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Diffstat (limited to 'src/main/java/org/apache/commons/math3/optimization/linear/SimplexSolver.java')
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1 files changed, 238 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/optimization/linear/SimplexSolver.java b/src/main/java/org/apache/commons/math3/optimization/linear/SimplexSolver.java new file mode 100644 index 0000000..1e5dbda --- /dev/null +++ b/src/main/java/org/apache/commons/math3/optimization/linear/SimplexSolver.java @@ -0,0 +1,238 @@ +/* + * Licensed to the Apache Software Foundation (ASF) under one or more + * contributor license agreements. See the NOTICE file distributed with + * this work for additional information regarding copyright ownership. + * The ASF licenses this file to You under the Apache License, Version 2.0 + * (the "License"); you may not use this file except in compliance with + * the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +package org.apache.commons.math3.optimization.linear; + +import java.util.ArrayList; +import java.util.List; + +import org.apache.commons.math3.exception.MaxCountExceededException; +import org.apache.commons.math3.optimization.PointValuePair; +import org.apache.commons.math3.util.Precision; + + +/** + * Solves a linear problem using the Two-Phase Simplex Method. + * + * @deprecated As of 3.1 (to be removed in 4.0). + * @since 2.0 + */ +@Deprecated +public class SimplexSolver extends AbstractLinearOptimizer { + + /** Default amount of error to accept for algorithm convergence. */ + private static final double DEFAULT_EPSILON = 1.0e-6; + + /** Default amount of error to accept in floating point comparisons (as ulps). */ + private static final int DEFAULT_ULPS = 10; + + /** Amount of error to accept for algorithm convergence. */ + private final double epsilon; + + /** Amount of error to accept in floating point comparisons (as ulps). */ + private final int maxUlps; + + /** + * Build a simplex solver with default settings. + */ + public SimplexSolver() { + this(DEFAULT_EPSILON, DEFAULT_ULPS); + } + + /** + * Build a simplex solver with a specified accepted amount of error + * @param epsilon the amount of error to accept for algorithm convergence + * @param maxUlps amount of error to accept in floating point comparisons + */ + public SimplexSolver(final double epsilon, final int maxUlps) { + this.epsilon = epsilon; + this.maxUlps = maxUlps; + } + + /** + * Returns the column with the most negative coefficient in the objective function row. + * @param tableau simple tableau for the problem + * @return column with the most negative coefficient + */ + private Integer getPivotColumn(SimplexTableau tableau) { + double minValue = 0; + Integer minPos = null; + for (int i = tableau.getNumObjectiveFunctions(); i < tableau.getWidth() - 1; i++) { + final double entry = tableau.getEntry(0, i); + // check if the entry is strictly smaller than the current minimum + // do not use a ulp/epsilon check + if (entry < minValue) { + minValue = entry; + minPos = i; + } + } + return minPos; + } + + /** + * Returns the row with the minimum ratio as given by the minimum ratio test (MRT). + * @param tableau simple tableau for the problem + * @param col the column to test the ratio of. See {@link #getPivotColumn(SimplexTableau)} + * @return row with the minimum ratio + */ + private Integer getPivotRow(SimplexTableau tableau, final int col) { + // create a list of all the rows that tie for the lowest score in the minimum ratio test + List<Integer> minRatioPositions = new ArrayList<Integer>(); + double minRatio = Double.MAX_VALUE; + for (int i = tableau.getNumObjectiveFunctions(); i < tableau.getHeight(); i++) { + final double rhs = tableau.getEntry(i, tableau.getWidth() - 1); + final double entry = tableau.getEntry(i, col); + + if (Precision.compareTo(entry, 0d, maxUlps) > 0) { + final double ratio = rhs / entry; + // check if the entry is strictly equal to the current min ratio + // do not use a ulp/epsilon check + final int cmp = Double.compare(ratio, minRatio); + if (cmp == 0) { + minRatioPositions.add(i); + } else if (cmp < 0) { + minRatio = ratio; + minRatioPositions = new ArrayList<Integer>(); + minRatioPositions.add(i); + } + } + } + + if (minRatioPositions.size() == 0) { + return null; + } else if (minRatioPositions.size() > 1) { + // there's a degeneracy as indicated by a tie in the minimum ratio test + + // 1. check if there's an artificial variable that can be forced out of the basis + if (tableau.getNumArtificialVariables() > 0) { + for (Integer row : minRatioPositions) { + for (int i = 0; i < tableau.getNumArtificialVariables(); i++) { + int column = i + tableau.getArtificialVariableOffset(); + final double entry = tableau.getEntry(row, column); + if (Precision.equals(entry, 1d, maxUlps) && row.equals(tableau.getBasicRow(column))) { + return row; + } + } + } + } + + // 2. apply Bland's rule to prevent cycling: + // take the row for which the corresponding basic variable has the smallest index + // + // see http://www.stanford.edu/class/msande310/blandrule.pdf + // see http://en.wikipedia.org/wiki/Bland%27s_rule (not equivalent to the above paper) + // + // Additional heuristic: if we did not get a solution after half of maxIterations + // revert to the simple case of just returning the top-most row + // This heuristic is based on empirical data gathered while investigating MATH-828. + if (getIterations() < getMaxIterations() / 2) { + Integer minRow = null; + int minIndex = tableau.getWidth(); + final int varStart = tableau.getNumObjectiveFunctions(); + final int varEnd = tableau.getWidth() - 1; + for (Integer row : minRatioPositions) { + for (int i = varStart; i < varEnd && !row.equals(minRow); i++) { + final Integer basicRow = tableau.getBasicRow(i); + if (basicRow != null && basicRow.equals(row) && i < minIndex) { + minIndex = i; + minRow = row; + } + } + } + return minRow; + } + } + return minRatioPositions.get(0); + } + + /** + * Runs one iteration of the Simplex method on the given model. + * @param tableau simple tableau for the problem + * @throws MaxCountExceededException if the maximal iteration count has been exceeded + * @throws UnboundedSolutionException if the model is found not to have a bounded solution + */ + protected void doIteration(final SimplexTableau tableau) + throws MaxCountExceededException, UnboundedSolutionException { + + incrementIterationsCounter(); + + Integer pivotCol = getPivotColumn(tableau); + Integer pivotRow = getPivotRow(tableau, pivotCol); + if (pivotRow == null) { + throw new UnboundedSolutionException(); + } + + // set the pivot element to 1 + double pivotVal = tableau.getEntry(pivotRow, pivotCol); + tableau.divideRow(pivotRow, pivotVal); + + // set the rest of the pivot column to 0 + for (int i = 0; i < tableau.getHeight(); i++) { + if (i != pivotRow) { + final double multiplier = tableau.getEntry(i, pivotCol); + tableau.subtractRow(i, pivotRow, multiplier); + } + } + } + + /** + * Solves Phase 1 of the Simplex method. + * @param tableau simple tableau for the problem + * @throws MaxCountExceededException if the maximal iteration count has been exceeded + * @throws UnboundedSolutionException if the model is found not to have a bounded solution + * @throws NoFeasibleSolutionException if there is no feasible solution + */ + protected void solvePhase1(final SimplexTableau tableau) + throws MaxCountExceededException, UnboundedSolutionException, NoFeasibleSolutionException { + + // make sure we're in Phase 1 + if (tableau.getNumArtificialVariables() == 0) { + return; + } + + while (!tableau.isOptimal()) { + doIteration(tableau); + } + + // if W is not zero then we have no feasible solution + if (!Precision.equals(tableau.getEntry(0, tableau.getRhsOffset()), 0d, epsilon)) { + throw new NoFeasibleSolutionException(); + } + } + + /** {@inheritDoc} */ + @Override + public PointValuePair doOptimize() + throws MaxCountExceededException, UnboundedSolutionException, NoFeasibleSolutionException { + final SimplexTableau tableau = + new SimplexTableau(getFunction(), + getConstraints(), + getGoalType(), + restrictToNonNegative(), + epsilon, + maxUlps); + + solvePhase1(tableau); + tableau.dropPhase1Objective(); + + while (!tableau.isOptimal()) { + doIteration(tableau); + } + return tableau.getSolution(); + } + +} |