001 /*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements. See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License. You may obtain a copy of the License at
008 *
009 * http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018 package org.apache.commons.math3.optimization.linear;
019
020 import java.util.ArrayList;
021 import java.util.List;
022
023 import org.apache.commons.math3.exception.MaxCountExceededException;
024 import org.apache.commons.math3.optimization.PointValuePair;
025 import org.apache.commons.math3.util.Precision;
026
027
028 /**
029 * Solves a linear problem using the Two-Phase Simplex Method.
030 *
031 * @version $Id: SimplexSolver.java 1422230 2012-12-15 12:11:13Z erans $
032 * @deprecated As of 3.1 (to be removed in 4.0).
033 * @since 2.0
034 */
035 @Deprecated
036 public class SimplexSolver extends AbstractLinearOptimizer {
037
038 /** Default amount of error to accept for algorithm convergence. */
039 private static final double DEFAULT_EPSILON = 1.0e-6;
040
041 /** Default amount of error to accept in floating point comparisons (as ulps). */
042 private static final int DEFAULT_ULPS = 10;
043
044 /** Amount of error to accept for algorithm convergence. */
045 private final double epsilon;
046
047 /** Amount of error to accept in floating point comparisons (as ulps). */
048 private final int maxUlps;
049
050 /**
051 * Build a simplex solver with default settings.
052 */
053 public SimplexSolver() {
054 this(DEFAULT_EPSILON, DEFAULT_ULPS);
055 }
056
057 /**
058 * Build a simplex solver with a specified accepted amount of error
059 * @param epsilon the amount of error to accept for algorithm convergence
060 * @param maxUlps amount of error to accept in floating point comparisons
061 */
062 public SimplexSolver(final double epsilon, final int maxUlps) {
063 this.epsilon = epsilon;
064 this.maxUlps = maxUlps;
065 }
066
067 /**
068 * Returns the column with the most negative coefficient in the objective function row.
069 * @param tableau simple tableau for the problem
070 * @return column with the most negative coefficient
071 */
072 private Integer getPivotColumn(SimplexTableau tableau) {
073 double minValue = 0;
074 Integer minPos = null;
075 for (int i = tableau.getNumObjectiveFunctions(); i < tableau.getWidth() - 1; i++) {
076 final double entry = tableau.getEntry(0, i);
077 // check if the entry is strictly smaller than the current minimum
078 // do not use a ulp/epsilon check
079 if (entry < minValue) {
080 minValue = entry;
081 minPos = i;
082 }
083 }
084 return minPos;
085 }
086
087 /**
088 * Returns the row with the minimum ratio as given by the minimum ratio test (MRT).
089 * @param tableau simple tableau for the problem
090 * @param col the column to test the ratio of. See {@link #getPivotColumn(SimplexTableau)}
091 * @return row with the minimum ratio
092 */
093 private Integer getPivotRow(SimplexTableau tableau, final int col) {
094 // create a list of all the rows that tie for the lowest score in the minimum ratio test
095 List<Integer> minRatioPositions = new ArrayList<Integer>();
096 double minRatio = Double.MAX_VALUE;
097 for (int i = tableau.getNumObjectiveFunctions(); i < tableau.getHeight(); i++) {
098 final double rhs = tableau.getEntry(i, tableau.getWidth() - 1);
099 final double entry = tableau.getEntry(i, col);
100
101 if (Precision.compareTo(entry, 0d, maxUlps) > 0) {
102 final double ratio = rhs / entry;
103 // check if the entry is strictly equal to the current min ratio
104 // do not use a ulp/epsilon check
105 final int cmp = Double.compare(ratio, minRatio);
106 if (cmp == 0) {
107 minRatioPositions.add(i);
108 } else if (cmp < 0) {
109 minRatio = ratio;
110 minRatioPositions = new ArrayList<Integer>();
111 minRatioPositions.add(i);
112 }
113 }
114 }
115
116 if (minRatioPositions.size() == 0) {
117 return null;
118 } else if (minRatioPositions.size() > 1) {
119 // there's a degeneracy as indicated by a tie in the minimum ratio test
120
121 // 1. check if there's an artificial variable that can be forced out of the basis
122 if (tableau.getNumArtificialVariables() > 0) {
123 for (Integer row : minRatioPositions) {
124 for (int i = 0; i < tableau.getNumArtificialVariables(); i++) {
125 int column = i + tableau.getArtificialVariableOffset();
126 final double entry = tableau.getEntry(row, column);
127 if (Precision.equals(entry, 1d, maxUlps) && row.equals(tableau.getBasicRow(column))) {
128 return row;
129 }
130 }
131 }
132 }
133
134 // 2. apply Bland's rule to prevent cycling:
135 // take the row for which the corresponding basic variable has the smallest index
136 //
137 // see http://www.stanford.edu/class/msande310/blandrule.pdf
138 // see http://en.wikipedia.org/wiki/Bland%27s_rule (not equivalent to the above paper)
139 //
140 // Additional heuristic: if we did not get a solution after half of maxIterations
141 // revert to the simple case of just returning the top-most row
142 // This heuristic is based on empirical data gathered while investigating MATH-828.
