Re: [ojAlgo-user] Problems with the quadratic solver (format problems fixed)
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Re: [ojAlgo-user] Problems with the quadratic solver (format problems fixed)
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From: Joao M. <ma...@gm...> - 2010-02-22 00:50:18
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Anders,
Thank you for your help. I removed the code about the objective
function, and after studying MarkowitzModel.generateOptimisationModel
method, I concluded I should set lower limits for variables that have
lower limits. It also looked like the method addSimpleWeightExpression
is used to define the objective function, however, when I tried this,
I got a NullPointerException because my objective function has
quadratic terms. So, I used the method addEmptyQuadraticExpression,
and defined a big "contribution weight" (BigMath.VERY_POSITIVE) by
calling method setContributionWeight. I think that, by doing this, I
defined this quadratic equation as my objective function, is this
correct?
The objective function is dm1^2 + dm2^2 + dm3^2, so, my final code
for the expression looks like this:
model.addEmptyQuadraticExpression( "eq9" );
model.getExpression( "eq9" ).setQuadraticFactor(
model.indexOfVariable( "dm1" ),
model.indexOfVariable( "dm1" ),
BigMath.ONE );
model.getExpression( "eq9" ).setQuadraticFactor(
model.indexOfVariable( "dm2" ),
model.indexOfVariable( "dm2" ),
BigMath.ONE );
model.getExpression( "eq9" ).setQuadraticFactor(
model.indexOfVariable( "dm3" ),
model.indexOfVariable( "dm3" ),
BigMath.ONE );
model.getExpression( "eq9" ).setContributionWeight( BigMath.VERY_POSITIVE );
The model I created has all these variables (the complete code is
at the end of this message)
However, I am not quite sure about how to set the constraints of my
problem. They are the following:
eq1: 0.5*a + 2*b + 3*c - e1 = 2
eq2: a - 0.5*b - 2*c - e2 = 3
eq3: -0.3*a + 3*c - e3 = 0
eq4: e1 + e2 + e3 - 3*mean = 0
eq5: e1 - mean - dm1 = 0
eq6: e2 - mean - dm2 = 0
eq7: e3 - mean - dm3 = 0
eq8: a + b + c = 1
By reading the javadocs, I understood that the method I should use
is addConstraint, which receives the lower and the upper limits. So,
in order to get an equality, I just have to make upperLimit =
lowerLimit. So, my code looked like this (notice that I used
upperLimit = lowerLimit = 0, and setConstant to define the equality):
model.addConstraint( "eq1", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq2", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq3", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq4", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq5", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq6", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq7", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq8", BigMath.ZERO, BigMath.ZERO );
model.getExpression( "eq1" ).setLinearFactor( model.indexOfVariable(
"A" ), BigMath.HALF );
model.getExpression( "eq1" ).setLinearFactor( model.indexOfVariable(
"B" ), new BigDecimal( 2 ) );
model.getExpression( "eq1" ).setLinearFactor( model.indexOfVariable(
"C" ), new BigDecimal( 3 ) );
model.getExpression( "eq1" ).setLinearFactor( model.indexOfVariable(
"e1" ), new BigDecimal( -1 ) );
model.getExpression( "eq1" ).setConstant( new BigDecimal( -2 ) );
