category:AMPL]]

Henry Chan: Knitro solution for this benchmark tested by Henry Kar Ming Chan

2009-07-17T04:14:13Z

Knitro solution for this benchmark tested by Henry Kar Ming Chan

← Older revision		Revision as of 04:14, 17 July 2009
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	The solution calculated by Bonmin (subversion revision number 1453, default settings, 3 GHz, Linux 2.6.28-13-generic, with ASL(20081205)) has an objective function value of <MATH>\Phi= 1.34434</MATH>, while the optimum of the relaxation is <MATH>\Phi=1.3423368</MATH>. Bonmin needs 35301 iterations and 2741 nodes (4899.97 seconds). Strong branching is done 81 times (1859 iterations), with 0 fathomed nodes and 0 fixed variables. The intervals on the equidistant grid on which <MATH>w(t) = 1</MATH> holds, counting from 0 to 99, are 20-32, 34, 36, 38, 40, 44, 53.		The solution calculated by Bonmin (subversion revision number 1453, default settings, 3 GHz, Linux 2.6.28-13-generic, with ASL(20081205)) has an objective function value of <MATH>\Phi= 1.34434</MATH>, while the optimum of the relaxation is <MATH>\Phi=1.3423368</MATH>. Bonmin needs 35301 iterations and 2741 nodes (4899.97 seconds). Strong branching is done 81 times (1859 iterations), with 0 fathomed nodes and 0 fixed variables. The intervals on the equidistant grid on which <MATH>w(t) = 1</MATH> holds, counting from 0 to 99, are 20-32, 34, 36, 38, 40, 44, 53.

			A faster solution obtained by Knitro version 6.0 under NEOS server environment and tested by Henry Kar Ming Chan. The standard defaults are used except the strong branching strategies and the integrality gap tolerances without parallel features. Final objective value is 1.34521362. Number of nodes processed is 508 and number of subproblems solved is 671. Total program CPU time is 2823.85 seconds with time spent in evaluations for 684.37 seconds. The intervals on the equidistant grid on which <MATH>w(t) = 1</MATH> holds, counting from 0 to 99, are 20-32, 34, 36-37, 42, 44, 52.

	[[Category:AMPL]]		[[Category:AMPL]]

SebastianSager at 15:31, 9 July 2009

2009-07-09T15:31:57Z

← Older revision		Revision as of 15:31, 9 July 2009
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	This page contains a discretized version of the MIOCP [[Lotka Volterra fishing problem]] in [http://www.ampl.org AMPL] format. You should be aware of the comments regarding discretization made on the [[:Category:AMPL\|AMPL overview]] page. Note that you will need to include two generic [[support AMPL files]].		This page contains a discretized version of the MIOCP [[Lotka Volterra fishing problem]] in [http://www.ampl.org AMPL] format. You should be aware of the comments regarding discretization made on the [[:Category:AMPL\|AMPL overview]] page. Note that you will need to include two generic [[support AMPL files]], ampl_general.mod and ampl_general.dat.

	=== AMPL ===		=== AMPL ===
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	# ------------------------------------		# ------------------------------------

	model ~~../general/~~ampl_general.mod;		model ampl_general.mod;
	model ~~ampl_lotka_paper~~.mod;		model ampl_lotka.mod;
	data ~~ampl_lotka_paper~~.dat;		data ampl_lotka.dat;
	data ~~../general/~~ampl_general.dat;		data ampl_general.dat;

	option presolve_eps 1e-10;		option presolve_eps 1e-10;

SebastianSager at 15:17, 9 July 2009

2009-07-09T15:17:38Z

← Older revision		Revision as of 15:17, 9 July 2009
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	This page contains a discretized version of the MIOCP [[Lotka Volterra fishing problem]] in [http://www.ampl.org AMPL] format. You should be aware of the comments regarding discretization made on the [[:Category:AMPL\|AMPL overview]] page.		This page contains a discretized version of the MIOCP [[Lotka Volterra fishing problem]] in [http://www.ampl.org AMPL] format. You should be aware of the comments regarding discretization made on the [[:Category:AMPL\|AMPL overview]] page. Note that you will need to include two generic [[support AMPL files]].

