SimplexSolver.java
- /*
- * 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.
- *
- * @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) && 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();
- }
- }