Re: [ojAlgo-user] QuadraticSolver with unsatisfiable constraints
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Re: [ojAlgo-user] QuadraticSolver with unsatisfiable constraints
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From: Anders P. <an...@op...> - 2009-11-17 09:33:02
|
On 17 nov 2009, at 09.47, Pierre AUSLAENDER wrote:
> Yes, that seems perfectly correct. Sorry I didn't notice the null
> solution.
>
> However I still have two failures, tests 2 and 5.
We agree that 2 and 5 are "problematic"...
> In the following code, I use the LinearSolver to get an
> initialIterationPoint for the QuandraticSolver, or to detect that
> the system is not feasible. The LinearSolver seems to behave very
> well. It seems to work and I get rid of the two remaining failures.
>
> Do you think this is generally safe and not too time consuming?
> Would you suggest I can use this in my code to get initial iteration
> points and also to check if the system is feasible?
That's probably a good idea. If you can make things easier for the
ActiveSetSolver you have gained something. I'll probably include this
as an built-in option for future versions of the ActiveSetSolver.
The weak spot of the QuadraticSolver is to determine if the problem is
infeasible or not (in combination with finding the correct combination
of active inequality constraints).
The LinearSolver has problems with redundant model elements. More
advanced linear solvers have presolvers that eliminate redundant
variables and constraints. ojAlgo does not yet have this.
/Anders
> /*
> * (c) Copyright Pictet & Cie 2009
> */
> package com.pictet.pam.bam.test;
>
> import java.math.BigDecimal;
> import java.util.Arrays;
>
> import org.junit.Assert;
> import org.junit.Test;
> import org.ojalgo.constant.BigMath;
> import org.ojalgo.matrix.store.MatrixStore;
> import org.ojalgo.optimisation.Expression;
> import org.ojalgo.optimisation.State;
> import org.ojalgo.optimisation.Variable;
> import org.ojalgo.optimisation.OptimisationSolver.Result;
> import org.ojalgo.optimisation.linear.LinearExpressionsModel;
> import org.ojalgo.optimisation.linear.LinearSolver;
> import org.ojalgo.optimisation.quadratic.QuadraticExpressionsModel;
> import org.ojalgo.optimisation.quadratic.QuadraticSolver;
>
> /**
> * @author pauslaender
> *
> */
> public class OptimisationSolverTest {
>
> Variable[] vars;
> BigDecimal[] point;
> QuadraticExpressionsModel quadraticModel;
> LinearExpressionsModel linearModel;
>
> /**
> *
> * @param numberOfVars
> * greater than 6
> */
> void setupModels(int numberOfVars) {
> if (numberOfVars < 6) {
> throw new
> IllegalArgumentException("numberOfVars must be >= 6 !!!");
> }
> //
> // variables
> //
> vars = new Variable[numberOfVars];
> vars[0] = new Variable("x0").lower(new
> BigDecimal(00.0)).upper(new BigDecimal(15.0));
> vars[1] = new Variable("x1").lower(new
> BigDecimal(17.0)).upper(new BigDecimal(27.0));
> vars[2] = new Variable("x2").lower(new
> BigDecimal(19.0)).upper(new BigDecimal(34.0));
> vars[3] = new Variable("x3").lower(new
> BigDecimal(25.0)).upper(new BigDecimal(48.0));
> vars[4] = new Variable("x4").lower(new
> BigDecimal(05.0)).upper(new BigDecimal(18.0));
> vars[5] = new Variable("x5").lower(new
> BigDecimal(02.0)).upper(new BigDecimal(09.0));
> for (int i = 6; i < numberOfVars; ++i) {
> vars[i] = new Variable("x" +
> i).level(BigMath.ZERO);
> }
> //
> // minimize distance to this point
> //
> point = new BigDecimal[numberOfVars];
