Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 1 | /* |
| 2 | * Licensed to the Apache Software Foundation (ASF) under one or more |
| 3 | * contributor license agreements. See the NOTICE file distributed with |
| 4 | * this work for additional information regarding copyright ownership. |
| 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 |
| 6 | * (the "License"); you may not use this file except in compliance with |
| 7 | * the License. You may obtain a copy of the License at |
| 8 | * |
| 9 | * http://www.apache.org/licenses/LICENSE-2.0 |
| 10 | * |
| 11 | * Unless required by applicable law or agreed to in writing, software |
| 12 | * distributed under the License is distributed on an "AS IS" BASIS, |
| 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 14 | * See the License for the specific language governing permissions and |
| 15 | * limitations under the License. |
| 16 | */ |
| 17 | |
| 18 | package org.apache.commons.math.optimization.linear; |
| 19 | |
| 20 | import java.util.ArrayList; |
| 21 | import java.util.List; |
| 22 | |
| 23 | import org.apache.commons.math.optimization.OptimizationException; |
| 24 | import org.apache.commons.math.optimization.RealPointValuePair; |
| 25 | import org.apache.commons.math.util.MathUtils; |
| 26 | |
| 27 | |
| 28 | /** |
| 29 | * Solves a linear problem using the Two-Phase Simplex Method. |
| 30 | * @version $Revision: 812831 $ $Date: 2009-09-09 10:48:03 +0200 (mer. 09 sept. 2009) $ |
| 31 | * @since 2.0 |
| 32 | */ |
| 33 | public class SimplexSolver extends AbstractLinearOptimizer { |
| 34 | |
| 35 | /** Default amount of error to accept in floating point comparisons. */ |
| 36 | private static final double DEFAULT_EPSILON = 1.0e-6; |
| 37 | |
| 38 | /** Amount of error to accept in floating point comparisons. */ |
| 39 | protected final double epsilon; |
| 40 | |
| 41 | /** |
| 42 | * Build a simplex solver with default settings. |
| 43 | */ |
| 44 | public SimplexSolver() { |
| 45 | this(DEFAULT_EPSILON); |
| 46 | } |
| 47 | |
| 48 | /** |
| 49 | * Build a simplex solver with a specified accepted amount of error |
| 50 | * @param epsilon the amount of error to accept in floating point comparisons |
| 51 | */ |
| 52 | public SimplexSolver(final double epsilon) { |
| 53 | this.epsilon = epsilon; |
| 54 | } |
| 55 | |
| 56 | /** |
| 57 | * Returns the column with the most negative coefficient in the objective function row. |
| 58 | * @param tableau simple tableau for the problem |
| 59 | * @return column with the most negative coefficient |
| 60 | */ |
| 61 | private Integer getPivotColumn(SimplexTableau tableau) { |
| 62 | double minValue = 0; |
| 63 | Integer minPos = null; |
| 64 | for (int i = tableau.getNumObjectiveFunctions(); i < tableau.getWidth() - 1; i++) { |
| 65 | if (MathUtils.compareTo(tableau.getEntry(0, i), minValue, epsilon) < 0) { |
| 66 | minValue = tableau.getEntry(0, i); |
| 67 | minPos = i; |
| 68 | } |
| 69 | } |
| 70 | return minPos; |
| 71 | } |
| 72 | |
| 73 | /** |
| 74 | * Returns the row with the minimum ratio as given by the minimum ratio test (MRT). |
| 75 | * @param tableau simple tableau for the problem |
| 76 | * @param col the column to test the ratio of. See {@link #getPivotColumn(SimplexTableau)} |
| 77 | * @return row with the minimum ratio |
| 78 | */ |
| 79 | private Integer getPivotRow(SimplexTableau tableau, final int col) { |
| 80 | // create a list of all the rows that tie for the lowest score in the minimum ratio test |
| 81 | List<Integer> minRatioPositions = new ArrayList<Integer>(); |
| 82 | double minRatio = Double.MAX_VALUE; |
| 83 | for (int i = tableau.getNumObjectiveFunctions(); i < tableau.getHeight(); i++) { |
| 84 | final double rhs = tableau.getEntry(i, tableau.getWidth() - 1); |
