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    }