Apache Commons SimplexSolver：OutOfMemoryError

Question

I have a problem with 841 variables and 23382 constraints (not particularly large for LP).

Nevertheless, i get an OutOfMemoryError when using the Apache SimplexSolver, even for a heap size of 1GB.

According to the error trace this happens when creating the Tableau. The matrix is quite sparse as most of the constraints only involve two or three variables. For the LinearConstraints i'm using the SparseRealVector (though not sure if it brings anything).

Is there anything i can configure on the solver to overcome this problem? Or is this simply a limitation of the simplex solver?

Thank you

An example below:

@Test
public void simplexTest(){

    long[][] net = new long[][]{    
     {0, 746, 746, 797, 796, 846, 797, 848, 847, 847, 848, 848, 848, 898, 898, 898, 948, 899, 899, 949, 949, 950, 950, 1000, 1000, 1000, 1000, 1000, 1000}
    ,{-11, 0, 50, 786, 100, 100, 786, 837, 836, 836, 837, 837, 837, 887, 887, 887, 937, 888, 888, 938, 938, 939, 939, 989, 989, 989, 989, 989, 989}
    ,{-11, 0, 0, 786, 100, 100, 786, 837, 836, 836, 837, 837, 837, 887, 887, 887, 937, 888, 888, 938, 938, 939, 939, 989, 989, 989, 989, 989, 989}
    ,{-12, -1, -1, 0, 49, 99, 50, 836, 100, 100, 836, 836, 836, 886, 886, 886, 936, 887, 887, 937, 937, 938, 938, 988, 988, 988, 988, 988, 988}
    ,{-61, -50, -50, 736, 0, 50, 736, 787, 786, 786, 787, 787, 787, 837, 837, 837, 887, 838, 838, 888, 888, 889, 889, 939, 939, 939, 939, 939, 939}
    ,{-61, -50, -50, 736, 0, 0, 736, 787, 786, 786, 787, 787, 787, 837, 837, 837, 887, 838, 838, 888, 888, 889, 889, 939, 939, 939, 939, 939, 939}
    ,{-62, -51, -51, 0, -1, 49, 0, 786, 100, 100, 786, 786, 786, 836, 836, 836, 886, 837, 837, 887, 887, 888, 888, 938, 938, 938, 938, 938, 938}
    ,{-63, -52, -52, -1, -2, 48, -1, 0, 99, 49, 785, 785, 50, 100, 835, 100, 885, 836, 836, 886, 886, 887, 887, 937, 937, 937, 937, 937, 937}
    ,{-112, -101, -101, -50, -51, -1, -50, 736, 0, 0, 736, 736, 736, 786, 786, 786, 836, 787, 787, 837, 837, 838, 838, 888, 888, 888, 888, 888, 888}
    ,{-112, -101, -101, -50, -51, -1, -50, 736, 50, 0, 736, 736, 736, 786, 786, 786, 836, 787, 787, 837, 837, 838, 838, 888, 888, 888, 888, 888, 888}
    ,{-113, -102, -102, -51, -52, -2, -51, 735, -1, -1, 0, 50, 735, 785, 100, 785, 100, 786, 786, 836, 836, 837, 837, 887, 887, 887, 887, 887, 887}
    ,{-113, -102, -102, -51, -52, -2, -51, 735, -1, -1, 0, 0, 735, 785, 100, 785, 100, 786, 786, 836, 836, 837, 837, 887, 887, 887, 887, 887, 887}
    ,{-113, -102, -102, -51, -52, -2, -51, 0, 49, -1, 735, 735, 0, 100, 785, 100, 835, 786, 786, 836, 836, 837, 837, 887, 887, 887, 887, 887, 887}
    ,{-163, -152, -152, -101, -102, -52, -101, -50, -1, -51, 685, 685, -50, 0, 735, 0, 785, 736, 736, 786, 786, 787, 787, 837, 837, 837, 837, 837, 837}
    ,{-163, -152, -152, -101, -102, -52, -101, 685, -51, -51, -50, -50, 685, 735, 0, 735, 50, 736, 736, 786, 786, 787, 787, 837, 837, 837, 837, 837, 837}
    ,{-163, -152, -152, -101, -102, -52, -101, -50, -1, -51, 685, 685, -50, 50, 735, 0, 785, 736, 736, 786, 786, 787, 787, 837, 837, 837, 837, 837, 837}
    ,{-163, -152, -152, -101, -102, -52, -101, 685, -51, -51, -50, -50, 685, 735, 0, 735, 0, 736, 736, 786, 786, 787, 787, 837, 837, 837, 837, 837, 837}
    ,{-164, -153, -153, -102, -103, -53, -102, -51, -2, -52, -1, -1, -51, -1, 49, -1, 99, 0, 50, 100, 100, 786, 786, 836, 836, 836, 836, 836, 836}
    ,{-164, -153, -153, -102, -103, -53, -102, -51, -52, -52, -51, -51, -51, -1, -1, -1, 49, 0, 0, 100, 100, 786, 786, 836, 836, 836, 836, 836, 836}
    ,{-214, -203, -203, -152, -153, -103, -152, -101, -102, -102, -101, -101, -101, -51, -51, -51, -1, -50, -50, 0, 0, 736, 736, 786, 786, 786, 786, 786, 786}
    ,{-214, -203, -203, -152, -153, -103, -152, -101, -102, -102, -101, -101, -101, -51, -51, -51, -1, -50, -50, 50, 0, 736, 736, 786, 786, 786, 786, 786, 786}
    ,{-215, -204, -204, -153, -154, -104, -153, -102, -103, -103, -102, -102, -102, -52, -52, -52, -2, -51, -51, -1, -1, 0, 50, 100, 100, 785, 785, 785, 785}
    ,{-215, -204, -204, -153, -154, -104, -153, -102, -103, -103, -102, -102, -102, -52, -52, -52, -2, -51, -51, -1, -1, 0, 0, 100, 100, 785, 785, 785, 785}
    ,{-265, -254, -254, -203, -204, -154, -203, -152, -153, -153, -152, -152, -152, -102, -102, -102, -52, -101, -101, -51, -51, -50, -50, 0, 0, 735, 735, 735, 735}
    ,{-265, -254, -254, -203, -204, -154, -203, -152, -153, -153, -152, -152, -152, -102, -102, -102, -52, -101, -101, -51, -51, -50, -50, 50, 0, 735, 735, 735, 735}
    ,{-1000, -254, -254, -203, -204, -154, -203, -152, -153, -153, -152, -152, -152, -102, -102, -102, -52, -101, -101, -51, -51, -50, -50, 0, 0, 0, 0, 0, 0}
    ,{-1000, -254, -254, -203, -204, -154, -203, -152, -153, -153, -152, -152, -152, -102, -102, -102, -52, -101, -101, -51, -51, -50, -50, 0, 0, 0, 0, 0, 0}
    ,{-1000, -254, -254, -203, -204, -154, -203, -152, -153, -153, -152, -152, -152, -102, -102, -102, -52, -101, -101, -51, -51, -50, -50, 0, 0, 0, 0, 0, 0}
    ,{-1000, -254, -254, -203, -204, -154, -203, -152, -153, -153, -152, -152, -152, -102, -102, -102, -52, -101, -101, -51, -51, -50, -50, 0, 0, 0, 0, 0, 0}};

