Hello, I liniarized the following constraint:

if(r1<r2)
A1<A2

r1 and r2 are integers in [1,30] A1 and A2 are deciimals in ]0,10]

the linear form:

r2 * b1 + 30 * ( 1-b1 ) - r1 >= 0

b2 - b1 >= 0

A2 * b2 + 30 * ( 1-b2 ) - A1 >= 0

Where b1 and B2 are two binary variables

However this is not working. Your hel is highly appreciated

asked 29 Jan, 10:08

nardinebasta's gravatar image

nardinebasta
613
accept rate: 0%


Are r1,r2,b1,b2,A1,A2 decision variables? if both r2, b1, A2, b2 are all decision variables, the formulation is not linear because of terms like r2*b1. Correct me if I am wrong

One possible answer is:

r2-r1 <= 29*b1

A2-A1>=((10+e)*b1-10)

is the set of constrains if 'e' is a very small constant (tolerance like 10^-6 or so) you are ready to use, because in linear programs a strict ">" is not solvable with the available algorithms. This set of constraints will work only if r2<=r1 also means A2<A1.

Let me know if this helped.

link

answered 29 Jan, 10:16

Naveen%20Divakaran's gravatar image

Naveen Divak...
7418
accept rate: 25%

edited 31 Jan, 00:10

thank you so much for your assistance. I didn't work though

(30 Jan, 19:30) nardinebasta

when you say it didnt work, what exactly do you mean? You get infeasible solution? Or the result is contrary to expectation?

There is a correction I need to make. The first constraint should look like this: r2-r1 >= (30*b1-29) because as per the requirement in the problem the binary variable should be active (1) when r2 > r1, and since they are integers the difference should be atleast 1. Was it this that caused it to not work?

(30 Jan, 19:32) Naveen Divak...

it didn't so much affect the result. May be because i was inaccurate when answering your question. r1,r2 are parameters whose values are predefined. A2 and A1 are variables whose values should be calculated. b1 and b2 are binary variables that i introduced to manage the constraints.

(30 Jan, 20:00) nardinebasta

if r1, and r2 are constants, you wouldnt need the binary variables, you can already construct the constraint saing A2 -A1 >= e, or A2 - A1 <= 0, based on what the values of r1 and r2 at the time you generate the lp model to solve. Maybe I am still not understanding your problem.

(30 Jan, 20:26) Naveen Divak...

in more details: r is the rank where r(u)<r(v) implies that the rank of u is smaller than the rank of v. 1 is the smallest rank and 30 is the highest rank. i want to force A(u) to be smaller than A(v) in the case that r(u)<r(v)

(30 Jan, 23:52) nardinebasta

Sorry, I was wrong again. With my earlier suggestion r2-r1 could still have been negative with b1 being 1 or 0. Please take a look at the edited answer. Maybe thats what we were looking for. Let me know

(31 Jan, 00:11) Naveen Divak...

it worked, many many thanks :)

(31 Jan, 08:28) nardinebasta

Great! Sorry I started off with the wrong answer. Can you mark the answer as accepted then? I am glad I could help.

(31 Jan, 09:19) Naveen Divak...
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Asked: 29 Jan, 10:08

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