On Tue, Aug 12, 2008 at 12:01 AM, Meketon, Marc
<address@hidden> wrote:
Your semantics are incorrect.
Irrational means the number can not be
represented as P/Q, where P and Q are integers.
For example, 1/3 is not irrational. It is
a rational number that is repeating in the base 10 numbering system.
The sqrt(2) is irrational.
You are right. I should have used term "repeating decimal" instead of "irrational". Should have looked up before using it.
Note that your proposed fix – to represent
the objective value using only integer coefficients – is not a fix in
general since the course of the linear/integer program will probably have many
non-integer values in the tableau.
More importantly, note that your problem
has multiple optimal. x_1 = 0, x_2 = 6 is feasible with objective value of 1.
Your proposed solution of x_1=2, x_2=2 is
feasible, with the same objective value of 1.
Yes. Integer solution (x_1 = 2, x_2 = 2) is one of 3 optimal integer solutions. It is desired (rather than proposed), in order to solve the original issue (about not generating corressponing pattern). Right now I am making a claim about the reason this solution is not being produced. That claim the "repeating decimals" are approximated when used in obj. func. coeff. Specifically 0.3333... is approximated as 0.333333333333333, and more importantly 0.166... is approximated as 0.166666666666667.
However other possibility is that even with the approximate values, GLPK can give optimal integer solution (x_1 = 2, x_2 = 2). Since there are 3 optimal integer solutions, it is matter of finding all of them, instead of accepting first optimal solution. I need to work on this to find out.
Thanks