> point[0] = new BigDecimal(1.0);
> point[1] = new BigDecimal(25.0);
> point[2] = new BigDecimal(33.0);
> point[3] = new BigDecimal(29.0);
> point[4] = new BigDecimal(9.0);
> point[5] = new BigDecimal(2.0);
> for (int i = 6; i < numberOfVars; ++i) {
> point[i] = new BigDecimal(0.0);
> }
> //
> // models
> //
> linearModel = new LinearExpressionsModel(vars);
> quadraticModel = new QuadraticExpressionsModel(vars);
> //
> // objective function - only assigned to the
> quadratic model
> //
> {
> Expression e =
> quadraticModel.addOffsetExpression("objective", Arrays.asList(point));
> e.setContributionWeight(BigMath.HALF);
> }
> //
> // sum(xi) = 100.0
> //
> {
> Expression e =
> quadraticModel.addSimpleWeightExpression("sum(xi) = 100.0");
> e.level(BigMath.HUNDRED);
> e =
> linearModel.addSimpleWeightExpression("sum(xi) = 100.0");
> e.level(BigMath.HUNDRED);
> }
> //
> // x1 + x2 <= 45
> //
> {
> Expression e =
> quadraticModel.addEmptyLinearExpression("x1 + x2 <= 45.0");
> e.setLinearFactor(1, BigMath.ONE);
> e.setLinearFactor(2, BigMath.ONE);
> e.lower(BigMath.ZERO).upper(new
> BigDecimal(45.0));
> e = linearModel.addEmptyLinearExpression("x1
> + x2 <= 45.0");
> e.setLinearFactor(1, BigMath.ONE);
> e.setLinearFactor(2, BigMath.ONE);
> e.lower(BigMath.ZERO).upper(new
> BigDecimal(45.0));
> }
> //
> // x4 - 2*x5 = 0
> //
> {
> Expression e =
> quadraticModel.addEmptyLinearExpression("x4 - 2*x5 = 0");
> e.setLinearFactor(4, BigMath.ONE);
> e.setLinearFactor(5, BigMath.TWO.negate());
> e.level(BigMath.ZERO);
> e = linearModel.addEmptyLinearExpression("x4
> - 2*x5 = 0");
> e.setLinearFactor(4, BigMath.ONE);
> e.setLinearFactor(5, BigMath.TWO.negate());
> e.level(BigMath.ZERO);
> }
> }
>
> @Test
> public void test1() {
> setupModels(6);
> MatrixStore<Double> initialIterationPoint =
> solveLinear();
> Assert.assertTrue(initialIterationPoint != null);
> MatrixStore<Double> solution =
> solveQuadratic(initialIterationPoint);
> Assert.assertTrue(solution != null);
> }
>
> @Test
> public void test2() {
> setupModels(6);
> vars[3].level(new BigDecimal(40.0));
> vars[4].level(new BigDecimal(18.0));
> MatrixStore<Double> initialIterationPoint =
> solveLinear();
> Assert.assertFalse(initialIterationPoint != null);
> MatrixStore<Double> solution =
> solveQuadratic(initialIterationPoint);
> Assert.assertFalse(solution != null);
> }
>
> @Test
> public void test3() {
> setupModels(6);
> vars[3].level(new BigDecimal(48.0));
> vars[4].level(new BigDecimal(18.0));
> vars[5].level(new BigDecimal(5.0));
> MatrixStore<Double> initialIterationPoint =
> solveLinear();
> Assert.assertFalse(initialIterationPoint != null);
> MatrixStore<Double> solution =
> solveQuadratic(initialIterationPoint);
> Assert.assertFalse(solution != null);
> }
>
> @Test
> public void test4() {
> setupModels(42);
> MatrixStore<Double> initialIterationPoint =
> solveLinear();
> Assert.assertTrue(initialIterationPoint != null);
> MatrixStore<Double> solution =
> solveQuadratic(initialIterationPoint);
> Assert.assertTrue(solution != null);
> }
>
> @Test
> public void test5() {
> setupModels(42);
> vars[3].level(new BigDecimal(40.0));
> vars[4].level(new BigDecimal(18.0));
> MatrixStore<Double> initialIterationPoint =
> solveLinear();
> Assert.assertFalse(initialIterationPoint != null);
> MatrixStore<Double> solution =
> solveQuadratic(initialIterationPoint);
> Assert.assertFalse(solution != null);
> }
>
> @Test
> public void test6() {
