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Diffstat (limited to 'src/main/java/org/apache/commons/math/optimization/linear/SimplexSolver.java')
-rw-r--r-- | src/main/java/org/apache/commons/math/optimization/linear/SimplexSolver.java | 185 |
1 files changed, 185 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math/optimization/linear/SimplexSolver.java b/src/main/java/org/apache/commons/math/optimization/linear/SimplexSolver.java new file mode 100644 index 0000000..830f65c --- /dev/null +++ b/src/main/java/org/apache/commons/math/optimization/linear/SimplexSolver.java @@ -0,0 +1,185 @@ +/* + * 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.math.optimization.linear; + +import java.util.ArrayList; +import java.util.List; + +import org.apache.commons.math.optimization.OptimizationException; +import org.apache.commons.math.optimization.RealPointValuePair; +import org.apache.commons.math.util.MathUtils; + + +/** + * Solves a linear problem using the Two-Phase Simplex Method. + * @version $Revision: 812831 $ $Date: 2009-09-09 10:48:03 +0200 (mer. 09 sept. 2009) $ + * @since 2.0 + */ +public class SimplexSolver extends AbstractLinearOptimizer { + + /** Default amount of error to accept in floating point comparisons. */ + private static final double DEFAULT_EPSILON = 1.0e-6; + + /** Amount of error to accept in floating point comparisons. */ + protected final double epsilon; + + /** + * Build a simplex solver with default settings. + */ + public SimplexSolver() { + this(DEFAULT_EPSILON); + } + + /** + * Build a simplex solver with a specified accepted amount of error + * @param epsilon the amount of error to accept in floating point comparisons + */ + public SimplexSolver(final double epsilon) { + this.epsilon = epsilon; + } + + /** + * 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++) { + if (MathUtils.compareTo(tableau.getEntry(0, i), minValue, epsilon) < 0) { + minValue = tableau.getEntry(0, i); + 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 (MathUtils.compareTo(entry, 0, epsilon) > 0) { + final double ratio = rhs / entry; + if (MathUtils.equals(ratio, minRatio, epsilon)) { + minRatioPositions.add(i); + } else if (ratio < minRatio) { + 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 + // check if there's an artificial variable that can be forced out of the basis + for (Integer row : minRatioPositions) { + for (int i = 0; i < tableau.getNumArtificialVariables(); i++) { + int column = i + tableau.getArtificialVariableOffset(); + if (MathUtils.equals(tableau.getEntry(row, column), 1, epsilon) && + row.equals(tableau.getBasicRow(column))) { + return row; + } + } + } + } + return minRatioPositions.get(0); + } + + /** + * Runs one iteration of the Simplex method on the given model. + * @param tableau simple tableau for the problem + * @throws OptimizationException if the maximal iteration count has been + * exceeded or if the model is found not to have a bounded solution + */ + protected void doIteration(final SimplexTableau tableau) + throws OptimizationException { + + 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) { + 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 + * @exception OptimizationException if the maximal number of iterations is + * exceeded, or if the problem is found not to have a bounded solution, or + * if there is no feasible solution + */ + protected void solvePhase1(final SimplexTableau tableau) throws OptimizationException { + + // 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 (!MathUtils.equals(tableau.getEntry(0, tableau.getRhsOffset()), 0, epsilon)) { + throw new NoFeasibleSolutionException(); + } + } + + /** {@inheritDoc} */ + @Override + public RealPointValuePair doOptimize() throws OptimizationException { + final SimplexTableau tableau = + new SimplexTableau(function, linearConstraints, goal, nonNegative, epsilon); + + solvePhase1(tableau); + tableau.dropPhase1Objective(); + + while (!tableau.isOptimal()) { + doIteration(tableau); + } + return tableau.getSolution(); + } + +} |