model.getExpression( "eq2" ).setLinearFactor( model.indexOfVariable(
"A" ), BigMath.ONE );
model.getExpression( "eq2" ).setLinearFactor( model.indexOfVariable(
"B" ), new BigDecimal( -0.5 ) );
model.getExpression( "eq2" ).setLinearFactor( model.indexOfVariable(
"C" ), new BigDecimal( -2 ) );
model.getExpression( "eq2" ).setLinearFactor( model.indexOfVariable(
"e2" ), new BigDecimal( -1 ) );
model.getExpression( "eq2" ).setConstant( new BigDecimal( -3 ) );
model.getExpression( "eq3" ).setLinearFactor( model.indexOfVariable(
"A" ), new BigDecimal( -0.3 ) );
model.getExpression( "eq3" ).setLinearFactor( model.indexOfVariable(
"B" ), new BigDecimal( 3 ) );
model.getExpression( "eq3" ).setLinearFactor( model.indexOfVariable(
"C" ), new BigDecimal( -0.8 ) );
model.getExpression( "eq3" ).setLinearFactor( model.indexOfVariable(
"e3" ), new BigDecimal( -1 ) );
model.getExpression( "eq3" ).setConstant( BigMath.ZERO );
model.getExpression( "eq4" ).setLinearFactor( model.indexOfVariable(
"e1" ), BigMath.ONE );
model.getExpression( "eq4" ).setLinearFactor( model.indexOfVariable(
"e2" ), BigMath.ONE );
model.getExpression( "eq4" ).setLinearFactor( model.indexOfVariable(
"e3" ), BigMath.ONE );
model.getExpression( "eq4" ).setLinearFactor( model.indexOfVariable(
"mean" ), new BigDecimal( -3 ) );
model.getExpression( "eq4" ).setConstant( BigMath.ZERO );
model.getExpression( "eq5" ).setLinearFactor( model.indexOfVariable(
"e1" ), BigMath.ONE );
model.getExpression( "eq5" ).setLinearFactor( model.indexOfVariable(
"mean" ), new BigDecimal( -1 ) );
model.getExpression( "eq5" ).setLinearFactor( model.indexOfVariable(
"dm1" ), new BigDecimal( -1 ) );
model.getExpression( "eq5" ).setConstant( BigMath.ZERO );
model.getExpression( "eq6" ).setLinearFactor( model.indexOfVariable(
"e2" ), BigMath.ONE );
model.getExpression( "eq6" ).setLinearFactor( model.indexOfVariable(
"mean" ), new BigDecimal( -1 ) );
model.getExpression( "eq6" ).setLinearFactor( model.indexOfVariable(
"dm2" ), new BigDecimal( -1 ) );
model.getExpression( "eq6" ).setConstant( BigMath.ZERO );
model.getExpression( "eq7" ).setLinearFactor( model.indexOfVariable(
"e3" ), BigMath.ONE );
model.getExpression( "eq7" ).setLinearFactor( model.indexOfVariable(
"mean" ), new BigDecimal( -1 ) );
model.getExpression( "eq7" ).setLinearFactor( model.indexOfVariable(
"dm3" ), new BigDecimal( -1 ) );
model.getExpression( "eq7" ).setConstant( BigMath.ZERO );
model.getExpression( "eq8" ).setLinearFactor( model.indexOfVariable(
"A" ), BigMath.ONE );
model.getExpression( "eq8" ).setLinearFactor( model.indexOfVariable(
"B" ), BigMath.ONE );
model.getExpression( "eq8" ).setLinearFactor( model.indexOfVariable(
"C" ), BigMath.ONE );
model.getExpression( "eq8" ).setConstant( new BigDecimal( -1 ) );
So, I defined minimisation (by calling setMinimisation), generated
a solver (by calling getDefaultSolver), and invoked the method solve,
as in the following code:
model.setMaximisation( false );
model.setMinimisation( true );
final OptimisationSolver solver = model.getDefaultSolver();
final Result res = solver.solve();
This time, I did not get an exception, but the following result:
OPTIMAL (1) { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 }
But this is not what I expected.
Please, can you tell me what I am doing wrong?
