CglKnapsackCover::exactSolveKnapsack returns suboptimal solutions

[tosttost]

CglKnapsackCover::exactSolveKnapsack sometimes returns suboptimal solutions. Example:

int main()
{
    const int n = 6;
    const double c = 7.0;
    const double pp[] = { 10.0, 5.0, 2, 2, 1.4, 1.1 };
    const double ww[] = { 2.0,  2.0, 2, 2, 1.5, 1.4 };

    //verify that items are sorted
    for(int i = 1; i < n; ++i)
    {
        assert(pp[i] / ww[i] <= pp[i - 1] / ww[i - 1]);
    }

    double z = 42;
    int* x = new int[n];
    exactSolveKnapsack(n, c, pp, ww, z, x);
    printf("z=%f\n", z);
    assert(fabs(z - 17.5) < 1e-3);
    delete[] x;
}

In fact Matthew Galati beat me by 6 years: https://list.coin-or.org/pipermail/cgl/2013-July/000156.html See his post for details.

I verified that the profits are in fact fractional - simply put a "printf" into the function... Based on the comments inside CglKnapsackCover::findExactMostViolatedMinCover it looks like this can lead to weaker (as Matthew suspected) or missed cuts (if the knapsack solution is suboptimal, "oofv = (sum (1-xstar_j))- max sum (1-xstar)y_j" gets larger and the test "oofv < 1" might fail).

By the way: there some typos in CglKnapsackCover.cpp: "inequalty", "appraoch"