Modeling the absolute value

Problems with modeling
Manassaldi
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Re: Modeling the absolute value

Post by Manassaldi » 1 year ago

Hi, the dollar command is used to manipulate the sets.
For example, if the restrictions eq1, eq2, eq3 and eq4 does not apply to the last "t":

eq1(n,m,t)$(ord(t) ne card(t)).. 1 - z(n,m,t) + z(n,m,t+1) + absvalue(n,m,t) =g= 1;
eq2(n,m,t)$(ord(t) ne card(t)).. 1 - z(n,m,t) + 1-z(n,m,t+1) + 1-absvalue(n,m,t) =g= 1;
eq3(n,m,t)$(ord(t) ne card(t)).. z(n,m,t) + 1-z(n,m,t+1) + absvalue(n,m,t) =g= 1;
eq4(n,m,t)$(ord(t) ne card(t)).. z(n,m,t) + z(n,m,t+1) + 1-absvalue(n,m,t) =g= 1;
eq5.. sum((n,m,t),absvalue(n,m,t)) =l= 2*j;

"$(ord(t) ne card(t))" is mean that the position of the set "t" (card(t)) is not equal (ne) to the last position (card(t)).

I hope this can help you
Bye!

gnaeidj
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Re: Modeling the absolute value

Post by gnaeidj » 1 year ago

Manassaldi wrote:Hi, the dollar command is used to manipulate the sets.
For example, if the restrictions eq1, eq2, eq3 and eq4 does not apply to the last "t":

eq1(n,m,t)$(ord(t) ne card(t)).. 1 - z(n,m,t) + z(n,m,t+1) + absvalue(n,m,t) =g= 1;
eq2(n,m,t)$(ord(t) ne card(t)).. 1 - z(n,m,t) + 1-z(n,m,t+1) + 1-absvalue(n,m,t) =g= 1;
eq3(n,m,t)$(ord(t) ne card(t)).. z(n,m,t) + 1-z(n,m,t+1) + absvalue(n,m,t) =g= 1;
eq4(n,m,t)$(ord(t) ne card(t)).. z(n,m,t) + z(n,m,t+1) + 1-absvalue(n,m,t) =g= 1;
eq5.. sum((n,m,t),absvalue(n,m,t)) =l= 2*j;

"$(ord(t) ne card(t))" is mean that the position of the set "t" (card(t)) is not equal (ne) to the last position (card(t)).

I hope this can help you
Bye!

Hi
Thank you so much
it was such a great help

Monsef
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Re: Modeling the absolute value

Post by Monsef » 1 week ago

Does someone know how to linearize and optimize this absolute term |A - B|, where both A and B are free integers. And what if the term changed to |A-1|, what will the minimization look like?.

Here is my Linearization for |A-1|
X>=A-1
X>=1-A
X>=0.

Min X

Is this correct?
Last edited by Monsef 3 days ago, edited 1 time in total.
Monsef Tahir

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bussieck
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Re: Modeling the absolute value

Post by bussieck » 1 week ago

Look at GAMS Model Library model absmip (https://www.gams.com/latest/gamslib_ml/ ... bsmip.html) This shows how to linearly (with discrete variables) model abs, min, max, and sign.

-Michael

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