Java tutorial
/* * 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. * * @version $Id: SimplexSolver.java 1422230 2012-12-15 12:11:13Z erans $ * @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)) { if (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(); } }