Originally posted by: SystemAdmin

[a_shraideh said:]

Hello every body,
i am working with cplex in my research,
currently i am working on Bin packing problem model, but i dont know if ceplex is capaple to form bilinear probelm

ie,min  X1*X2+X2*X3  ... etc
thnx u in advance


#DecisionOptimization
#MathematicalProgramming-General

Originally posted by: SystemAdmin

[a_shraideh said:]

Hello every body,
i am working with cplex in my research,
currently i am working on Bin packing problem model, but i dont know if ceplex is capaple to form bilinear probelm

my objectiv function is

Min y1+y2.....yi

and my constraints have multiplication of variable and they dont have quadratic degree
for exemple
subject to
x1+X2+y1*x1+y2X2 ....>C

which model in cplex is suitable for folving this problem
thank in advacne
#DecisionOptimization
#MathematicalProgramming-General

Originally posted by: SystemAdmin

[Didier Vidal said:]

Hello,

If your objective function is convex, (and your constraints are linear) this falls in the class of problems that CPLEX can minimize.

If you add quadratic constraints, you will also have to check that the constraints define a convex region.

Didier Vidal.
#DecisionOptimization
#MathematicalProgramming-General

Originally posted by: SystemAdmin

[a_shraideh said:]

thank didier ,
in fact i didnt explain my problem correctly.
my objectiv function is
Min y1+y2.....yi

and my constraints have multiplication of variable and they dont have quadratic degree
for exemple
subject to
x1+X2+y1*x1+y2X2 ....

which model in cplex is suitable for folving this problem
thank in advacne

#DecisionOptimization
#MathematicalProgramming-General

Originally posted by: SystemAdmin

[oussedik said:]

Hi,

You can also, if possible for you, use a linear approximation of X1*X2. First you need to set some bounds on X1 and X2

a < X1 < b with a > 0 and b > 0
c < X2 < d with c > 0 and d > 0

Then it is possible to replace X1*X2 by a new variable Z where Z satisfies the constraints
Z ≤ aX2 + dX1 − ad
Z ≤ bX2 + cX1 − bc
Z ≥ aX2 + cX1 − ac
Z ≥ bX2 + dX1 − bd

For bin packing problems, X1 and X2 are probably binaries in your model, then the linear transformation is exact. With Z binary, this makes:
Z ≤ X1
Z ≤ X2
Z ≥ 0
Then, If X1 or X2 = 0 => Z= 0

Z ≥ X2 + X1 − 1
If both X1, X2 are at 1 then Z=1

Sofiane
#DecisionOptimization
#MathematicalProgramming-General