    int[][] edges = new int[][]{{7, 3},{7, 8},{7, 10},{7, 16},{7, 22},{7, 24},{7, 26},{13, 3},{13, 8},{13, 10},{13, 16},{13, 22},{13, 24},{13, 26},{17, 3},{17, 8},{17, 10},{17, 16},{17, 22},{17, 24},{17, 26}
    ,{19, 3},{19, 8},{19, 10},{19, 16},{19, 22},{19, 24},{19, 26},{21, 3},{21, 8},{21, 10},{21, 16},{21, 22},{21, 24},{21, 26},{23, 3},{23, 8},{23, 10},{23, 16},{23, 22},{23, 24},{23, 26}
    ,{25, 3},{25, 8},{25, 10},{25, 16},{25, 22},{25, 24},{25, 26},{7, 1},{7, 5},{7, 11},{7, 14},{7, 18},{7, 20},{7, 27},{13, 1},{13, 5},{13, 11},{13, 14},{13, 18},{13, 20},{13, 27}
    ,{17, 1},{17, 5},{17, 11},{17, 14},{17, 18},{17, 20},{17, 27},{19, 1},{19, 5},{19, 11},{19, 14},{19, 18},{19, 20},{19, 27},{21, 1},{21, 5},{21, 11},{21, 14},{21, 18},{21, 20},{21, 27}
    ,{23, 1},{23, 5},{23, 11},{23, 14},{23, 18},{23, 20},{23, 27},{25, 1},{25, 5},{25, 11},{25, 14},{25, 18},{25, 20},{25, 27},{7, 2},{7, 4},{7, 6},{7, 9},{7, 12},{7, 15},{7, 28}
    ,{13, 2},{13, 4},{13, 6},{13, 9},{13, 12},{13, 15},{13, 28},{17, 2},{17, 4},{17, 6},{17, 9},{17, 12},{17, 15},{17, 28},{19, 2},{19, 4},{19, 6},{19, 9},{19, 12},{19, 15},{19, 28}
    ,{21, 2},{21, 4},{21, 6},{21, 9},{21, 12},{21, 15},{21, 28},{23, 2},{23, 4},{23, 6},{23, 9},{23, 12},{23, 15},{23, 28},{25, 2},{25, 4},{25, 6},{25, 9},{25, 12},{25, 15},{25, 28}
    ,{3, 7},{3, 13},{3, 17},{3, 19},{3, 21},{3, 23},{3, 25},{8, 7},{8, 13},{8, 17},{8, 19},{8, 21},{8, 23},{8, 25},{10, 7},{10, 13},{10, 17},{10, 19},{10, 21},{10, 23},{10, 25}
    ,{16, 7},{16, 13},{16, 17},{16, 19},{16, 21},{16, 23},{16, 25},{22, 7},{22, 13},{22, 17},{22, 19},{22, 21},{22, 23},{22, 25},{24, 7},{24, 13},{24, 17},{24, 19},{24, 21},{24, 23},{24, 25}
    ,{26, 7},{26, 13},{26, 17},{26, 19},{26, 21},{26, 23},{26, 25},{3, 1},{3, 5},{3, 11},{3, 14},{3, 18},{3, 20},{3, 27},{8, 1},{8, 5},{8, 11},{8, 14},{8, 18},{8, 20},{8, 27}
    ,{10, 1},{10, 5},{10, 11},{10, 14},{10, 18},{10, 20},{10, 27},{16, 1},{16, 5},{16, 11},{16, 14},{16, 18},{16, 20},{16, 27},{22, 1},{22, 5},{22, 11},{22, 14},{22, 18},{22, 20},{22, 27}
    ,{24, 1},{24, 5},{24, 11},{24, 14},{24, 18},{24, 20},{24, 27},{26, 1},{26, 5},{26, 11},{26, 14},{26, 18},{26, 20},{26, 27},{3, 2},{3, 4},{3, 6},{3, 9},{3, 12},{3, 15},{3, 28}
    ,{8, 2},{8, 4},{8, 6},{8, 9},{8, 12},{8, 15},{8, 28},{10, 2},{10, 4},{10, 6},{10, 9},{10, 12},{10, 15},{10, 28},{16, 2},{16, 4},{16, 6},{16, 9},{16, 12},{16, 15},{16, 28}
    ,{22, 2},{22, 4},{22, 6},{22, 9},{22, 12},{22, 15},{22, 28},{24, 2},{24, 4},{24, 6},{24, 9},{24, 12},{24, 15},{24, 28},{26, 2},{26, 4},{26, 6},{26, 9},{26, 12},{26, 15},{26, 28}