> setupModels(42);
> vars[3].level(new BigDecimal(40.0));
> vars[4].level(new BigDecimal(18.0));
> vars[5].level(new BigDecimal(5.0));
> MatrixStore<Double> initialIterationPoint =
> solveLinear();
> Assert.assertFalse(initialIterationPoint != null);
> MatrixStore<Double> solution =
> solveQuadratic(initialIterationPoint);
> Assert.assertFalse(solution != null);
> }
>
> MatrixStore<Double> solveLinear() {
> final LinearSolver solver = new
> LinearSolver.Builder(linearModel).build();
> final Result result = solver.solve();
>
> if (result.getSolution() != null) {
> if
> (result.getState().isNotLessThan(State.FEASIBLE)) {
> if
> (linearModel.validateSolution(result.getSolution(),
> solver.options.solutionContext)) {
> return
> result.getSolution().toPrimitiveStore();
> }
> }
> }
>
> return null;
> }
>
> MatrixStore<Double> solveQuadratic(final MatrixStore<Double>
> initialIterationPoint) {
> if (initialIterationPoint == null) {
> return null;
> }
> final QuadraticSolver solver = new
> QuadraticSolver.Builder(quadraticModel).build();
> final Result result = solver.solve();
>
> if (result.getSolution() != null) {
> final boolean validated =
> quadraticModel.validateSolution(result.getSolution(),
> solver.options.solutionContext);
> if
> (result.getState().isNotLessThan(State.FEASIBLE)) {
> final String message = "State: " +
> result.getState() + ", validated: " + validated;
> Assert.assertTrue(message, validated);
> if (validated) {
> return
> result.getSolution().toPrimitiveStore();
> }
> } else {
> final String message = "State: " +
> result.getState() + ", validated: " + validated;
> Assert.assertFalse(message,
> validated);
> }
> } else {
> Assert.assertFalse("No solution but state
> FEASIBLE", result.getState().isNotLessThan(State.FEASIBLE));
> }
>
> return null;
> }
>
> }
>
> Thanks,
> Pierre
>
>
>
> "Anders Peterson" <an...@op...>
> 16.11.2009 22:10
> Please respond to
> oja...@li...
>
>
> To
> oja...@li...
> cc
> Subject
> Re: [ojAlgo-user] QuadraticSolver with unsatisfiable constraints
>
>
>
> Warning: this message has been delivered from outside the Pictet
> Group. If the content is related to banking matters, please apply
> the same procedure as for an incoming Fax or letter.
> Attention: Ce message provient de l'extérieur du Groupe Pictet. S'il
> possède un caractère bancaire, veuillez le traiter de la même
> manière qu'un Fax ou une lettre entrante.
>
>
>
>
>
> I modified the solve-method to be
>
> void solve() {
>
> final QuadraticSolver solver = new
> QuadraticSolver.Builder(model).build();
> final Result result = solver.solve();
>
> if (result.getSolution() != null) {
> final boolean validated =
> model.validateSolution(result.getSolution(),
> solver.options.solutionContext);
> if (result.getState().isNotLessThan(State.FEASIBLE)) {
> final String message = "State: " + result.getState()
> + ", validated: " + validated;
> Assert.assertTrue(message, validated);
> } else {
> final String message = "State: " + result.getState()
> + ", validated: " + validated;
> Assert.assertFalse(message, validated);
> }
> } else {
> Assert.assertFalse("No solution but state FEASIBLE",
> result.getState().isNotLessThan(State.FEASIBLE));
> }
> }
>
> Does that seem correct to you?
>
>
> Then, when I run the tests I only get a failure (failed test) with
> test "2", and I get no error (like an NPE).
>
> Tests "2" and "5" takes very long - long enough to suggest that
> there is something the algorithm can't handle.
