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Defining a linear relaxation

Description
Example of defining linear relaxations (this feature requires Xpress Optimizer in addition to Xpress Kalis)
• knapsackalld_cp.mos: Integer knapsack problem with 'alldifferent' constraint solved with standard CP search.
• knapsackalld_relax.mos: Defining a linear relaxation and corresponding search.
• customrelax.mos: Defining a customized linear relaxation
Further explanation of this example: 'Xpress Kalis Mosel Reference Manual'

 customrelax.zip [download all files]

Source Files
By clicking on a file name, a preview is opened at the bottom of this page.
 customrelax.mos [download] knapsackalld_cp.mos [download] knapsackalld_relax.mos [download]

customrelax.mos

(!****************************************************************
CP example problems
===================

file customrelax.mos

Defining customized linear relaxations.

(c) 2009 Artelys S.A. and Fair Isaac Corporation
Creation: 2009
*****************************************************************!)
model "Custom relaxations"
uses "kalis"

declarations
myrelax: cplinrelax               ! A linear relaxation
a1,a2  : cpauxvar                 ! Auxiliary variables for relaxation
taux   : array(1..4) of cpauxvar  ! Array of auxiliary variables

x1,x2,x3: cpvar                   ! Finite domain variables
z       : cpfloatvar              ! CP variable with continuous domain
CAlld   : cpctr                   ! A CP constraint
end-declarations

! Define an 'alldifferent' constraint
CAlld := all_different({x1,x2,x3})

! Build an automatic 'LP' oriented linear relaxation
myrelax1 := cp_get_linrelax(0)

! Setting bounds on the auxiliary variables
setdomain(a2,0,1)
setdomain(a1,0.56,18.67)

! Adding linear inequalities to the relaxation
myrelax += 3*a1      <= 3
myrelax += a1+a2     >= 3.1
myrelax += 2*a1-4*a2  = 3
myrelax += a1-x1      <= 3.4
myrelax += a1+4*a2-z <= 3
myrelax += get_linrelax(CAlld,0)
myrelax +=
get_indicator(x1,1) + get_indicator(x2,1) + get_indicator(x3,1) <= 1
myrelax += sum(i in 1..4) taux(i) = 4

! Set integrality condition for variables in the relaxation
set_integer(myrelax,a2,true)
set_integer(myrelax,x1,true)

! Output the resulting relaxation to the screen
cp_show_relax(myrelax)

end-model