143 if (getIterations() < getMaxIterations() / 2) {
144 Integer minRow = null;
145 int minIndex = tableau.getWidth();
146 final int varStart = tableau.getNumObjectiveFunctions();
147 final int varEnd = tableau.getWidth() - 1;
148 for (Integer row : minRatioPositions) {
149 for (int i = varStart; i < varEnd && !row.equals(minRow); i++) {
150 final Integer basicRow = tableau.getBasicRow(i);
151 if (basicRow != null && basicRow.equals(row)) {
152 if (i < minIndex) {
153 minIndex = i;
154 minRow = row;
155 }
156 }
157 }
158 }
159 return minRow;
160 }
161 }
162 return minRatioPositions.get(0);
163 }
164
165 /**
166 * Runs one iteration of the Simplex method on the given model.
167 * @param tableau simple tableau for the problem
168 * @throws MaxCountExceededException if the maximal iteration count has been exceeded
169 * @throws UnboundedSolutionException if the model is found not to have a bounded solution
170 */
171 protected void doIteration(final SimplexTableau tableau)
172 throws MaxCountExceededException, UnboundedSolutionException {
173
174 incrementIterationsCounter();
175
176 Integer pivotCol = getPivotColumn(tableau);
177 Integer pivotRow = getPivotRow(tableau, pivotCol);
178 if (pivotRow == null) {
179 throw new UnboundedSolutionException();
180 }
181
182 // set the pivot element to 1
183 double pivotVal = tableau.getEntry(pivotRow, pivotCol);
184 tableau.divideRow(pivotRow, pivotVal);
185
186 // set the rest of the pivot column to 0
187 for (int i = 0; i < tableau.getHeight(); i++) {
188 if (i != pivotRow) {
189 final double multiplier = tableau.getEntry(i, pivotCol);
190 tableau.subtractRow(i, pivotRow, multiplier);
191 }
192 }
193 }
194
195 /**
196 * Solves Phase 1 of the Simplex method.
197 * @param tableau simple tableau for the problem
198 * @throws MaxCountExceededException if the maximal iteration count has been exceeded
199 * @throws UnboundedSolutionException if the model is found not to have a bounded solution
200 * @throws NoFeasibleSolutionException if there is no feasible solution
201 */
202 protected void solvePhase1(final SimplexTableau tableau)
203 throws MaxCountExceededException, UnboundedSolutionException, NoFeasibleSolutionException {
204
205 // make sure we're in Phase 1
206 if (tableau.getNumArtificialVariables() == 0) {
207 return;
208 }
209
210 while (!tableau.isOptimal()) {
211 doIteration(tableau);
212 }
213
214 // if W is not zero then we have no feasible solution
215 if (!Precision.equals(tableau.getEntry(0, tableau.getRhsOffset()), 0d, epsilon)) {
216 throw new NoFeasibleSolutionException();
217 }
218 }
219
220 /** {@inheritDoc} */
221 @Override
222 public PointValuePair doOptimize()
223 throws MaxCountExceededException, UnboundedSolutionException, NoFeasibleSolutionException {
224 final SimplexTableau tableau =
225 new SimplexTableau(getFunction(),
226 getConstraints(),
227 getGoalType(),
228 restrictToNonNegative(),
229 epsilon,
230 maxUlps);
231
232 solvePhase1(tableau);
233 tableau.dropPhase1Objective();
234
235 while (!tableau.isOptimal()) {
236 doIteration(tableau);
237 }
238 return tableau.getSolution();
239 }
240
241 }