Cheers
Joao Magalhaes
--- -------- Code:
import java.math.BigDecimal;
import java.util.HashSet;
import java.util.Set;
import org.ojalgo.constant.BigMath;
import org.ojalgo.optimisation.ModelValidationException;
import org.ojalgo.optimisation.OptimisationSolver;
import org.ojalgo.optimisation.Variable;
import org.ojalgo.optimisation.OptimisationSolver.Result;
import org.ojalgo.optimisation.quadratic.QuadraticExpressionsModel;
public class Test
{
public static void main( final String[] args )
throws ModelValidationException
{
final Set<Variable> variables = new HashSet<Variable>();
final Variable A = new Variable( "A" );
final Variable B = new Variable( "B" );
final Variable C = new Variable( "C" );
final Variable e1 = new Variable( "e1" );
final Variable e2 = new Variable( "e2" );
final Variable e3 = new Variable( "e3" );
final Variable mean = new Variable( "mean" );
final Variable dm1 = new Variable( "dm1" );
final Variable dm2 = new Variable( "dm2" );
final Variable dm3 = new Variable( "dm3" );
variables.add( A );
variables.add( B );
variables.add( C );
variables.add( e1 );
variables.add( e2 );
variables.add( e3 );
variables.add( mean );
variables.add( dm1 );
variables.add( dm2 );
variables.add( dm3 );
A.setLowerLimit( BigMath.ZERO );
B.setLowerLimit( BigMath.ZERO );
C.setLowerLimit( BigMath.ZERO );
e1.setLowerLimit( BigMath.ZERO );
e2.setLowerLimit( BigMath.ZERO );
e3.setLowerLimit( BigMath.ZERO );
mean.setLowerLimit( BigMath.ZERO );
dm1.setLowerLimit( BigMath.VERY_NEGATIVE );
dm2.setLowerLimit( BigMath.VERY_NEGATIVE );
dm3.setLowerLimit( BigMath.VERY_NEGATIVE );
A.setUpperLimit( BigMath.VERY_POSITIVE );
B.setUpperLimit( BigMath.VERY_POSITIVE );
C.setUpperLimit( BigMath.VERY_POSITIVE );
e1.setUpperLimit( BigMath.VERY_POSITIVE );
e2.setUpperLimit( BigMath.VERY_POSITIVE );
e3.setUpperLimit( BigMath.VERY_POSITIVE );
mean.setUpperLimit( BigMath.VERY_POSITIVE );
dm1.setUpperLimit( BigMath.VERY_POSITIVE );
dm2.setUpperLimit( BigMath.VERY_POSITIVE );
dm3.setUpperLimit( BigMath.VERY_POSITIVE );
final QuadraticExpressionsModel model = new
QuadraticExpressionsModel( variables );
model.addConstraint( "eq1", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq2", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq3", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq4", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq5", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq6", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq7", BigMath.ZERO, BigMath.ZERO );
model.addConstraint( "eq8", BigMath.ZERO, BigMath.ZERO );
model.addEmptyQuadraticExpression( "eq9" );
model.getExpression( "eq1" ).setLinearFactor( model.indexOfVariable(
"A" ), BigMath.HALF );
model.getExpression( "eq1" ).setLinearFactor( model.indexOfVariable(
"B" ), new BigDecimal( 2 ) );
model.getExpression( "eq1" ).setLinearFactor( model.indexOfVariable(
"C" ), new BigDecimal( 3 ) );
model.getExpression( "eq1" ).setLinearFactor( model.indexOfVariable(
"e1" ), new BigDecimal( -1 ) );
model.getExpression( "eq1" ).setConstant( new BigDecimal( -2 ) );
model.getExpression( "eq2" ).setLinearFactor( model.indexOfVariable(
"A" ), BigMath.ONE );
model.getExpression( "eq2" ).setLinearFactor( model.indexOfVariable(
"B" ), new BigDecimal( -0.5 ) );
model.getExpression( "eq2" ).setLinearFactor( model.indexOfVariable(
"C" ), new BigDecimal( -2 ) );
model.getExpression( "eq2" ).setLinearFactor( model.indexOfVariable(
"e2" ), new BigDecimal( -1 ) );
