How To Write A Conditional Constraint In Cplex Python?

I have a model that has one binary variable x [i] [j] [k]. I need to add a constraint that fullfils this condition: if x[i][j][k1]==1 and x[j][i][k2]==1 Then: k2-k1>8 I

Solution 1:

let me share the if then example from

https://www.linkedin.com/pulse/making-optimization-simple-python-alex-fleischer/

from docplex.mp.model import Model

mdl = Model(name='buses')
nbbus40 = mdl.integer_var(name='nbBus40')
nbbus30 = mdl.integer_var(name='nbBus30')
mdl.add_constraint(nbbus40*40 + nbbus30*30 >= 300, 'kids')
mdl.minimize(nbbus40*500 + nbbus30*400)

mdl.solve()

for v in mdl.iter_integer_vars():
   print(v," = ",v.solution_value)

print()
print("with if nb buses 40 more than 3  then nbBuses30 more than 7")

#if then constraint
mdl.add(mdl.if_then(nbbus40>=3,nbbus30>=7))
mdl.minimize(nbbus40*500 + nbbus30*400)

mdl.solve()



for v in mdl.iter_integer_vars():
    print(v," = ",v.solution_value) 

and if you want to see and in the if

from docplex.mp.model import Model

mdl = Model(name='buses')
nbbus40 = mdl.integer_var(name='nbBus40')
nbbus30 = mdl.integer_var(name='nbBus30')
mdl.add_constraint(nbbus40*40 + nbbus30*30 >= 300, 'kids')
mdl.minimize(nbbus40*500 + nbbus30*400)

mdl.solve()

for v in mdl.iter_integer_vars():
   print(v," = ",v.solution_value)

print()
print("with if nb buses 40 more than 3 and less than 7 then nbBuses30 more than 7")

#if then constraint
mdl.add(mdl.if_then((nbbus40>=3) + (nbbus40<=7)>=2,nbbus30>=7))
mdl.minimize(nbbus40*500 + nbbus30*400)

mdl.solve()



for v in mdl.iter_integer_vars():
    print(v," = ",v.solution_value) 

which you can also rewrite

from docplex.mp.model import Model

mdl = Model(name='buses')
nbbus40 = mdl.integer_var(name='nbBus40')
nbbus30 = mdl.integer_var(name='nbBus30')
mdl.add_constraint(nbbus40*40 + nbbus30*30 >= 300, 'kids')
mdl.minimize(nbbus40*500 + nbbus30*400)

mdl.solve()

for v in mdl.iter_integer_vars():
   print(v," = ",v.solution_value)

print()
print("with if nb buses 40 more than 3 and less than 7 then nbBuses30 more than 7")

#if then constraint
mdl.add((((nbbus40>=3) + (nbbus40<=7)>=2))<=(nbbus30>=7))
mdl.minimize(nbbus40*500 + nbbus30*400)

mdl.solve()



for v in mdl.iter_integer_vars():
    print(v," = ",v.solution_value) 

Solution 2:

Model.if_then links two linear constraints left-to-right. If the first one becomes satisfied, the second will be satisfied too.

In your case , I understand that in k2-k1>8 there are no decision variables involved. SO this is purely data-dependent, known at model build time.

In that case, the causality works the other way round: if k2-k1>8 then both x[i,j,k1] and x[i,j,k2] must be equal to 1.

The simplest code is then:

if k2-k1>8:
   m.add(x[i,j,k1] == 1)
   m.add(x[i,j,k2] == 1)