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### genconstr.py

#!/usr/bin/env python3.11

# Copyright 2024, Gurobi Optimization, LLC

# In this example we show the use of general constraints for modeling
# some common expressions. We use as an example a SAT-problem where we
# want to see if it is possible to satisfy at least four (or all) clauses
# of the logical form
#
# L = (x0 or ~x1 or x2)  and (x1 or ~x2 or x3)  and
#     (x2 or ~x3 or x0)  and (x3 or ~x0 or x1)  and
#     (~x0 or ~x1 or x2) and (~x1 or ~x2 or x3) and
#     (~x2 or ~x3 or x0) and (~x3 or ~x0 or x1)
#
# We do this by introducing two variables for each literal (itself and its
# negated value), one variable for each clause, one variable indicating
# whether we can satisfy at least four clauses, and one last variable to
# identify the minimum of the clauses (so if it is one, we can satisfy all
# clauses). Then we put these last two variables in the objective.
# The objective function is therefore
#
# maximize Obj0 + Obj1
#
#  Obj0 = MIN(Clause1, ... , Clause8)
#  Obj1 = 1 -> Clause1 + ... + Clause8 >= 4
#
# thus, the objective value will be two if and only if we can satisfy all
# clauses; one if and only if at least four but not all clauses can be satisfied,
# and zero otherwise.

import gurobipy as gp
from gurobipy import GRB
import sys

try:
NLITERALS = 4

n = NLITERALS

# Example data:
#   e.g. {0, n+1, 2} means clause (x0 or ~x1 or x2)
Clauses = [
[0, n + 1, 2],
[1, n + 2, 3],
[2, n + 3, 0],
[3, n + 0, 1],
[n + 0, n + 1, 2],
[n + 1, n + 2, 3],
[n + 2, n + 3, 0],
[n + 3, n + 0, 1],
]

# Create a new model
model = gp.Model("Genconstr")

# initialize decision variables and objective

(Lit[i] + NotLit[i] == 1.0 for i in range(NLITERALS)), name="CNSTR_X"
)

for i, c in enumerate(Clauses):
clause = []
for l in c:
if l >= n:
clause.append(NotLit[l - n])
else:
clause.append(Lit[l])
model.addConstr(Cla[i] == gp.or_(clause), "CNSTR_Clause" + str(i))

model.addConstr((Obj1 == 1) >> (Cla.sum() >= 4.0), name="CNSTR_Obj1")

# Set optimization objective
model.setObjective(Obj0 + Obj1, GRB.MAXIMIZE)

# Save problem
model.write("genconstr.mps")
model.write("genconstr.lp")

# Optimize
model.optimize()

# Status checking
status = model.getAttr(GRB.Attr.Status)

if status in (GRB.INF_OR_UNBD, GRB.INFEASIBLE, GRB.UNBOUNDED):
print("The model cannot be solved because it is infeasible or unbounded")
sys.exit(1)

if status != GRB.OPTIMAL:
print("Optimization was stopped with status ", status)
sys.exit(1)

# Print result
objval = model.getAttr(GRB.Attr.ObjVal)

if objval > 1.9:
print("Logical expression is satisfiable")
elif objval > 0.9:
print("At least four clauses can be satisfied")
else:
print("Not even three clauses can be satisfied")

except gp.GurobiError as e:
print(f"Error code {e.errno}: {e}")

except AttributeError:
print("Encountered an attribute error")


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