[ojAlgo-user] Integer Linear Programming: ojAlgo calculates invalid solution

[Uli S. <Uli...@In...>]

Hi everyone,

the attached Java program solves a relatively simple ILP with ojAlgo. 
However, the solution calculates is invalid. Can somehow shed some light 
into why this is?

Hopefully the program explains itself, but here is some more text:

The function getCoefficients() returns the coefficients for 202 
inequalities of the form coef[0]*x + coef[1]*y < 0. The main function 
creates an ExpressionsBasedModel from this, transformimg the "< 0" into 
"<= -1" (which is valid since this is about integer values). It prints 
the solution calculated and then checks if all the inequalities really 
are satisfied.

However, this fails since the solution calculated doesn't solve all 
inequalities:

x = 19.999999999999993 ~ 20
y = -0.9950000000000006 ~ -1
Exception in thread "main" java.lang.Exception: -10*x + -200*y = 0 must 
be negative (exact: -0.9999999999998100)
	at Solve.main(Solve.java:60)

The program also prints the exact solutions calculated from the 
BigDecimals that ojAlgo produced. This is the "exact" value you see in 
the error message above and, as you see, this value (almost) satisfies 
the condition "<= -1".

Valid solutions to this inequality systems would be x=21, y=-1 or x=201, 
y=-10.

Obviously, this seems to be a rounding issue. Is there anything that can 
be done about it?

Cheers,
Uli
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