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Java example source code file (SimplexSolverTest.java)

This example Java source code file (SimplexSolverTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

arraylist, collection, illegalargumentexception, linearconstraint, linearconstraintset, linearobjectivefunction, maxiter, nonnegativeconstraint, pointvaluepair, simplexsolver, solutioncallback, string, test, toomanyiterationsexception, util

The SimplexSolverTest.java Java example source code

/*
 * 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.optim.linear;

import java.util.ArrayList;
import java.util.Collection;
import java.util.List;

import org.apache.commons.math3.exception.TooManyIterationsException;
import org.apache.commons.math3.optim.MaxIter;
import org.apache.commons.math3.optim.nonlinear.scalar.GoalType;
import org.apache.commons.math3.optim.PointValuePair;
import org.apache.commons.math3.util.Precision;
import org.junit.Test;
import org.junit.Assert;

public class SimplexSolverTest {
    private static final MaxIter DEFAULT_MAX_ITER = new MaxIter(100);

    @Test
    public void testMath842Cycle() {
        // from http://www.math.toronto.edu/mpugh/Teaching/APM236_04/bland
        //      maximize 10 x1 - 57 x2 - 9 x3 - 24 x4
        //      subject to
        //          1/2 x1 - 11/2 x2 - 5/2 x3 + 9 x4  <= 0
        //          1/2 x1 -  3/2 x2 - 1/2 x3 +   x4  <= 0
        //              x1                  <= 1
        //      x1,x2,x3,x4 >= 0

        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 10, -57, -9, -24}, 0);

        ArrayList<LinearConstraint> constraints = new ArrayList();

        constraints.add(new LinearConstraint(new double[] {0.5, -5.5, -2.5, 9}, Relationship.LEQ, 0));
        constraints.add(new LinearConstraint(new double[] {0.5, -1.5, -0.5, 1}, Relationship.LEQ, 0));
        constraints.add(new LinearConstraint(new double[] {  1,    0,    0, 0}, Relationship.LEQ, 1));

        double epsilon = 1e-6;
        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE,
                                                  new NonNegativeConstraint(true),
                                                  PivotSelectionRule.BLAND);
        Assert.assertEquals(1.0d, solution.getValue(), epsilon);
        Assert.assertTrue(validSolution(solution, constraints, epsilon));
    }

    @Test
    public void testMath828() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(
                new double[] { 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, 0.0);

        ArrayList <LinearConstraint>constraints = new ArrayList();

        constraints.add(new LinearConstraint(new double[] {0.0, 39.0, 23.0, 96.0, 15.0, 48.0, 9.0, 21.0, 48.0, 36.0, 76.0, 19.0, 88.0, 17.0, 16.0, 36.0,}, Relationship.GEQ, 15.0));
        constraints.add(new LinearConstraint(new double[] {0.0, 59.0, 93.0, 12.0, 29.0, 78.0, 73.0, 87.0, 32.0, 70.0, 68.0, 24.0, 11.0, 26.0, 65.0, 25.0,}, Relationship.GEQ, 29.0));
        constraints.add(new LinearConstraint(new double[] {0.0, 74.0, 5.0, 82.0, 6.0, 97.0, 55.0, 44.0, 52.0, 54.0, 5.0, 93.0, 91.0, 8.0, 20.0, 97.0,}, Relationship.GEQ, 6.0));
        constraints.add(new LinearConstraint(new double[] {8.0, -3.0, -28.0, -72.0, -8.0, -31.0, -31.0, -74.0, -47.0, -59.0, -24.0, -57.0, -56.0, -16.0, -92.0, -59.0,}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {25.0, -7.0, -99.0, -78.0, -25.0, -14.0, -16.0, -89.0, -39.0, -56.0, -53.0, -9.0, -18.0, -26.0, -11.0, -61.0,}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {33.0, -95.0, -15.0, -4.0, -33.0, -3.0, -20.0, -96.0, -27.0, -13.0, -80.0, -24.0, -3.0, -13.0, -57.0, -76.0,}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {7.0, -95.0, -39.0, -93.0, -7.0, -94.0, -94.0, -62.0, -76.0, -26.0, -53.0, -57.0, -31.0, -76.0, -53.0, -52.0,}, Relationship.GEQ, 0.0));

        double epsilon = 1e-6;
        PointValuePair solution = new SimplexSolver().optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                               GoalType.MINIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(1.0d, solution.getValue(), epsilon);
        Assert.assertTrue(validSolution(solution, constraints, epsilon));
    }

    @Test
    public void testMath828Cycle() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(
                new double[] { 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0}, 0.0);

