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https://issues.apache.org/jira/browse/MATH-434?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]
Wayne Witzel updated MATH-434:
------------------------------
Description:
The SimplexSolver is returning an unfeasible solution:
import java.util.ArrayList;
import java.text.DecimalFormat;
import org.apache.commons.math.linear.ArrayRealVector;
import org.apache.commons.math.optimization.GoalType;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.linear.*;
public class SimplexSolverBug {
public static void main(String[] args) throws OptimizationException {
LinearObjectiveFunction c = new LinearObjectiveFunction(new
double[]{0.0d, 1.0d, 1.0d, 0.0d, 0.0d, 0.0d, 0.0d}, 0.0d);
ArrayList<LinearConstraint> cnsts = new ArrayList<LinearConstraint>(5);
LinearConstraint cnst;
cnst = new LinearConstraint(new double[] {1.0d, -0.1d, 0.0d, 0.0d,
0.0d, 0.0d, 0.0d}, Relationship.EQ, -0.1d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {1.0d, 0.0d, 0.0d, 0.0d, 0.0d,
0.0d, 0.0d}, Relationship.GEQ, -1e-18d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 1.0d, 0.0d, 0.0d, 0.0d,
0.0d, 0.0d}, Relationship.GEQ, 0.0d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 0.0d, 1.0d, 0.0d,
-0.0128588d, 1e-5d}, Relationship.EQ, 0.0d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 0.0d, 0.0d, 1.0d,
1e-5d, -0.0128586d}, Relationship.EQ, 1e-10d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, -1.0d,
0.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 1.0d, 0.0d,
0.0d, 0.0d}, Relationship.GEQ, 0.0d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 0.0d,
-1.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 0.0d, 1.0d,
0.0d, 0.0d}, Relationship.GEQ, 0.0d);
cnsts.add(cnst);
DecimalFormat df = new java.text.DecimalFormat("0.#####E0");
System.out.println("Constraints:");
for(LinearConstraint con : cnsts) {
for (int i = 0; i < con.getCoefficients().getDimension(); ++i)
System.out.print(df.format(con.getCoefficients().getData()[i])
+ " ");
System.out.println(con.getRelationship() + " " + con.getValue());
}
SimplexSolver simplex = new SimplexSolver(1e-7);
double[] sol = simplex.optimize(c, cnsts, GoalType.MINIMIZE,
false).getPointRef();
System.out.println("Solution:\n" + new ArrayRealVector(sol));
System.out.println("Second constraint is violated!");
}
}
It's an odd problem, but something I ran across. I tracked the problem to the
getPivotRow routine in SimplexSolver. It was choosing a pivot that resulted in
a negative right-hand-side. I recommend a fix by replacing
...
if (MathUtils.equals(ratio, minRatio, epsilon)) {
...
with
...
if (MathUtils.equals(ratio, minRatio, Math.abs(epsilon/entry)))
{
...
I believe this would be more appropriate (and at least resolves this particular
problem).
Also, you may want to consider making a change in getPivotColumn to replace
...
if (MathUtils.compareTo(tableau.getEntry(0, i), minValue, epsilon)
< 0) {
...
with
...
if (tableau.getEntry(0, i) < minValue)
...
because I don't see the point of biasing earlier columns when multiple entries
are within epsilon of each other. Why not pick the absolute smallest. I don't
know that any problem can result from doing it the other way, but the latter
may be a safer bet.
VERY IMPORTANT: I discovered another bug that occurs when not restricting to
non-negatives. In SimplexTableu::getSolution(),
...
if (basicRows.contains(basicRow))
// if multiple variables can take a given value
// then we choose the first and set the rest equal to 0
coefficients[i] = 0;
...
should be
...
if (basicRows.contains(basicRow)) {
// if multiple variables can take a given value
// then we choose the first and set the rest equal to 0
coefficients[i] = (restrictToNonNegative ? 0 : -mostNegative);
...