>
> I see no problem with test "1", "3", "4" or "6".
>
> Do you agree with this?
>
>
> Have you tried setting different contexts for
> "options.solutionContext"? I don't believe the
> "options.problemContext" affect anything with the QuadraticSolver
> (yet).
>
> /Anders
>
>
> On 16 nov 2009, at 16.30, Pierre AUSLAENDER wrote:
>
> >
> > Sure, here it is (and sorry, the NPE was not in the SVD, but in
> the validateSolution)
> >
> > test1: OK
> > test2: KO with STATE = FAILED, VALIDATION = TRUE
> > test3: KO with NPE in ExpressionBasedModel.validateSolution
> > test4: OK
> > test5: KO with STATE = OPTIMAL, VALIDATION = FALSE
> > test6: KO with NPE in ExpressionBasedModel.validateSolution
> >
> > /*
> > * (c) Copyright Pictet & Cie 2009
> > */
> > package com.pictet.pam.bam.test;
> >
> > import java.math.BigDecimal;
> > import java.util.Arrays;
> >
> > import org.junit.Assert;
> > import org.junit.Test;
> > import org.ojalgo.constant.BigMath;
> > import org.ojalgo.optimisation.Expression;
> > import org.ojalgo.optimisation.State;
> > import org.ojalgo.optimisation.Variable;
> > import org.ojalgo.optimisation.OptimisationSolver.Result;
> > import org.ojalgo.optimisation.quadratic.QuadraticExpressionsModel;
> > import org.ojalgo.optimisation.quadratic.QuadraticSolver;
> >
> > /**
> > * @author pauslaender
> > *
> > */
> > public class OptimisationSolverTest {
> >
> > Variable[] vars;
> > BigDecimal[] point;
> > QuadraticExpressionsModel model;
> >
> > /**
> > *
> > * @param numberOfVars greater than 6
> > */
> > void setupModel(int numberOfVars) {
> > if (numberOfVars < 6) {
> > throw new
> IllegalArgumentException("numberOfVars must be >= 6 !!!");
> > }
> > //
> > // variables
> > //
> > vars = new Variable[numberOfVars];
> > vars[0] = new Variable("x0").lower(new
> BigDecimal(00.0)).upper(new BigDecimal(15.0));
> > vars[1] = new Variable("x1").lower(new
> BigDecimal(17.0)).upper(new BigDecimal(27.0));
> > vars[2] = new Variable("x2").lower(new
> BigDecimal(19.0)).upper(new BigDecimal(34.0));
> > vars[3] = new Variable("x3").lower(new
> BigDecimal(25.0)).upper(new BigDecimal(48.0));
> > vars[4] = new Variable("x4").lower(new
> BigDecimal(05.0)).upper(new BigDecimal(18.0));
> > vars[5] = new Variable("x5").lower(new
> BigDecimal(02.0)).upper(new BigDecimal(09.0));
> > for (int i = 6; i < numberOfVars; ++i) {
> > vars[i] = new Variable("x" +
> i).level(BigMath.ZERO);
> > }
> > //
> > // minimise distance to this point
> > //
> > point = new BigDecimal[numberOfVars];
> > point[0] = new BigDecimal(1.0);
> > point[1] = new BigDecimal(25.0);
> > point[2] = new BigDecimal(33.0);
> > point[3] = new BigDecimal(29.0);
> > point[4] = new BigDecimal(9.0);
> > point[5] = new BigDecimal(2.0);
> > for (int i = 6; i < numberOfVars; ++i) {
> > point[i] = new BigDecimal(0.0);
> > }
> > //
> > // model
> > //
> > model = new QuadraticExpressionsModel(vars);
> > //
> > // objective function
> > //
> > {
> > Expression e =
> model.addOffsetExpression("objective", Arrays.asList(point));
> > e.setContributionWeight(BigMath.HALF);
> > }
> > //
> > // sum(xi) = 100.0
> > //
> > {
> > Expression e =
> model.addSimpleWeightExpression("sum(xi) = 100.0");
> > e.level(BigMath.HUNDRED);
> > }
> > //
> > // x1 + x2 <= 45
> > //