        ArrayList <LinearConstraint>constraints = new ArrayList();

        constraints.add(new LinearConstraint(new double[] {0.0, 16.0, 14.0, 69.0, 1.0, 85.0, 52.0, 43.0, 64.0, 97.0, 14.0, 74.0, 89.0, 28.0, 94.0, 58.0, 13.0, 22.0, 21.0, 17.0, 30.0, 25.0, 1.0, 59.0, 91.0, 78.0, 12.0, 74.0, 56.0, 3.0, 88.0,}, Relationship.GEQ, 91.0));
        constraints.add(new LinearConstraint(new double[] {0.0, 60.0, 40.0, 81.0, 71.0, 72.0, 46.0, 45.0, 38.0, 48.0, 40.0, 17.0, 33.0, 85.0, 64.0, 32.0, 84.0, 3.0, 54.0, 44.0, 71.0, 67.0, 90.0, 95.0, 54.0, 99.0, 99.0, 29.0, 52.0, 98.0, 9.0,}, Relationship.GEQ, 54.0));
        constraints.add(new LinearConstraint(new double[] {0.0, 41.0, 12.0, 86.0, 90.0, 61.0, 31.0, 41.0, 23.0, 89.0, 17.0, 74.0, 44.0, 27.0, 16.0, 47.0, 80.0, 32.0, 11.0, 56.0, 68.0, 82.0, 11.0, 62.0, 62.0, 53.0, 39.0, 16.0, 48.0, 1.0, 63.0,}, Relationship.GEQ, 62.0));
        constraints.add(new LinearConstraint(new double[] {83.0, -76.0, -94.0, -19.0, -15.0, -70.0, -72.0, -57.0, -63.0, -65.0, -22.0, -94.0, -22.0, -88.0, -86.0, -89.0, -72.0, -16.0, -80.0, -49.0, -70.0, -93.0, -95.0, -17.0, -83.0, -97.0, -31.0, -47.0, -31.0, -13.0, -23.0,}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {41.0, -96.0, -41.0, -48.0, -70.0, -43.0, -43.0, -43.0, -97.0, -37.0, -85.0, -70.0, -45.0, -67.0, -87.0, -69.0, -94.0, -54.0, -54.0, -92.0, -79.0, -10.0, -35.0, -20.0, -41.0, -41.0, -65.0, -25.0, -12.0, -8.0, -46.0,}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {27.0, -42.0, -65.0, -49.0, -53.0, -42.0, -17.0, -2.0, -61.0, -31.0, -76.0, -47.0, -8.0, -93.0, -86.0, -62.0, -65.0, -63.0, -22.0, -43.0, -27.0, -23.0, -32.0, -74.0, -27.0, -63.0, -47.0, -78.0, -29.0, -95.0, -73.0,}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {15.0, -46.0, -41.0, -83.0, -98.0, -99.0, -21.0, -35.0, -7.0, -14.0, -80.0, -63.0, -18.0, -42.0, -5.0, -34.0, -56.0, -70.0, -16.0, -18.0, -74.0, -61.0, -47.0, -41.0, -15.0, -79.0, -18.0, -47.0, -88.0, -68.0, -55.0,}, Relationship.GEQ, 0.0));

        double epsilon = 1e-6;
        PointValuePair solution = new SimplexSolver().optimize(DEFAULT_MAX_ITER, f,
                                                               new LinearConstraintSet(constraints),
                                                               GoalType.MINIMIZE, new NonNegativeConstraint(true),
                                                               PivotSelectionRule.BLAND);
        Assert.assertEquals(1.0d, solution.getValue(), epsilon);
        Assert.assertTrue(validSolution(solution, constraints, epsilon));
    }

    @Test
    public void testMath781() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 2, 6, 7 }, 0);

        ArrayList<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 1, 2, 1 }, Relationship.LEQ, 2));
        constraints.add(new LinearConstraint(new double[] { -1, 1, 1 }, Relationship.LEQ, -1));
        constraints.add(new LinearConstraint(new double[] { 2, -3, 1 }, Relationship.LEQ, -1));

        double epsilon = 1e-6;
        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(false));

        Assert.assertTrue(Precision.compareTo(solution.getPoint()[0], 0.0d, epsilon) > 0);
        Assert.assertTrue(Precision.compareTo(solution.getPoint()[1], 0.0d, epsilon) > 0);
        Assert.assertTrue(Precision.compareTo(solution.getPoint()[2], 0.0d, epsilon) < 0);
        Assert.assertEquals(2.0d, solution.getValue(), epsilon);
    }

    @Test
    public void testMath713NegativeVariable() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] {1.0, 1.0}, 0.0d);
        ArrayList<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] {1, 0}, Relationship.EQ, 1));

        double epsilon = 1e-6;
        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(true));

        Assert.assertTrue(Precision.compareTo(solution.getPoint()[0], 0.0d, epsilon) >= 0);
        Assert.assertTrue(Precision.compareTo(solution.getPoint()[1], 0.0d, epsilon) >= 0);
    }

    @Test
    public void testMath434NegativeVariable() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] {0.0, 0.0, 1.0}, 0.0d);
        ArrayList<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] {1, 1, 0}, Relationship.EQ, 5));
        constraints.add(new LinearConstraint(new double[] {0, 0, 1}, Relationship.GEQ, -10));

        double epsilon = 1e-6;
        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(false));

        Assert.assertEquals(5.0, solution.getPoint()[0] + solution.getPoint()[1], epsilon);
        Assert.assertEquals(-10.0, solution.getPoint()[2], epsilon);
        Assert.assertEquals(-10.0, solution.getValue(), epsilon);

    }

    @Test(expected = NoFeasibleSolutionException.class)
    public void testMath434UnfeasibleSolution() {
        double epsilon = 1e-6;