	=== AMPL ===		=== AMPL ===

SebastianSager: Replaced code with realistic values and implicit Euler

2009-07-09T15:14:13Z

Replaced code with realistic values and implicit Euler

Show changes

SebastianSager: moved content from Lotka Volterra fishing problem page

2009-07-09T15:03:44Z

moved content from Lotka Volterra fishing problem page

New page

=== AMPL ===

The model in AMPL code for a fixed control discretization grid with a collocation method. We need a model file lotka_ampl.mod,
<source lang="AMPL">
# ----------------------------------------------------------------
# Lotka Volterra fishing problem with collocation (explicit Euler)
# (c) Sebastian Sager
# ----------------------------------------------------------------

param T > 0;
param nt > 0;
param nu > 0;
param ntperu > 0;
param c1 > 0;
param c2 > 0;
param ref1 > 0;
param ref2 > 0;
param dt := T / (nt-1);
set I:= 0..nt;
set U:= 0..nu-1;

param uidx {I};

var x {I, 1..2} >= 0;
var w {U} >= 0, <= 1 binary;

minimize Deviation:
0.5 * dt * ( (x[0,1] - ref1)*(x[0,1] - ref1) + (x[0,2] - ref2)*(x[0,2] - ref2) )
+ 0.5 * dt * ( (x[nt,1] - ref1)*(x[nt,1] - ref1) + (x[nt,2] - ref2)*(x[nt,2] - ref2) )
+ dt * sum {i in I diff {0,nt} } ( (x[i,1] - ref1)*(x[i,1] - ref1)
+ (x[i,2] - ref2)*(x[i,2] - ref2) ) ;

subj to ODE_DISC_1 {i in I diff {0}}:
x[i,1] = x[i-1,1] + dt * ( x[i-1,1] - x[i-1,1]*x[i-1,2] - x[i-1,1]*c1*w[uidx[i-1]] );

subj to ODE_DISC_2 {i in I diff {0}}:
x[i,2] = x[i-1,2] + dt * ( - x[i-1,2] + x[i-1,1]*x[i-1,2] - x[i-1,2]*c2*w[uidx[i-1]] );
</source>
a data file lotka_ampl.dat,
<source lang="AMPL">
# ------------------------------------
# Data: Lotka Volterra fishing problem
# ------------------------------------

# Algorithmic parameters
param ntperu := 1;
param nu := 100;
param nt := 100;

# Problem parameters
param T := 12.0;
param c1 := 0.4;
param c2 := 0.2;
param ref1 := 1.0;
param ref2 := 1.0;

# Initial values differential states
let x[0,1] := 0.5;
let x[0,2] := 0.7;
fix x[0,1];
fix x[0,2];

# Initial values control
let {i in U} w[i] := 0.0;

param mysum;

# Set indices of controls corresponding to time points
for {i in 0..nu-1} {
for {j in 0..ntperu-1} {
let uidx[i*ntperu+j] := i;
}
}
let uidx[nt] := nu-1;
</source>
and a running script lotka_ampl.run,
<source lang="AMPL">
# ----------------------------------------------------
# Solve Lotka Volterra fishing problem via collocation
# ----------------------------------------------------

model ampl_lotka.mod;
data ampl_lotka.dat;

option solver bonmin;

solve;
</source>

== Preliminary Results ==

Default values for all the options are used in all the solvers under NEOS Server environment using AMPL.

The preliminary results are as follows:
* MINLP : Infeasible problem
* FilMINT : Error in MINTO
* Bonmin : (options = B-BB, B-OA, B-QG and B-Hyb) Infeasible problem
* KNITRO : problem solved with objective value 1.5847 when using Branch and Bound; the solution can be obtained around 15 seconds (CPU time) by some branching strategies without parallel features

The preliminary results are tested by Henry Kar Ming Chan

[[Category:AMPL]]