> > {
> > Expression e =
> model.addEmptyLinearExpression("x1 + x2 <= 45.0");
> > e.setLinearFactor(1, BigMath.ONE);
> > e.setLinearFactor(2, BigMath.ONE);
> > e.lower(BigMath.ZERO).upper(new
> BigDecimal(45.0));
> > }
> > //
> > // x4 - 2*x5 = 0
> > //
> > {
> > Expression e =
> model.addEmptyLinearExpression("x4 - 2*x5 = 0");
> > e.setLinearFactor(4, BigMath.ONE);
> > e.setLinearFactor(5, BigMath.TWO.negate());
> > e.level(BigMath.ZERO);
> > }
> > }
> >
> > @Test
> > public void test1() {
> > setupModel(6);
> > solve();
> > }
> >
> > @Test
> > public void test2() {
> > setupModel(6);
> > vars[3].level(new BigDecimal(40.0));
> > vars[4].level(new BigDecimal(18.0));
> > solve();
> > }
> >
> > @Test
> > public void test3() {
> > setupModel(6);
> > vars[3].level(new BigDecimal(48.0));
> > vars[4].level(new BigDecimal(18.0));
> > vars[5].level(new BigDecimal(5.0));
> > solve();
> > }
> >
> > @Test
> > public void test4() {
> > setupModel(42);
> > solve();
> > }
> >
> > @Test
> > public void test5() {
> > setupModel(42);
> > vars[3].level(new BigDecimal(40.0));
> > vars[4].level(new BigDecimal(18.0));
> > solve();
> > }
> >
> > @Test
> > public void test6() {
> > setupModel(42);
> > vars[3].level(new BigDecimal(40.0));
> > vars[4].level(new BigDecimal(18.0));
> > vars[5].level(new BigDecimal(5.0));
> > solve();
> > }
> >
> > void solve() {
> > QuadraticSolver solver = new
> QuadraticSolver.Builder(model).build();
> > // QuadraticSolver.DEBUG = true;
> > // System.out.println(model);
> > Result result = solver.solve();
> > // System.out.println(result);
> > //
> System.out.println(result.getSolution().toListOfElements());
> > boolean validated =
> model.validateSolution(result.getSolution(),
> solver.options.solutionContext);
> > if (result.getState() == State.OPTIMAL) {
> > String message = "State: " +
> result.getState() + ", validated: " + validated;
> > Assert.assertTrue(message, validated);
> > } else {
> > String message = "State: " +
> result.getState() + ", validated: " + validated;
> > Assert.assertFalse(message, validated);
> > }
> > }
> >
> > }
> >
> >
> >
> > "Anders Peterson" <an...@op...>
> > 16.11.2009 15:42
> > Please respond to
> > oja...@li...
> >
> > To
> > oja...@li...
> > cc
> > Subject
> > Re: [ojAlgo-user] QuadraticSolver with unsatisfiable constraints
> >
> >
> >
> > Warning: this message has been delivered from outside the Pictet
> Group. If the content is related to banking matters, please apply
> the same procedure as for an incoming Fax or letter.
> > Attention: Ce message provient de l'extérieur du Groupe Pictet.
> S'il possède un caractère bancaire, veuillez le traiter de la même
> manière qu'un Fax ou une lettre entrante.
> >
> >
> >
> >
> >
> > Can you perhaps give me 2 test cases; 1 for the NPE case and 1 for
> the
> > incorrect state case. /Anders
> >
> >
> > On 16 nov 2009, at 14.33, Pierre AUSLAENDER wrote:
> >
> > >
> > > Hello Anders,
> > >
> > > Thanks a lot for the swift reply.
> > >
> > > I 've played with the latest snapshot and here are my findings:
> > > - Most of the times now, when the constraints cannot be satisfied,
> > > the solver terminates with the state FAILED, which is what one
> would
> > > expect, albeit after a great lot of iterations.