        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] {1.0, 0.0}, 0.0);
        ArrayList<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] {epsilon/2, 0.5}, Relationship.EQ, 0));
        constraints.add(new LinearConstraint(new double[] {1e-3, 0.1}, Relationship.EQ, 10));

        SimplexSolver solver = new SimplexSolver();
        // allowing only non-negative values, no feasible solution shall be found
        solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                        GoalType.MINIMIZE, new NonNegativeConstraint(true));
    }

    @Test
    public void testMath434PivotRowSelection() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] {1.0}, 0.0);

        double epsilon = 1e-6;
        ArrayList<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] {200}, Relationship.GEQ, 1));
        constraints.add(new LinearConstraint(new double[] {100}, Relationship.GEQ, 0.499900001));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(false));

        Assert.assertTrue(Precision.compareTo(solution.getPoint()[0] * 200.d, 1.d, epsilon) >= 0);
        Assert.assertEquals(0.0050, solution.getValue(), epsilon);
    }

    @Test
    public void testMath434PivotRowSelection2() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] {0.0d, 1.0d, 1.0d, 0.0d, 0.0d, 0.0d, 0.0d}, 0.0d);

        ArrayList<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] {1.0d, -0.1d, 0.0d, 0.0d, 0.0d, 0.0d, 0.0d}, Relationship.EQ, -0.1d));
        constraints.add(new LinearConstraint(new double[] {1.0d, 0.0d, 0.0d, 0.0d, 0.0d, 0.0d, 0.0d}, Relationship.GEQ, -1e-18d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 1.0d, 0.0d, 0.0d, 0.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 0.0d, 0.0d, 1.0d, 0.0d, -0.0128588d, 1e-5d}, Relationship.EQ, 0.0d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 0.0d, 0.0d, 0.0d, 1.0d, 1e-5d, -0.0128586d}, Relationship.EQ, 1e-10d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, -1.0d, 0.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 1.0d, 0.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 0.0d, -1.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d));
        constraints.add(new LinearConstraint(new double[] {0.0d, 0.0d, 1.0d, 0.0d, 1.0d, 0.0d, 0.0d}, Relationship.GEQ, 0.0d));

        double epsilon = 1e-7;
        SimplexSolver simplex = new SimplexSolver();
        PointValuePair solution = simplex.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                   GoalType.MINIMIZE, new NonNegativeConstraint(false));

        Assert.assertTrue(Precision.compareTo(solution.getPoint()[0], -1e-18d, epsilon) >= 0);
        Assert.assertEquals(1.0d, solution.getPoint()[1], epsilon);
        Assert.assertEquals(0.0d, solution.getPoint()[2], epsilon);
        Assert.assertEquals(1.0d, solution.getValue(), epsilon);
    }

    @Test
    public void testMath272() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 2, 2, 1 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 1, 1, 0 }, Relationship.GEQ,  1));
        constraints.add(new LinearConstraint(new double[] { 1, 0, 1 }, Relationship.GEQ,  1));
        constraints.add(new LinearConstraint(new double[] { 0, 1, 0 }, Relationship.GEQ,  1));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(true));

        Assert.assertEquals(0.0, solution.getPoint()[0], .0000001);
        Assert.assertEquals(1.0, solution.getPoint()[1], .0000001);
        Assert.assertEquals(1.0, solution.getPoint()[2], .0000001);
        Assert.assertEquals(3.0, solution.getValue(), .0000001);
    }

    @Test
    public void testMath286() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 0.8, 0.2, 0.7, 0.3, 0.6, 0.4 }, 0 );
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 1, 0, 1, 0, 1, 0 }, Relationship.EQ, 23.0));
        constraints.add(new LinearConstraint(new double[] { 0, 1, 0, 1, 0, 1 }, Relationship.EQ, 23.0));
        constraints.add(new LinearConstraint(new double[] { 1, 0, 0, 0, 0, 0 }, Relationship.GEQ, 10.0));
        constraints.add(new LinearConstraint(new double[] { 0, 0, 1, 0, 0, 0 }, Relationship.GEQ, 8.0));
        constraints.add(new LinearConstraint(new double[] { 0, 0, 0, 0, 1, 0 }, Relationship.GEQ, 5.0));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(true));

        Assert.assertEquals(25.8, solution.getValue(), .0000001);
        Assert.assertEquals(23.0, solution.getPoint()[0] + solution.getPoint()[2] + solution.getPoint()[4], 0.0000001);
        Assert.assertEquals(23.0, solution.getPoint()[1] + solution.getPoint()[3] + solution.getPoint()[5], 0.0000001);
        Assert.assertTrue(solution.getPoint()[0] >= 10.0 - 0.0000001);
        Assert.assertTrue(solution.getPoint()[2] >= 8.0 - 0.0000001);
        Assert.assertTrue(solution.getPoint()[4] >= 5.0 - 0.0000001);
    }

    @Test
    public void testDegeneracy() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 0.8, 0.7 }, 0 );
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 1, 1 }, Relationship.LEQ, 18.0));
        constraints.add(new LinearConstraint(new double[] { 1, 0 }, Relationship.GEQ, 10.0));
        constraints.add(new LinearConstraint(new double[] { 0, 1 }, Relationship.GEQ, 8.0));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(13.6, solution.getValue(), .0000001);
    }