    ,{1, 7},{1, 13},{1, 17},{1, 19},{1, 21},{1, 23},{1, 25},{5, 7},{5, 13},{5, 17},{5, 19},{5, 21},{5, 23},{5, 25},{11, 7},{11, 13},{11, 17},{11, 19},{11, 21},{11, 23},{11, 25}
    ,{14, 7},{14, 13},{14, 17},{14, 19},{14, 21},{14, 23},{14, 25},{18, 7},{18, 13},{18, 17},{18, 19},{18, 21},{18, 23},{18, 25},{20, 7},{20, 13},{20, 17},{20, 19},{20, 21},{20, 23},{20, 25}
    ,{27, 7},{27, 13},{27, 17},{27, 19},{27, 21},{27, 23},{27, 25},{1, 3},{1, 8},{1, 10},{1, 16},{1, 22},{1, 24},{1, 26},{5, 3},{5, 8},{5, 10},{5, 16},{5, 22},{5, 24},{5, 26}
    ,{11, 3},{11, 8},{11, 10},{11, 16},{11, 22},{11, 24},{11, 26},{14, 3},{14, 8},{14, 10},{14, 16},{14, 22},{14, 24},{14, 26},{18, 3},{18, 8},{18, 10},{18, 16},{18, 22},{18, 24},{18, 26}
    ,{20, 3},{20, 8},{20, 10},{20, 16},{20, 22},{20, 24},{20, 26},{27, 3},{27, 8},{27, 10},{27, 16},{27, 22},{27, 24},{27, 26},{1, 2},{1, 4},{1, 6},{1, 9},{1, 12},{1, 15},{1, 28}
    ,{5, 2},{5, 4},{5, 6},{5, 9},{5, 12},{5, 15},{5, 28},{11, 2},{11, 4},{11, 6},{11, 9},{11, 12},{11, 15},{11, 28},{14, 2},{14, 4},{14, 6},{14, 9},{14, 12},{14, 15},{14, 28}
    ,{18, 2},{18, 4},{18, 6},{18, 9},{18, 12},{18, 15},{18, 28},{20, 2},{20, 4},{20, 6},{20, 9},{20, 12},{20, 15},{20, 28},{27, 2},{27, 4},{27, 6},{27, 9},{27, 12},{27, 15},{27, 28}
    ,{2, 7},{2, 13},{2, 17},{2, 19},{2, 21},{2, 23},{2, 25},{4, 7},{4, 13},{4, 17},{4, 19},{4, 21},{4, 23},{4, 25},{6, 7},{6, 13},{6, 17},{6, 19},{6, 21},{6, 23},{6, 25}
    ,{9, 7},{9, 13},{9, 17},{9, 19},{9, 21},{9, 23},{9, 25},{12, 7},{12, 13},{12, 17},{12, 19},{12, 21},{12, 23},{12, 25},{15, 7},{15, 13},{15, 17},{15, 19},{15, 21},{15, 23},{15, 25}
    ,{28, 7},{28, 13},{28, 17},{28, 19},{28, 21},{28, 23},{28, 25},{2, 3},{2, 8},{2, 10},{2, 16},{2, 22},{2, 24},{2, 26},{4, 3},{4, 8},{4, 10},{4, 16},{4, 22},{4, 24},{4, 26}
    ,{6, 3},{6, 8},{6, 10},{6, 16},{6, 22},{6, 24},{6, 26},{9, 3},{9, 8},{9, 10},{9, 16},{9, 22},{9, 24},{9, 26},{12, 3},{12, 8},{12, 10},{12, 16},{12, 22},{12, 24},{12, 26}
    ,{15, 3},{15, 8},{15, 10},{15, 16},{15, 22},{15, 24},{15, 26},{28, 3},{28, 8},{28, 10},{28, 16},{28, 22},{28, 24},{28, 26},{2, 1},{2, 5},{2, 11},{2, 14},{2, 18},{2, 20},{2, 27}
    ,{4, 1},{4, 5},{4, 11},{4, 14},{4, 18},{4, 20},{4, 27},{6, 1},{6, 5},{6, 11},{6, 14},{6, 18},{6, 20},{6, 27},{9, 1},{9, 5},{9, 11},{9, 14},{9, 18},{9, 20},{9, 27}
    ,{12, 1},{12, 5},{12, 11},{12, 14},{12, 18},{12, 20},{12, 27},{15, 1},{15, 5},{15, 11},{15, 14},{15, 18},{15, 20},{15, 27},{28, 1},{28, 5},{28, 11},{28, 14},{28, 18},{28, 20},{28, 27}};