If necessary, I can give an example of where this bug causes a problem, but it
should be fairly obvious why this was wrong.
was:
The SimplexSolver is returning an unfeasible solution:
import java.util.ArrayList;
import java.text.DecimalFormat;
import org.apache.commons.math.linear.ArrayRealVector;
import org.apache.commons.math.optimization.GoalType;
import org.apache.commons.math.optimization.OptimizationException;
import org.apache.commons.math.optimization.linear.*;
public class SimplexSolverBug {
public static void main(String[] args) throws OptimizationException {
LinearObjectiveFunction c = new LinearObjectiveFunction(new
double[]{0.0d, 1.0d, 1.0d, 0.0d, 0.0d, 0.0d, 0.0d}, 0.0d);
ArrayList<LinearConstraint> cnsts = new ArrayList<LinearConstraint>(5);
LinearConstraint cnst;
cnst = new LinearConstraint(new double[] {1.0d, -0.1d, 0.0d, 0.0d,
0.0d, 0.0d, 0.0d}, Relationship.EQ, -0.1d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {1.0d, 0.0d, 0.0d, 0.0d, 0.0d,
0.0d, 0.0d}, Relationship.GEQ, -1e-18d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 1.0d, 0.0d, 0.0d, 0.0d,
0.0d, 0.0d}, Relationship.GEQ, 0.0d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 0.0d, 1.0d, 0.0d,
-0.0128588d, 1e-5d}, Relationship.EQ, 0.0d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 0.0d, 0.0d, 1.0d,
1e-5d, -0.0128586d}, Relationship.EQ, 1e-10d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, -1.0d,
0.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 1.0d, 0.0d,
0.0d, 0.0d}, Relationship.GEQ, 0.0d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 0.0d,
-1.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d);
cnsts.add(cnst);
cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 0.0d, 1.0d,
0.0d, 0.0d}, Relationship.GEQ, 0.0d);
cnsts.add(cnst);
DecimalFormat df = new java.text.DecimalFormat("0.#####E0");
System.out.println("Constraints:");
for(LinearConstraint con : cnsts) {
for (int i = 0; i < con.getCoefficients().getDimension(); ++i)
System.out.print(df.format(con.getCoefficients().getData()[i])
+ " ");
System.out.println(con.getRelationship() + " " + con.getValue());
}
SimplexSolver simplex = new SimplexSolver(1e-7);
double[] sol = simplex.optimize(c, cnsts, GoalType.MINIMIZE,
false).getPointRef();
System.out.println("Solution:\n" + new ArrayRealVector(sol));
System.out.println("Second constraint is violated!");
}
}
It's an odd problem, but something I ran across. I tracked the problem to the
getPivotRow routine in SimplexSolver. It was choosing a pivot that resulted in
a negative right-hand-side. I recommend a fix by replacing
...
final double ratio = rhs / entry;
if (MathUtils.equals(ratio, minRatio, epsilon)) {
minRatioPositions.add(i);
} else {
...
with
...
if (MathUtils.equals(rhs, minRatio*entry, epsilon)) {
minRatioPositions.add(i);
} else {
final double ratio = rhs / entry;
...
I believe this would be more appropriate (and at least resolves this particular
problem).
My original suggested fix had a potential for overflow errors (since minRatio
is initialized to Double.MAX_VALUE). Also, I added another suggestion and
pointed out another bug which leads to invalid solutions.