    @Test
    public void testMath288() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 7, 3, 0, 0 }, 0 );
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 3, 0, -5, 0 }, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] { 2, 0, 0, -5 }, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] { 0, 3, 0, -5 }, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] { 1, 0, 0, 0 }, Relationship.LEQ, 1.0));
        constraints.add(new LinearConstraint(new double[] { 0, 1, 0, 0 }, Relationship.LEQ, 1.0));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(10.0, solution.getValue(), .0000001);
    }

    @Test
    public void testMath290GEQ() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 1, 5 }, 0 );
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 2, 0 }, Relationship.GEQ, -1.0));
        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(0, solution.getValue(), .0000001);
        Assert.assertEquals(0, solution.getPoint()[0], .0000001);
        Assert.assertEquals(0, solution.getPoint()[1], .0000001);
    }

    @Test(expected=NoFeasibleSolutionException.class)
    public void testMath290LEQ() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 1, 5 }, 0 );
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 2, 0 }, Relationship.LEQ, -1.0));
        SimplexSolver solver = new SimplexSolver();
        solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                        GoalType.MINIMIZE, new NonNegativeConstraint(true));
    }

    @Test
    public void testMath293() {
      LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 0.8, 0.2, 0.7, 0.3, 0.4, 0.6}, 0 );
      Collection<LinearConstraint> constraints = new ArrayList();
      constraints.add(new LinearConstraint(new double[] { 1, 0, 1, 0, 1, 0 }, Relationship.EQ, 30.0));
      constraints.add(new LinearConstraint(new double[] { 0, 1, 0, 1, 0, 1 }, Relationship.EQ, 30.0));
      constraints.add(new LinearConstraint(new double[] { 0.8, 0.2, 0.0, 0.0, 0.0, 0.0 }, Relationship.GEQ, 10.0));
      constraints.add(new LinearConstraint(new double[] { 0.0, 0.0, 0.7, 0.3, 0.0, 0.0 }, Relationship.GEQ, 10.0));
      constraints.add(new LinearConstraint(new double[] { 0.0, 0.0, 0.0, 0.0, 0.4, 0.6 }, Relationship.GEQ, 10.0));

      SimplexSolver solver = new SimplexSolver();
      PointValuePair solution1 = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                 GoalType.MAXIMIZE, new NonNegativeConstraint(true));

      Assert.assertEquals(15.7143, solution1.getPoint()[0], .0001);
      Assert.assertEquals(0.0, solution1.getPoint()[1], .0001);
      Assert.assertEquals(14.2857, solution1.getPoint()[2], .0001);
      Assert.assertEquals(0.0, solution1.getPoint()[3], .0001);
      Assert.assertEquals(0.0, solution1.getPoint()[4], .0001);
      Assert.assertEquals(30.0, solution1.getPoint()[5], .0001);
      Assert.assertEquals(40.57143, solution1.getValue(), .0001);

      double valA = 0.8 * solution1.getPoint()[0] + 0.2 * solution1.getPoint()[1];
      double valB = 0.7 * solution1.getPoint()[2] + 0.3 * solution1.getPoint()[3];
      double valC = 0.4 * solution1.getPoint()[4] + 0.6 * solution1.getPoint()[5];

      f = new LinearObjectiveFunction(new double[] { 0.8, 0.2, 0.7, 0.3, 0.4, 0.6}, 0 );
      constraints = new ArrayList<LinearConstraint>();
      constraints.add(new LinearConstraint(new double[] { 1, 0, 1, 0, 1, 0 }, Relationship.EQ, 30.0));
      constraints.add(new LinearConstraint(new double[] { 0, 1, 0, 1, 0, 1 }, Relationship.EQ, 30.0));
      constraints.add(new LinearConstraint(new double[] { 0.8, 0.2, 0.0, 0.0, 0.0, 0.0 }, Relationship.GEQ, valA));
      constraints.add(new LinearConstraint(new double[] { 0.0, 0.0, 0.7, 0.3, 0.0, 0.0 }, Relationship.GEQ, valB));
      constraints.add(new LinearConstraint(new double[] { 0.0, 0.0, 0.0, 0.0, 0.4, 0.6 }, Relationship.GEQ, valC));

      PointValuePair solution2 = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                 GoalType.MAXIMIZE, new NonNegativeConstraint(true));
      Assert.assertEquals(40.57143, solution2.getValue(), .0001);
    }

    @Test
    public void testMath930() {
        Collection<LinearConstraint> constraints = createMath930Constraints();

        double[] objFunctionCoeff = new double[33];
        objFunctionCoeff[3] = 1;
        LinearObjectiveFunction f = new LinearObjectiveFunction(objFunctionCoeff, 0);
        SimplexSolver solver = new SimplexSolver(1e-4, 10, 1e-6);

