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: Anders P. <an...@op...> - 2010-02-22 19:57:30
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Use one of these methods:
addEmptyLinearExpression(String) // Linear only
addEmptyQuadraticExpression(String) // Quadratic only
addGeneralExpression(String) // Linear and Quadratic
Don't call getExpression(?) all the time - keep the reference instead.
Turn those expressions into constraints and/or objectives by setting the lower/upper limits or the contribution weight.
/Anders
On 22 feb 2010, at 01.44, Joao Magalhaes wrote:
> 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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