logical.py

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from pyscipopt import Model
from pyscipopt import quicksum
 
"""
 
 AND/OR/XOR CONSTRAINTS
 
 Tutorial example on how to use AND/OR/XOR constraints.
 
 N.B.: standard SCIP XOR constraint works differently from AND/OR by design.
 The constraint is set with a boolean rhs instead of an integer resultant.
 cf. http://listserv.zib.de/pipermail/scip/2018-May/003392.html
 A workaround to get the resultant as variable is here proposed.
 
"""
 
 
def printFunc(name, m):
    """prints results"""
    print("* %s *" % name)
    objSet = bool(m.getObjective().terms.keys())
    print("* Is objective set? %s" % objSet)
    if objSet:
        print("* Sense: %s" % m.getObjectiveSense())
    for v in m.getVars():
        if v.name != "n":
            print("%s: %d" % (v, round(m.getVal(v))))
    print("\n")
 
 
# AND
model = Model()
model.hideOutput()
x = model.addVar("x", "B")
y = model.addVar("y", "B")
z = model.addVar("z", "B")
r = model.addVar("r", "B")
model.addConsAnd([x, y, z], r)
model.addCons(x == 1)
model.setObjective(r, sense="minimize")
model.optimize()
printFunc("AND", model)
 
# OR 
model = Model()
model.hideOutput()
x = model.addVar("x", "B")
y = model.addVar("y", "B")
z = model.addVar("z", "B")
r = model.addVar("r", "B")
model.addConsOr([x, y, z], r)
model.addCons(x == 0)
model.setObjective(r, sense="maximize")
model.optimize()
printFunc("OR", model)
 
# XOR (r as boolean, standard) 
model = Model()
model.hideOutput()
x = model.addVar("x", "B")
y = model.addVar("y", "B")
z = model.addVar("z", "B")
r = True
model.addConsXor([x, y, z], r)
model.addCons(x == 1)
model.optimize()
printFunc("Standard XOR (as boolean)", model)
 
# XOR (r as variable, custom) 
model = Model()
model.hideOutput()
x = model.addVar("x", "B")
y = model.addVar("y", "B")
z = model.addVar("z", "B")
r = model.addVar("r", "B")
n = model.addVar("n", "I")  # auxiliary
model.addCons(r + quicksum([x, y, z]) == 2 * n)
model.addCons(x == 0)
model.setObjective(r, sense="maximize")
model.optimize()
printFunc("Custom XOR (as variable)", model)