        PointValuePair solution = solver.optimize(new MaxIter(1000), f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(0.3752298, solution.getValue(), 1e-4);
    }

    private List<LinearConstraint> createMath930Constraints() {
        List<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] {1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.628803}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.676993}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 1, -1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.136677}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.444434}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.254028}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.302218}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0, 0, -1, 1, 1, -1, 0, 0, 0, 0, 1, -1, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.653981}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.690437}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.423786}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.486717}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.049232}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.304747}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.129826}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.205625}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 1, -1, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.621944}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.764385}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 1, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.432572}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.480762}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.055983}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.11378}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.009607}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.057797}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.407308}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.452749}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.269677}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.321806}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.049232}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.06902}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.028754}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.484254}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.524607}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.385492}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.430134}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.34983}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.375781}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.254028}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.281308}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 0, -1, 1, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.304995}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.345347}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -1, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.288899}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.332212}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.14351}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -0.17057}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -0.129826}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -0.157435}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, -1, 1, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -0.141071}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -0.232574}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -0.009607}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -0.057797}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -0.091644}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -0.203531}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, Relationship.GEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -0.028754}, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, Relationship.EQ, 1.0));
        return constraints;
    }

    @Test
    public void testSimplexSolver() {
        LinearObjectiveFunction f =
            new LinearObjectiveFunction(new double[] { 15, 10 }, 7);
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 1, 0 }, Relationship.LEQ, 2));
        constraints.add(new LinearConstraint(new double[] { 0, 1 }, Relationship.LEQ, 3));
        constraints.add(new LinearConstraint(new double[] { 1, 1 }, Relationship.EQ, 4));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(2.0, solution.getPoint()[0], 0.0);
        Assert.assertEquals(2.0, solution.getPoint()[1], 0.0);
        Assert.assertEquals(57.0, solution.getValue(), 0.0);
    }

    @Test
    public void testSingleVariableAndConstraint() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 3 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 1 }, Relationship.LEQ, 10));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(false));
        Assert.assertEquals(10.0, solution.getPoint()[0], 0.0);
        Assert.assertEquals(30.0, solution.getValue(), 0.0);
    }

    /**
     * With no artificial variables needed (no equals and no greater than
     * constraints) we can go straight to Phase 2.
     */
    @Test
    public void testModelWithNoArtificialVars() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 15, 10 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 1, 0 }, Relationship.LEQ, 2));
        constraints.add(new LinearConstraint(new double[] { 0, 1 }, Relationship.LEQ, 3));
        constraints.add(new LinearConstraint(new double[] { 1, 1 }, Relationship.LEQ, 4));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(false));
        Assert.assertEquals(2.0, solution.getPoint()[0], 0.0);
        Assert.assertEquals(2.0, solution.getPoint()[1], 0.0);
        Assert.assertEquals(50.0, solution.getValue(), 0.0);
    }

    @Test
    public void testMinimization() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { -2, 1 }, -5);
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 1, 2 }, Relationship.LEQ, 6));
        constraints.add(new LinearConstraint(new double[] { 3, 2 }, Relationship.LEQ, 12));
        constraints.add(new LinearConstraint(new double[] { 0, 1 }, Relationship.GEQ, 0));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(false));
        Assert.assertEquals(4.0, solution.getPoint()[0], 0.0);
        Assert.assertEquals(0.0, solution.getPoint()[1], 0.0);
        Assert.assertEquals(-13.0, solution.getValue(), 0.0);
    }

    @Test
    public void testSolutionWithNegativeDecisionVariable() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { -2, 1 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 1, 1 }, Relationship.GEQ, 6));
        constraints.add(new LinearConstraint(new double[] { 1, 2 }, Relationship.LEQ, 14));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(false));
        Assert.assertEquals(-2.0, solution.getPoint()[0], 0.0);
        Assert.assertEquals(8.0, solution.getPoint()[1], 0.0);
        Assert.assertEquals(12.0, solution.getValue(), 0.0);
    }

    @Test(expected = NoFeasibleSolutionException.class)
    public void testInfeasibleSolution() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 15 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 1 }, Relationship.LEQ, 1));
        constraints.add(new LinearConstraint(new double[] { 1 }, Relationship.GEQ, 3));

        SimplexSolver solver = new SimplexSolver();
        solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                        GoalType.MAXIMIZE, new NonNegativeConstraint(false));
    }

    @Test(expected = UnboundedSolutionException.class)
    public void testUnboundedSolution() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 15, 10 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 1, 0 }, Relationship.EQ, 2));

        SimplexSolver solver = new SimplexSolver();
        solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                        GoalType.MAXIMIZE, new NonNegativeConstraint(false));
    }

    @Test
    public void testRestrictVariablesToNonNegative() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 409, 523, 70, 204, 339 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] {    43,   56, 345,  56,    5 }, Relationship.LEQ,  4567456));
        constraints.add(new LinearConstraint(new double[] {    12,   45,   7,  56,   23 }, Relationship.LEQ,    56454));
        constraints.add(new LinearConstraint(new double[] {     8,  768,   0,  34, 7456 }, Relationship.LEQ,  1923421));
        constraints.add(new LinearConstraint(new double[] { 12342, 2342,  34, 678, 2342 }, Relationship.GEQ,     4356));
        constraints.add(new LinearConstraint(new double[] {    45,  678,  76,  52,   23 }, Relationship.EQ,    456356));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(2902.92783505155, solution.getPoint()[0], .0000001);
        Assert.assertEquals(480.419243986254, solution.getPoint()[1], .0000001);
        Assert.assertEquals(0.0, solution.getPoint()[2], .0000001);
        Assert.assertEquals(0.0, solution.getPoint()[3], .0000001);
        Assert.assertEquals(0.0, solution.getPoint()[4], .0000001);
        Assert.assertEquals(1438556.7491409, solution.getValue(), .0000001);
    }

