[MATH-1079] Further improvements to SimplexSolver.
git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1552046 13f79535-47bb-0310-9956-ffa450edef68
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Thomas Neidhart
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@ -22,6 +22,7 @@ import java.util.List;
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import org.apache.commons.math3.exception.TooManyIterationsException;
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import org.apache.commons.math3.optim.OptimizationData;
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import org.apache.commons.math3.optim.PointValuePair;
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import org.apache.commons.math3.util.FastMath;
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import org.apache.commons.math3.util.Precision;
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/**
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@ -49,7 +50,7 @@ import org.apache.commons.math3.util.Precision;
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* <ul>
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* <li>Algorithm convergence: 1e-6</li>
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* <li>Floating-point comparisons: 10 ulp</li>
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* <li>Cut-Off value: 1e-12</li>
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* <li>Cut-Off value: 1e-10</li>
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* </ul>
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* <p>
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* The cut-off value has been introduced to zero out very small numbers in the Simplex tableau,
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@ -66,7 +67,7 @@ public class SimplexSolver extends LinearOptimizer {
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static final int DEFAULT_ULPS = 10;
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/** Default cut-off value. */
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static final double DEFAULT_CUT_OFF = 1e-12;
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static final double DEFAULT_CUT_OFF = 1e-10;
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/** Default amount of error to accept for algorithm convergence. */
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private static final double DEFAULT_EPSILON = 1.0e-6;
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@ -249,7 +250,11 @@ public class SimplexSolver extends LinearOptimizer {
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final double rhs = tableau.getEntry(i, tableau.getWidth() - 1);
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final double entry = tableau.getEntry(i, col);
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if (Precision.compareTo(entry, 0d, maxUlps) > 0) {
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// zero-out tableau entries that are too close to zero to avoid
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// numerical instabilities as these entries might be used as divisor
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if (FastMath.abs(entry) < cutOff) {
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tableau.setEntry(i, col, 0);
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} else if (Precision.compareTo(entry, 0d, maxUlps) > 0) {
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final double ratio = rhs / entry;
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// check if the entry is strictly equal to the current min ratio
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// do not use a ulp/epsilon check
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@ -371,8 +376,7 @@ public class SimplexSolver extends LinearOptimizer {
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getGoalType(),
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isRestrictedToNonNegative(),
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epsilon,
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maxUlps,
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cutOff);
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maxUlps);
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solvePhase1(tableau);
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tableau.dropPhase1Objective();
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@ -33,7 +33,6 @@ import org.apache.commons.math3.linear.MatrixUtils;
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import org.apache.commons.math3.linear.RealVector;
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import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;
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import org.apache.commons.math3.optim.PointValuePair;
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import org.apache.commons.math3.util.FastMath;
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import org.apache.commons.math3.util.Precision;
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/**
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@ -99,9 +98,6 @@ class SimplexTableau implements Serializable {
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/** Amount of error to accept in floating point comparisons. */
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private final int maxUlps;
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/** Cut-off value for entries in the tableau. */
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private final double cutOff;
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/** Maps basic variables to row they are basic in. */
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private int[] basicVariables;
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@ -123,8 +119,7 @@ class SimplexTableau implements Serializable {
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final GoalType goalType,
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final boolean restrictToNonNegative,
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final double epsilon) {
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this(f, constraints, goalType, restrictToNonNegative, epsilon,
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SimplexSolver.DEFAULT_ULPS, SimplexSolver.DEFAULT_CUT_OFF);
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this(f, constraints, goalType, restrictToNonNegative, epsilon, SimplexSolver.DEFAULT_ULPS);
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}
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/**
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@ -142,32 +137,11 @@ class SimplexTableau implements Serializable {
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final boolean restrictToNonNegative,
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final double epsilon,
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final int maxUlps) {
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this(f, constraints, goalType, restrictToNonNegative, epsilon, maxUlps, SimplexSolver.DEFAULT_CUT_OFF);
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}
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/**
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* Build a tableau for a linear problem.
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* @param f linear objective function
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* @param constraints linear constraints
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* @param goalType type of optimization goal: either {@link GoalType#MAXIMIZE} or {@link GoalType#MINIMIZE}
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* @param restrictToNonNegative whether to restrict the variables to non-negative values
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* @param epsilon amount of error to accept when checking for optimality
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* @param maxUlps amount of error to accept in floating point comparisons
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* @param cutOff the cut-off value for tableau entries
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*/
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SimplexTableau(final LinearObjectiveFunction f,
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final Collection<LinearConstraint> constraints,
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final GoalType goalType,
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final boolean restrictToNonNegative,
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final double epsilon,
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final int maxUlps,
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final double cutOff) {
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this.f = f;
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this.constraints = normalizeConstraints(constraints);
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this.restrictToNonNegative = restrictToNonNegative;
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this.epsilon = epsilon;
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this.maxUlps = maxUlps;
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this.cutOff = cutOff;
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this.numDecisionVariables = f.getCoefficients().getDimension() + (restrictToNonNegative ? 0 : 1);
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this.numSlackVariables = getConstraintTypeCounts(Relationship.LEQ) +
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getConstraintTypeCounts(Relationship.GEQ);
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@ -516,7 +490,9 @@ class SimplexTableau implements Serializable {
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for (int i = 0; i < getHeight(); i++) {
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if (i != pivotRow) {
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final double multiplier = getEntry(i, pivotCol);
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subtractRow(i, pivotRow, multiplier);
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if (multiplier != 0.0) {
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subtractRow(i, pivotRow, multiplier);
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}
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}
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}
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@ -557,12 +533,7 @@ class SimplexTableau implements Serializable {
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final double[] minuendRow = getRow(minuendRowIndex);
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final double[] subtrahendRow = getRow(subtrahendRowIndex);
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for (int i = 0; i < getWidth(); i++) {
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double result = minuendRow[i] - subtrahendRow[i] * multiplier;
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// cut-off values smaller than the cut-off threshold, otherwise may lead to numerical instabilities
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if (result != 0.0 && FastMath.abs(result) < cutOff) {
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result = 0.0;
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}
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minuendRow[i] = result;
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minuendRow[i] -= subtrahendRow[i] * multiplier;
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}
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}
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@ -750,7 +750,7 @@ public class SimplexSolverTest {
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@Test
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public void testSolutionCallback() {
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// re-use the problem from testcase for MATH-930
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// it normally requires 113 iterations
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// it normally requires 144 iterations
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final List<LinearConstraint> constraints = createMath930Constraints();
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double[] objFunctionCoeff = new double[33];
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@ -777,9 +777,10 @@ public class SimplexSolverTest {
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// 2. iteration limit allows to reach phase 2, but too low to find an optimal solution
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try {
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// we need to use a DeterministicLinearConstraintSet to always get the same behavior
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solver.optimize(new MaxIter(112), f, new LinearConstraintSet(constraints),
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solver.optimize(new MaxIter(140), f, new LinearConstraintSet(constraints),
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GoalType.MINIMIZE, new NonNegativeConstraint(true), callback,
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PivotSelectionRule.BLAND);
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PivotSelectionRule.DANTZIG);
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System.out.println(solver.getIterations());
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Assert.fail("expected TooManyIterationsException");
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} catch (TooManyIterationsException ex) {
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// expected
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