> > > - Sometimes however, it terminates with the state OPTIMAL, and the
> > > model validation returns FALSE, same as before I took the
> snapshot.
> > > - Sometimes as well, it throws a NPE in the SVD (after saying that
> > > LU is not solvable).
> > >
> > > I'm trying to build a simple JUnit and send it to you.
> > >
> > > Kind regards,
> > > Pierre
> > >
> > >
> > >
> > > "Anders Peterson" <an...@op...>
> > > 16.11.2009 12:57
> > > Please respond to
> > > oja...@li...
> > >
> > >
> > > To
> > > oja...@li...
> > > cc
> > > Subject
> > > Re: [ojAlgo-user] QuadraticSolver with unsatisfiable constraints
> > >
> > >
> > >
> > > Warning: this message has been delivered from outside the Pictet
> > > Group. If the content is related to banking matters, please apply
> > > the same procedure as for an incoming Fax or letter.
> > > Attention: Ce message provient de l'extérieur du Groupe Pictet.
> S'il
> > > possède un caractère bancaire, veuillez le traiter de la même
> > > manière qu'un Fax ou une lettre entrante.
> > >
> > >
> > >
> > >
> > >
> > > On 16 nov 2009, at 11.06, Pierre AUSLAENDER wrote:
> > >
> > > > Hello,
> > > >
> > > > Thank you for this library, which is a joy to use - once I got
> over
> > > > the lack of documentation.
> > > >
> > > > I'm using the QuadraticSolver (ActiveSetSolver) on a least
> squares
> > > > minimisation problem, under a set of linear constraints. When
> the
> > > > constraints can be satisfied, it works perfectly. However,
> when the
> > > > constraints cannot be satisfied, the solver still returns with
> an
> > > > OPTIMAL state after a few iterations. I was puzzled until I
> > > > discovered the QuadraticSolver.validateSolution(...) methods,
> which
> > > > I can use to effectively test the solution against the
> constraints.
> > > >
> > > > Is this the way it is supposed to work, or did I do something
> wrong?
> > > > I would have expected the solver to FAIL instead.
> > >
> > >
> > > I recently fixed a couple of bugs related to this. Get the latest
> > > snapshot download from Source Forge, and try if that solves your
> > > problem. If it doesn't I'd like you to give me (junit) test case.
> > >
> > >
> > > > As an aside question, there is the following JavaDoc comment on
> > > > ExpressionBasedModel.addConstraint(final String aName, ....):
> Note
> > > > that only the first constraint you add will be used by the
> solver.
> > > > What does this comment mean? Is it simply related to the
> uniqueness
> > > > of the constraint name, or has it wider implications?
> > >
> > >
> > > That comment should have been removed. It was only relevant for
> the
> > > now removed/replaced KnapsckSolver. That solver could only use 1
> > > constraint - the first one you added. I'll correct the javadoc
> comment
> > > now.
> > >
> > >
> > > /Anders
> > >
> > >
> > >
> > > > Thank you,
> > > > Pierre
> > > >
> > > > ________________________________________________________________
> > > >
> > > > PAM S.A Geneva Tel. +41 (0)58 323 3333
> > > > 60, route des Acacias Fax +41 (0)58 323 2324
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> ________________________________________________________________
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> PAM S.A Geneva Tel. +41 (0)58 323 3333
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> CH-1211 GENEVE 73 http://www.pictet.com/
> ________________________________________________________________
>
> This document should only be read by those persons to whom it is
> addressed and is not intended to be relied upon by any person
> without subsequent written confirmation of its contents. If you
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> ________________________________________________________________
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> ------------------------------------------------------------------------------
> Let Crystal Reports handle the reporting - Free Crystal Reports 2008
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> trial. Simplify your report design, integration and deployment - and
> focus on
> what you do best, core application coding. Discover what's new with
> Crystal Reports now. http://p.sf.net/sfu/bobj-july_______________________________________________
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