    @Test
    public void testEpsilon() {
      LinearObjectiveFunction f =
          new LinearObjectiveFunction(new double[] { 10, 5, 1 }, 0);
      Collection<LinearConstraint> constraints = new ArrayList();
      constraints.add(new LinearConstraint(new double[] {  9, 8, 0 }, Relationship.EQ,  17));
      constraints.add(new LinearConstraint(new double[] {  0, 7, 8 }, Relationship.LEQ,  7));
      constraints.add(new LinearConstraint(new double[] { 10, 0, 2 }, Relationship.LEQ, 10));

      SimplexSolver solver = new SimplexSolver();
      PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                GoalType.MAXIMIZE, new NonNegativeConstraint(false));
      Assert.assertEquals(1.0, solution.getPoint()[0], 0.0);
      Assert.assertEquals(1.0, solution.getPoint()[1], 0.0);
      Assert.assertEquals(0.0, solution.getPoint()[2], 0.0);
      Assert.assertEquals(15.0, solution.getValue(), 0.0);
  }

    @Test
    public void testTrivialModel() {
        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 1, 1 }, 0);
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 1, 1 }, Relationship.EQ,  0));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MAXIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(0, solution.getValue(), .0000001);
    }

    @Test
    public void testLargeModel() {
        double[] objective = new double[] {
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 12, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           12, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 12, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 12, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 12, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 12, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
                                           1, 1, 1, 1, 1, 1};