> SimplexSolver returns unfeasible solution
> -----------------------------------------
>
> Key: MATH-434
> URL: https://issues.apache.org/jira/browse/MATH-434
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.1
> Reporter: Wayne Witzel
>
> The SimplexSolver is returning an unfeasible solution:
> import java.util.ArrayList;
> import java.text.DecimalFormat;
> import org.apache.commons.math.linear.ArrayRealVector;
> import org.apache.commons.math.optimization.GoalType;
> import org.apache.commons.math.optimization.OptimizationException;
> import org.apache.commons.math.optimization.linear.*;
> public class SimplexSolverBug {
>
> public static void main(String[] args) throws OptimizationException {
>
> LinearObjectiveFunction c = new LinearObjectiveFunction(new
> double[]{0.0d, 1.0d, 1.0d, 0.0d, 0.0d, 0.0d, 0.0d}, 0.0d);
>
> ArrayList<LinearConstraint> cnsts = new
> ArrayList<LinearConstraint>(5);
> LinearConstraint cnst;
> cnst = new LinearConstraint(new double[] {1.0d, -0.1d, 0.0d, 0.0d,
> 0.0d, 0.0d, 0.0d}, Relationship.EQ, -0.1d);
> cnsts.add(cnst);
> cnst = new LinearConstraint(new double[] {1.0d, 0.0d, 0.0d, 0.0d,
> 0.0d, 0.0d, 0.0d}, Relationship.GEQ, -1e-18d);
> cnsts.add(cnst);
> cnst = new LinearConstraint(new double[] {0.0d, 1.0d, 0.0d, 0.0d,
> 0.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d);
> cnsts.add(cnst);
> cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 0.0d, 1.0d,
> 0.0d, -0.0128588d, 1e-5d}, Relationship.EQ, 0.0d);
> cnsts.add(cnst);
> cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 0.0d, 0.0d,
> 1.0d, 1e-5d, -0.0128586d}, Relationship.EQ, 1e-10d);
> cnsts.add(cnst);
> cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, -1.0d,
> 0.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d);
> cnsts.add(cnst);
> cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 1.0d,
> 0.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d);
> cnsts.add(cnst);
> cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 0.0d,
> -1.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d);
> cnsts.add(cnst);
> cnst = new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 0.0d,
> 1.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d);
> cnsts.add(cnst);
>
> DecimalFormat df = new java.text.DecimalFormat("0.#####E0");
>
> System.out.println("Constraints:");
> for(LinearConstraint con : cnsts) {
> for (int i = 0; i < con.getCoefficients().getDimension(); ++i)
>
> System.out.print(df.format(con.getCoefficients().getData()[i]) + " ");
> System.out.println(con.getRelationship() + " " + con.getValue());
> }
>
> SimplexSolver simplex = new SimplexSolver(1e-7);
> double[] sol = simplex.optimize(c, cnsts, GoalType.MINIMIZE,
> false).getPointRef();
> System.out.println("Solution:\n" + new ArrayRealVector(sol));
> System.out.println("Second constraint is violated!");
> }
> }
> It's an odd problem, but something I ran across. I tracked the problem to
> the getPivotRow routine in SimplexSolver. It was choosing a pivot that
> resulted in a negative right-hand-side. I recommend a fix by replacing
> ...
> if (MathUtils.equals(ratio, minRatio, epsilon)) {
> ...
> with
> ...
> if (MathUtils.equals(ratio, minRatio,
> Math.abs(epsilon/entry))) {
> ...
> I believe this would be more appropriate (and at least resolves this
> particular problem).
> Also, you may want to consider making a change in getPivotColumn to replace
> ...
> if (MathUtils.compareTo(tableau.getEntry(0, i), minValue,
> epsilon) < 0) {
> ...
> with
> ...
> if (tableau.getEntry(0, i) < minValue)
> ...
> because I don't see the point of biasing earlier columns when multiple
> entries are within epsilon of each other. Why not pick the absolute
> smallest. I don't know that any problem can result from doing it the other
> way, but the latter may be a safer bet.
> VERY IMPORTANT: I discovered another bug that occurs when not restricting to
> non-negatives. In SimplexTableu::getSolution(),
> ...
> if (basicRows.contains(basicRow))
> // if multiple variables can take a given value
> // then we choose the first and set the rest equal to 0
> coefficients[i] = 0;
> ...
> should be
> ...
> if (basicRows.contains(basicRow)) {
> // if multiple variables can take a given value
> // then we choose the first and set the rest equal to 0
> coefficients[i] = (restrictToNonNegative ? 0 : -mostNegative);
> ...
> If necessary, I can give an example of where this bug causes a problem, but
> it should be fairly obvious why this was wrong.
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