model.getExpression( "eq2" ).setConstant( new BigDecimal( -3 ) );
model.getExpression( "eq3" ).setLinearFactor( model.indexOfVariable(
"A" ), new BigDecimal( -0.3 ) );
model.getExpression( "eq3" ).setLinearFactor( model.indexOfVariable(
"B" ), new BigDecimal( 3 ) );
model.getExpression( "eq3" ).setLinearFactor( model.indexOfVariable(
"C" ), new BigDecimal( -0.8 ) );
model.getExpression( "eq3" ).setLinearFactor( model.indexOfVariable(
"e3" ), new BigDecimal( -1 ) );
model.getExpression( "eq3" ).setConstant( BigMath.ZERO );
model.getExpression( "eq4" ).setLinearFactor( model.indexOfVariable(
"e1" ), BigMath.ONE );
model.getExpression( "eq4" ).setLinearFactor( model.indexOfVariable(
"e2" ), BigMath.ONE );
model.getExpression( "eq4" ).setLinearFactor( model.indexOfVariable(
"e3" ), BigMath.ONE );
model.getExpression( "eq4" ).setLinearFactor( model.indexOfVariable(
"mean" ), new BigDecimal( -3 ) );
model.getExpression( "eq4" ).setConstant( BigMath.ZERO );
model.getExpression( "eq5" ).setLinearFactor( model.indexOfVariable(
"e1" ), BigMath.ONE );
model.getExpression( "eq5" ).setLinearFactor( model.indexOfVariable(
"mean" ), new BigDecimal( -1 ) );
model.getExpression( "eq5" ).setLinearFactor( model.indexOfVariable(
"dm1" ), new BigDecimal( -1 ) );
model.getExpression( "eq5" ).setConstant( BigMath.ZERO );
model.getExpression( "eq6" ).setLinearFactor( model.indexOfVariable(
"e2" ), BigMath.ONE );
model.getExpression( "eq6" ).setLinearFactor( model.indexOfVariable(
"mean" ), new BigDecimal( -1 ) );
model.getExpression( "eq6" ).setLinearFactor( model.indexOfVariable(
"dm2" ), new BigDecimal( -1 ) );
model.getExpression( "eq6" ).setConstant( BigMath.ZERO );
model.getExpression( "eq7" ).setLinearFactor( model.indexOfVariable(
"e3" ), BigMath.ONE );
model.getExpression( "eq7" ).setLinearFactor( model.indexOfVariable(
"mean" ), new BigDecimal( -1 ) );
model.getExpression( "eq7" ).setLinearFactor( model.indexOfVariable(
"dm3" ), new BigDecimal( -1 ) );
model.getExpression( "eq7" ).setConstant( BigMath.ZERO );
model.getExpression( "eq8" ).setLinearFactor( model.indexOfVariable(
"A" ), BigMath.ONE );
model.getExpression( "eq8" ).setLinearFactor( model.indexOfVariable(
"B" ), BigMath.ONE );
model.getExpression( "eq8" ).setLinearFactor( model.indexOfVariable(
"C" ), BigMath.ONE );
model.getExpression( "eq8" ).setConstant( new BigDecimal( -1 ) );
model.getExpression( "eq9" ).setQuadraticFactor(
model.indexOfVariable( "dm1" ),
model.indexOfVariable( "dm1" ),
BigMath.ONE );
model.getExpression( "eq9" ).setQuadraticFactor(
model.indexOfVariable( "dm2" ),
model.indexOfVariable( "dm2" ),
BigMath.ONE );
model.getExpression( "eq9" ).setQuadraticFactor(
model.indexOfVariable( "dm3" ),
model.indexOfVariable( "dm3" ),
BigMath.ONE );
model.getExpression( "eq9" ).setContributionWeight( BigMath.VERY_POSITIVE );
model.setMaximisation( false );
model.setMinimisation( true );
final OptimisationSolver solver = model.getDefaultSolver();
final Result res = solver.solve();
System.out.println( res.getState().toString() );
System.out.println( res.toString() );
}
}
> Haven't looked into exactly what your problem is, but:
> 1) You define the objective function by setting the "contribution weight" on one or more exssions and/or variables. The method getObjectiveExssion() will give
> you a derived/aggregated exssion. You most likely do not need to call this method. If you want to call it, you should do so when the optimization model is
> complete.