        LinearObjectiveFunction f = new LinearObjectiveFunction(objective, 0);
        Collection<LinearConstraint> constraints = new ArrayList();
        constraints.add(equationFromString(objective.length, "x0 + x1 + x2 + x3 - x12 = 0"));
        constraints.add(equationFromString(objective.length, "x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 - x13 = 0"));
        constraints.add(equationFromString(objective.length, "x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 >= 49"));
        constraints.add(equationFromString(objective.length, "x0 + x1 + x2 + x3 >= 42"));
        constraints.add(equationFromString(objective.length, "x14 + x15 + x16 + x17 - x26 = 0"));
        constraints.add(equationFromString(objective.length, "x18 + x19 + x20 + x21 + x22 + x23 + x24 + x25 - x27 = 0"));
        constraints.add(equationFromString(objective.length, "x14 + x15 + x16 + x17 - x12 = 0"));
        constraints.add(equationFromString(objective.length, "x18 + x19 + x20 + x21 + x22 + x23 + x24 + x25 - x13 = 0"));
        constraints.add(equationFromString(objective.length, "x28 + x29 + x30 + x31 - x40 = 0"));
        constraints.add(equationFromString(objective.length, "x32 + x33 + x34 + x35 + x36 + x37 + x38 + x39 - x41 = 0"));
        constraints.add(equationFromString(objective.length, "x32 + x33 + x34 + x35 + x36 + x37 + x38 + x39 >= 49"));
        constraints.add(equationFromString(objective.length, "x28 + x29 + x30 + x31 >= 42"));
        constraints.add(equationFromString(objective.length, "x42 + x43 + x44 + x45 - x54 = 0"));
        constraints.add(equationFromString(objective.length, "x46 + x47 + x48 + x49 + x50 + x51 + x52 + x53 - x55 = 0"));
        constraints.add(equationFromString(objective.length, "x42 + x43 + x44 + x45 - x40 = 0"));
        constraints.add(equationFromString(objective.length, "x46 + x47 + x48 + x49 + x50 + x51 + x52 + x53 - x41 = 0"));
        constraints.add(equationFromString(objective.length, "x56 + x57 + x58 + x59 - x68 = 0"));
        constraints.add(equationFromString(objective.length, "x60 + x61 + x62 + x63 + x64 + x65 + x66 + x67 - x69 = 0"));
        constraints.add(equationFromString(objective.length, "x60 + x61 + x62 + x63 + x64 + x65 + x66 + x67 >= 51"));
        constraints.add(equationFromString(objective.length, "x56 + x57 + x58 + x59 >= 44"));
        constraints.add(equationFromString(objective.length, "x70 + x71 + x72 + x73 - x82 = 0"));
        constraints.add(equationFromString(objective.length, "x74 + x75 + x76 + x77 + x78 + x79 + x80 + x81 - x83 = 0"));
        constraints.add(equationFromString(objective.length, "x70 + x71 + x72 + x73 - x68 = 0"));
        constraints.add(equationFromString(objective.length, "x74 + x75 + x76 + x77 + x78 + x79 + x80 + x81 - x69 = 0"));
        constraints.add(equationFromString(objective.length, "x84 + x85 + x86 + x87 - x96 = 0"));
        constraints.add(equationFromString(objective.length, "x88 + x89 + x90 + x91 + x92 + x93 + x94 + x95 - x97 = 0"));
        constraints.add(equationFromString(objective.length, "x88 + x89 + x90 + x91 + x92 + x93 + x94 + x95 >= 51"));
        constraints.add(equationFromString(objective.length, "x84 + x85 + x86 + x87 >= 44"));
        constraints.add(equationFromString(objective.length, "x98 + x99 + x100 + x101 - x110 = 0"));
        constraints.add(equationFromString(objective.length, "x102 + x103 + x104 + x105 + x106 + x107 + x108 + x109 - x111 = 0"));
        constraints.add(equationFromString(objective.length, "x98 + x99 + x100 + x101 - x96 = 0"));
        constraints.add(equationFromString(objective.length, "x102 + x103 + x104 + x105 + x106 + x107 + x108 + x109 - x97 = 0"));
        constraints.add(equationFromString(objective.length, "x112 + x113 + x114 + x115 - x124 = 0"));
        constraints.add(equationFromString(objective.length, "x116 + x117 + x118 + x119 + x120 + x121 + x122 + x123 - x125 = 0"));
        constraints.add(equationFromString(objective.length, "x116 + x117 + x118 + x119 + x120 + x121 + x122 + x123 >= 49"));
        constraints.add(equationFromString(objective.length, "x112 + x113 + x114 + x115 >= 42"));
        constraints.add(equationFromString(objective.length, "x126 + x127 + x128 + x129 - x138 = 0"));
        constraints.add(equationFromString(objective.length, "x130 + x131 + x132 + x133 + x134 + x135 + x136 + x137 - x139 = 0"));
        constraints.add(equationFromString(objective.length, "x126 + x127 + x128 + x129 - x124 = 0"));
        constraints.add(equationFromString(objective.length, "x130 + x131 + x132 + x133 + x134 + x135 + x136 + x137 - x125 = 0"));
        constraints.add(equationFromString(objective.length, "x140 + x141 + x142 + x143 - x152 = 0"));
        constraints.add(equationFromString(objective.length, "x144 + x145 + x146 + x147 + x148 + x149 + x150 + x151 - x153 = 0"));
        constraints.add(equationFromString(objective.length, "x144 + x145 + x146 + x147 + x148 + x149 + x150 + x151 >= 59"));
        constraints.add(equationFromString(objective.length, "x140 + x141 + x142 + x143 >= 42"));
        constraints.add(equationFromString(objective.length, "x154 + x155 + x156 + x157 - x166 = 0"));
        constraints.add(equationFromString(objective.length, "x158 + x159 + x160 + x161 + x162 + x163 + x164 + x165 - x167 = 0"));
        constraints.add(equationFromString(objective.length, "x154 + x155 + x156 + x157 - x152 = 0"));
        constraints.add(equationFromString(objective.length, "x158 + x159 + x160 + x161 + x162 + x163 + x164 + x165 - x153 = 0"));
        constraints.add(equationFromString(objective.length, "x83 + x82 - x168 = 0"));
        constraints.add(equationFromString(objective.length, "x111 + x110 - x169 = 0"));
        constraints.add(equationFromString(objective.length, "x170 - x182 = 0"));
        constraints.add(equationFromString(objective.length, "x171 - x183 = 0"));
        constraints.add(equationFromString(objective.length, "x172 - x184 = 0"));
        constraints.add(equationFromString(objective.length, "x173 - x185 = 0"));
        constraints.add(equationFromString(objective.length, "x174 - x186 = 0"));
        constraints.add(equationFromString(objective.length, "x175 + x176 - x187 = 0"));
        constraints.add(equationFromString(objective.length, "x177 - x188 = 0"));
        constraints.add(equationFromString(objective.length, "x178 - x189 = 0"));
        constraints.add(equationFromString(objective.length, "x179 - x190 = 0"));
        constraints.add(equationFromString(objective.length, "x180 - x191 = 0"));
        constraints.add(equationFromString(objective.length, "x181 - x192 = 0"));
        constraints.add(equationFromString(objective.length, "x170 - x26 = 0"));
        constraints.add(equationFromString(objective.length, "x171 - x27 = 0"));
        constraints.add(equationFromString(objective.length, "x172 - x54 = 0"));
        constraints.add(equationFromString(objective.length, "x173 - x55 = 0"));
        constraints.add(equationFromString(objective.length, "x174 - x168 = 0"));
        constraints.add(equationFromString(objective.length, "x177 - x169 = 0"));
        constraints.add(equationFromString(objective.length, "x178 - x138 = 0"));
        constraints.add(equationFromString(objective.length, "x179 - x139 = 0"));
        constraints.add(equationFromString(objective.length, "x180 - x166 = 0"));
        constraints.add(equationFromString(objective.length, "x181 - x167 = 0"));
        constraints.add(equationFromString(objective.length, "x193 - x205 = 0"));
        constraints.add(equationFromString(objective.length, "x194 - x206 = 0"));
        constraints.add(equationFromString(objective.length, "x195 - x207 = 0"));
        constraints.add(equationFromString(objective.length, "x196 - x208 = 0"));
        constraints.add(equationFromString(objective.length, "x197 - x209 = 0"));
        constraints.add(equationFromString(objective.length, "x198 + x199 - x210 = 0"));
        constraints.add(equationFromString(objective.length, "x200 - x211 = 0"));
        constraints.add(equationFromString(objective.length, "x201 - x212 = 0"));
        constraints.add(equationFromString(objective.length, "x202 - x213 = 0"));
        constraints.add(equationFromString(objective.length, "x203 - x214 = 0"));
        constraints.add(equationFromString(objective.length, "x204 - x215 = 0"));
        constraints.add(equationFromString(objective.length, "x193 - x182 = 0"));
        constraints.add(equationFromString(objective.length, "x194 - x183 = 0"));
        constraints.add(equationFromString(objective.length, "x195 - x184 = 0"));
        constraints.add(equationFromString(objective.length, "x196 - x185 = 0"));
        constraints.add(equationFromString(objective.length, "x197 - x186 = 0"));
        constraints.add(equationFromString(objective.length, "x198 + x199 - x187 = 0"));
        constraints.add(equationFromString(objective.length, "x200 - x188 = 0"));
        constraints.add(equationFromString(objective.length, "x201 - x189 = 0"));
        constraints.add(equationFromString(objective.length, "x202 - x190 = 0"));
        constraints.add(equationFromString(objective.length, "x203 - x191 = 0"));
        constraints.add(equationFromString(objective.length, "x204 - x192 = 0"));

