6.1.1.4.1.5. `pytfa.optim.reformulation`¶

MILP-fu to reformulate problems

6.1.1.4.1.5.1. Module Contents¶

`subs_bilinear`(expr)	Substitutes bilinear forms from an expression with dedicated variables
`glovers_linearization`(b, fy, z=None, L=0, U=1000)	Glover, Fred.
`petersen_linearization`(b, x, z=None, M=1000)	PETERSEN, C,,
`linearize_product`(model, b, x, queue=False)	param model

`ConstraintTuple`
`OPTLANG_BINARY`

pytfa.subs_bilinear(expr)¶: Substitutes bilinear forms from an expression with dedicated variables :param expr: :return:

pytfa.glovers_linearization(b, fy, z=None, L=0, U=1000)¶

Glover, Fred. “Improved linear integer programming formulations of nonlinear integer problems.” Management Science 22.4 (1975): 455-460.

Performs Glovers Linearization of a product z = b*f(y) <=> z - b*f(y) = 0 <=> { L*b <= z <= U*b { f(y) - U*(1-b) <= z <= f(y) - L*(1-b)

where : * b is a binary variable * f a linear combination of continuous or integer variables y

Parameters

b – Must be a binary optlang variable
z – Must be an optlang variable. Will be mapped to the product so that z = b*f(y)
fy – Must be an expression or variable
L – minimal value for fy
U – maximal value for fy

Returns

pytfa.petersen_linearization(b, x, z=None, M=1000)¶

PETERSEN, C,, “A Note on Transforming the Product of Variables to Linear Form in Linear CLIFFORD Programs,” Working Paper, Purdue University, 1971.

Performs Petersen Linearization of a product z = b*x <=> z - b*x = 0 <=> { x + M*b - M <= z <= M*b { z <= x

where : * b is a binary variable * f a linear combination of continuous or integer variables y

Parameters

x – Must be an expression or variable
b – Must be a binary optlang variable
z – Must be an optlang variable. Will be mapped to the product so that z = b*f(y)
M – big-M constraint

Returns

pytfa.linearize_product(model, b, x, queue=False)¶

Parameters

Returns