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From "Benjamin McCann (JIRA)" <j...@apache.org>
Subject [jira] Commented: (MATH-286) SimplexSolver not working as expected?
Date Tue, 01 Sep 2009 21:41:34 GMT

    [ https://issues.apache.org/jira/browse/MATH-286?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12750120#action_12750120
] 

Benjamin McCann commented on MATH-286:
--------------------------------------

phpsimplex said that when there's a tie, they make the artificial variable leave the basis,
which we're not doing and would solve the problem in this case:
http://www.phpsimplex.com/en/simplex_method_theory.htm#anomalous
i'll try putting together a patch, likely this weekend, to do that

> SimplexSolver not working as expected?
> --------------------------------------
>
>                 Key: MATH-286
>                 URL: https://issues.apache.org/jira/browse/MATH-286
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 2.0
>         Environment: Java 1.6.0_13 on  Windows XP 32-bit
>            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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