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.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(); } }