        SimplexSolver solver = new SimplexSolver();
        PointValuePair solution = solver.optimize(DEFAULT_MAX_ITER, f, new LinearConstraintSet(constraints),
                                                  GoalType.MINIMIZE, new NonNegativeConstraint(true));
        Assert.assertEquals(7518.0, solution.getValue(), .0000001);
    }

    @Test
    public void testSolutionCallback() {
        // re-use the problem from testcase for MATH-288
        // it normally requires 5 iterations

        LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 7, 3, 0, 0 }, 0 );

        List<LinearConstraint> constraints = new ArrayList();
        constraints.add(new LinearConstraint(new double[] { 3, 0, -5, 0 }, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] { 2, 0, 0, -5 }, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] { 0, 3, 0, -5 }, Relationship.LEQ, 0.0));
        constraints.add(new LinearConstraint(new double[] { 1, 0, 0, 0 }, Relationship.LEQ, 1.0));
        constraints.add(new LinearConstraint(new double[] { 0, 1, 0, 0 }, Relationship.LEQ, 1.0));

        final SimplexSolver solver = new SimplexSolver();
        final SolutionCallback callback = new SolutionCallback();

        Assert.assertNull(callback.getSolution());
        Assert.assertFalse(callback.isSolutionOptimal());

        try {
            solver.optimize(new MaxIter(3), f, new LinearConstraintSet(constraints),
                            GoalType.MAXIMIZE, new NonNegativeConstraint(true), callback);
            Assert.fail("expected TooManyIterationsException");
        } catch (TooManyIterationsException ex) {
            // expected
        }

        final PointValuePair solution = callback.getSolution();
        Assert.assertNotNull(solution);
        Assert.assertTrue(validSolution(solution, constraints, 1e-4));
        Assert.assertFalse(callback.isSolutionOptimal());
        // the solution is clearly not optimal: optimal = 10.0
        Assert.assertEquals(7.0, solution.getValue(), 1e-4);
    }

    /**
     * Converts a test string to a {@link LinearConstraint}.
     * Ex: x0 + x1 + x2 + x3 - x12 = 0
     */
    private LinearConstraint equationFromString(int numCoefficients, String s) {
        Relationship relationship;
        if (s.contains(">=")) {
            relationship = Relationship.GEQ;
        } else if (s.contains("<=")) {
            relationship = Relationship.LEQ;
        } else if (s.contains("=")) {
            relationship = Relationship.EQ;
        } else {
            throw new IllegalArgumentException();
        }

        String[] equationParts = s.split("[>|<]?=");
        double rhs = Double.parseDouble(equationParts[1].trim());

        double[] lhs = new double[numCoefficients];
        String left = equationParts[0].replaceAll(" ?x", "");
        String[] coefficients = left.split(" ");
        for (String coefficient : coefficients) {
            double value = coefficient.charAt(0) == '-' ? -1 : 1;
            int index = Integer.parseInt(coefficient.replaceFirst("[+|-]", "").trim());
            lhs[index] = value;
        }
        return new LinearConstraint(lhs, relationship, rhs);
    }

    private static boolean validSolution(PointValuePair solution, List<LinearConstraint> constraints, double epsilon) {
        double[] vals = solution.getPoint();
        for (LinearConstraint c : constraints) {
            double[] coeffs = c.getCoefficients().toArray();
            double result = 0.0d;
            for (int i = 0; i < vals.length; i++) {
                result += vals[i] * coeffs[i];
            }

            switch (c.getRelationship()) {
            case EQ:
                if (!Precision.equals(result, c.getValue(), epsilon)) {
                    return false;
                }
                break;

            case GEQ:
                if (Precision.compareTo(result, c.getValue(), epsilon) < 0) {
                    return false;
                }
                break;

            case LEQ:
                if (Precision.compareTo(result, c.getValue(), epsilon) > 0) {
                    return false;
                }
                break;
            }
        }

        return true;
    }

}

Other Java examples (source code examples)

Here is a short list of links related to this Java SimplexSolverTest.java source code file:



my book on functional programming

 

new blog posts

 

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