> 2) Lok in the MarkowitzModel class (even if that's not the model you're after). In that class there is a private method generateOptimisationModel(...). Study
> that code.
> /Anders
On Sun, Feb 21, 2010 at 6:18 PM, Joao Magalhaes <ma...@gm...> wrote:
> Hello again,
>
> Looks like the matrix got messed up in my previous post. So, I am
> sending the message again, but with the equations instead of the
> matrix.
> Apologies for this.
> My name is Joao Magalhaes, I am an undegraduate student from Brazil.
> I have to solve an optimization problem that has to do with
> financial stuff. It can be summarized by the equations below:
>
> Constraints:
>
> eq1: 0.5*a + 2*b + 3*c - e1 = 2
> eq2: a - 0.5*b - 2*c - e2 = 3
> eq3: -0.3*a + 3*c - e3 = 0
> eq4: e1 + e2 + e3 - 3*mean = 0
> eq5: e1 - mean - dm1 = 0
> eq6: e2 - mean - dm2 = 0
> eq7: e3 - mean - dm3 = 0
> eq8: a + b + c = 1
>
> Objective: minimize dm1^2 + dm2^2 + dm3^2
>
> The goal is to minimize the function dm1^2 + dm2^2 + dm3^2, subject to
> the constraints.
> I searched for Quadratic Solvers in google, and came across ojAlgo.
> Based on the javadocs and some source code inspection, I have written
> the code and the end of this message. However, I came across two
> problems:
>
> 1) I cannot set quadratic factors for the objective function. I get a
> NullPointerException. Inspecting the source code, I concluded that the
> objective function must be linear, is this correct? If so, it would be
> also possible to model the problem a little bit differently, by adding
> a new quadratic constraint and minimizing the new created variable,
> just as follows:
>
> eq1: 0.5*a + 2*b + 3*c - e1 = 2
> eq2: a - 0.5*b - 2*c - e2 = 3
> eq3: -0.3*a + 3*c - e3 = 0
> eq4: e1 + e2 + e3 - 3*mean = 0
> eq5: e1 - mean - dm1 = 0
> eq6: e2 - mean - dm2 = 0
> eq7: e3 - mean - dm3 = 0
> eq8: a + b + c = 1
> eq9: 3* var - dm1^2 - dm2^2 - dm3^2 = 0
>
> Objective: minimize var
>
> However, I tried this too, but it did not work.
>
> 2) In order to keep moving on, I used the first model with 8
> equations, but changed the objective function to something linear
> (just the sum of the dm variables), so that nothing in the problem is
> quadratic, everything is linear. But again, I get a
> NullPointerException in the Lagrange Solver:
>
> Exception in thread "main" java.lang.NullPointerException
> at org.ojalgo.matrix.store.MergedRowsStore.<init>(MergedRowsStore.java:46)
> at org.ojalgo.optimisation.quadratic.LagrangeSolver.buildIterationSolver(LagrangeSolver.java:56)
> at org.ojalgo.optimisation.quadratic.LagrangeSolver.performIteration(LagrangeSolver.java:84)
> at org.ojalgo.optimisation.quadratic.QuadraticSolver.iterate(QuadraticSolver.java:303)
> at org.ojalgo.optimisation.quadratic.QuadraticSolver.solve(QuadraticSolver.java:275)
> at org.ojalgo.optimisation.quadratic.QuadraticSolver.solve(QuadraticSolver.java:256)
> at br.com.mindsatwork.ojalgo.test.TestClass.main(TestClass.java:143)
>
> My source code is as follows. Can anyone give me some light on what I
> am doing wrong? Please, apologies if this is a very basic question,
> but it is the very first time I try ojAlgo. I promise to improve my
> questions in the future :-)
>
> Cheers,
> Joao Magalhaes
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