| 85 | final double entry = tableau.getEntry(i, col); |
| 86 | if (MathUtils.compareTo(entry, 0, epsilon) > 0) { |
| 87 | final double ratio = rhs / entry; |
| 88 | if (MathUtils.equals(ratio, minRatio, epsilon)) { |
| 89 | minRatioPositions.add(i); |
| 90 | } else if (ratio < minRatio) { |
| 91 | minRatio = ratio; |
| 92 | minRatioPositions = new ArrayList<Integer>(); |
| 93 | minRatioPositions.add(i); |
| 94 | } |
| 95 | } |
| 96 | } |
| 97 | |
| 98 | if (minRatioPositions.size() == 0) { |
| 99 | return null; |
| 100 | } else if (minRatioPositions.size() > 1) { |
| 101 | // there's a degeneracy as indicated by a tie in the minimum ratio test |
| 102 | // check if there's an artificial variable that can be forced out of the basis |
| 103 | for (Integer row : minRatioPositions) { |
| 104 | for (int i = 0; i < tableau.getNumArtificialVariables(); i++) { |
| 105 | int column = i + tableau.getArtificialVariableOffset(); |
| 106 | if (MathUtils.equals(tableau.getEntry(row, column), 1, epsilon) && |
| 107 | row.equals(tableau.getBasicRow(column))) { |
| 108 | return row; |
| 109 | } |
| 110 | } |
| 111 | } |
| 112 | } |
| 113 | return minRatioPositions.get(0); |
| 114 | } |
| 115 | |
| 116 | /** |
| 117 | * Runs one iteration of the Simplex method on the given model. |
| 118 | * @param tableau simple tableau for the problem |
| 119 | * @throws OptimizationException if the maximal iteration count has been |
| 120 | * exceeded or if the model is found not to have a bounded solution |
| 121 | */ |
| 122 | protected void doIteration(final SimplexTableau tableau) |
| 123 | throws OptimizationException { |
| 124 | |
| 125 | incrementIterationsCounter(); |
| 126 | |
| 127 | Integer pivotCol = getPivotColumn(tableau); |
| 128 | Integer pivotRow = getPivotRow(tableau, pivotCol); |
| 129 | if (pivotRow == null) { |
| 130 | throw new UnboundedSolutionException(); |
| 131 | } |
| 132 | |
| 133 | // set the pivot element to 1 |
| 134 | double pivotVal = tableau.getEntry(pivotRow, pivotCol); |
| 135 | tableau.divideRow(pivotRow, pivotVal); |
| 136 | |
| 137 | // set the rest of the pivot column to 0 |
| 138 | for (int i = 0; i < tableau.getHeight(); i++) { |
| 139 | if (i != pivotRow) { |
| 140 | double multiplier = tableau.getEntry(i, pivotCol); |
| 141 | tableau.subtractRow(i, pivotRow, multiplier); |
| 142 | } |
| 143 | } |
| 144 | } |
| 145 | |
| 146 | /** |
| 147 | * Solves Phase 1 of the Simplex method. |
| 148 | * @param tableau simple tableau for the problem |
| 149 | * @exception OptimizationException if the maximal number of iterations is |
| 150 | * exceeded, or if the problem is found not to have a bounded solution, or |
| 151 | * if there is no feasible solution |
| 152 | */ |
| 153 | protected void solvePhase1(final SimplexTableau tableau) throws OptimizationException { |
| 154 | |
| 155 | // make sure we're in Phase 1 |
| 156 | if (tableau.getNumArtificialVariables() == 0) { |
| 157 | return; |
| 158 | } |
| 159 | |
| 160 | while (!tableau.isOptimal()) { |
| 161 | doIteration(tableau); |
| 162 | } |
| 163 | |
| 164 | // if W is not zero then we have no feasible solution |
| 165 | if (!MathUtils.equals(tableau.getEntry(0, tableau.getRhsOffset()), 0, epsilon)) { |
| 166 | throw new NoFeasibleSolutionException(); |
| 167 | } |
| 168 | } |
| 169 | |
| 170 | /** {@inheritDoc} */ |
| 171 | @Override |
| 172 | public RealPointValuePair doOptimize() throws OptimizationException { |
| 173 | final SimplexTableau tableau = |
| 174 | new SimplexTableau(function, linearConstraints, goal, nonNegative, epsilon); |
| 175 | |
| 176 | solvePhase1(tableau); |
| 177 | tableau.dropPhase1Objective(); |
| 178 | |
| 179 | while (!tableau.isOptimal()) { |
| 180 | doIteration(tableau); |
| 181 | } |
| 182 | return tableau.getSolution(); |
| 183 | } |
| 184 | |
| 185 | } |