    // build constraints from matrix 'net' and 'edges'
    List<LinearConstraint> constraints = new ArrayList<LinearConstraint>();

    int n = net.length;         
    for(int v=0; v<n; v++){
        for(int w=0; w<n; w++){
            for(int x=0; x<n; x++){

                if(v!=w && v!=x && w!=x){
                    double[] lhs = new double[n*n];                 
                    lhs[v*n+x] = 1;
                    lhs[v*n+w] = -1;
                    lhs[w*n+x] = -1;                
                    SparseRealVector vlhs = new OpenMapRealVector(lhs);
                    constraints.add(new LinearConstraint(vlhs, Relationship.LEQ, 0));                       
                }

            }
            double[] lhs = new double[n*n];
            lhs[v*n+w] = 1;
            SparseRealVector vlhs = new OpenMapRealVector(lhs);
            constraints.add(new LinearConstraint(vlhs, Relationship.LEQ, (int)net[v][w]));          
        }
        double[] lhs = new double[n*n];
        lhs[v*n+v] = 1;
        SparseRealVector vlhs = new OpenMapRealVector(lhs);
        constraints.add(new LinearConstraint(vlhs, Relationship.EQ, 0));
    }

    for(int i=0; i<edges.length; i++){
        double[] lhs = new double[n*n];
        lhs[n*edges[i][0]] = 1; // x -> z
        lhs[edges[i][1]] = 1; // z -> y     
        SparseRealVector vlhs = new OpenMapRealVector(lhs);
        constraints.add(new LinearConstraint(vlhs, Relationship.LEQ, (int)net[edges[i][0]][edges[i][1]]));          
    }

    // objective function: maximise sum of all variables
    double[] obj = new double[n*n];
    for(int i = 0; i<n*n; i++) {
        obj[i] = 1;
    }

    // solve
    LinearObjectiveFunction objective = new LinearObjectiveFunction(obj, 0);
    LinearConstraintSet constraintSet = new LinearConstraintSet(constraints);
    SimplexSolver solver = new SimplexSolver();
    PointValuePair solution = solver.optimize(objective, constraintSet, GoalType.MAXIMIZE);
}

Answer 1

To summarise the comments above into an answer:

• This solver is a really a very simplistic implementation, basically using a dense text book algorithm (no one should use that in a practical implementation). There are much better solvers around, including solvers that deal with large sparse problems in a much more efficient way.

• Coin CLP is a good LP solver and there is a java interface. Others include glpk and google Or-Tools.