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Andrea commented on MATH286:

Hi Ben,
Even if I don't completely understand the format of the posted tableau, I guess the error
is in the last step...
You can solve the above problem on this homepage, where you can see all the steps of the simplex
method:
http://www.phpsimplex.com/simplex/page2.php?objetivo=max&x1=0.8&x2=0.7&restricciones=3&variables=2&l=en&x11=1&x12=1&desigualdad1=1&y1=18&x21=1&x22=0&desigualdad2=1&y2=10&x31=0&x32=1&desigualdad3=1&y3=8&Submit=Continue
The tables you posted and the tables on the above homepage look similar till the last step
(the first of the second phase)... Try look at it, maybe you find the problem
> SimplexSolver not working as expected?
> 
>
> Key: MATH286
> URL: https://issues.apache.org/jira/browse/MATH286
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.0
> Environment: Java 1.6.0_13 on Windows XP 32bit
> Reporter: Andrea
> Attachments: simplex.txt, SimplexSolverTest.patch, SimplexTableau.patch
>
>
> I guess (but I could be wrong) that SimplexSolver does not always return the optimal
solution, nor satisfies all the constraints...
> Consider this LP:
> max: 0.8 x0 + 0.2 x1 + 0.7 x2 + 0.3 x3 + 0.6 x4 + 0.4 x5;
> r1: x0 + x2 + x4 = 23.0;
> r2: x1 + x3 + x5 = 23.0;
> r3: x0 >= 10.0;
> r4: x2 >= 8.0;
> r5: x4 >= 5.0;
> LPSolve returns 25.8, with x0 = 10.0, x1 = 0.0, x2 = 8.0, x3 = 0.0, x4 = 5.0, x5 = 23.0;
> The same LP expressed in Apache commons math is:
> LinearObjectiveFunction f = new LinearObjectiveFunction(new double[] { 0.8, 0.2, 0.7,
0.3, 0.6, 0.4 }, 0 );
> Collection<LinearConstraint> constraints = new ArrayList<LinearConstraint>();
> 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));
> RealPointValuePair solution = new SimplexSolver().optimize(f, constraints, GoalType.MAXIMIZE,
true);
> that returns 22.20, with x0 = 15.0, x1 = 23.0, x2 = 8.0, x3 = 0.0, x4 = 0.0, x5 = 0.0;
> Is it possible SimplexSolver is buggy that way? The returned value is 22.20 instead of
25.8, and the last constraint (x4 >= 5.0) is not satisfied...
> Am I using the interface wrongly?

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