src/main/java/org/apache/commons/math/optimization/linear/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.
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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();
    }

}