# MINLP written by GAMS Convert at 02/17/22 17:22:56
#
# Equation counts
#     Total        E        G        L        N        X        C        B
#        10        0        0       10        0        0        0        0
#
# Variable counts
#                  x        b        i      s1s      s2s       sc       si
#     Total     cont   binary  integer     sos1     sos2    scont     sint
#        13        0        0       13        0        0        0        0
# FX      0
#
# Nonzero counts
#     Total    const       NL
#        28       28        0
#
# Reformulation has removed 1 variable and 1 equation

from pyomo.environ import *

model = m = ConcreteModel()

m.i1 = Var(within=Integers, bounds=(0,1), initialize=0)
m.i2 = Var(within=Integers, bounds=(0,1), initialize=0)
m.i3 = Var(within=Integers, bounds=(0,1), initialize=0)
m.i4 = Var(within=Integers, bounds=(0,1), initialize=0)
m.i5 = Var(within=Integers, bounds=(0,1), initialize=0)
m.i6 = Var(within=Integers, bounds=(0,1), initialize=0)
m.i7 = Var(within=Integers, bounds=(0,1), initialize=0)
m.i8 = Var(within=Integers, bounds=(0,1), initialize=0)
m.i9 = Var(within=Integers, bounds=(0,1), initialize=0)
m.i10 = Var(within=Integers, bounds=(0,1e+15), initialize=0)
m.i11 = Var(within=Integers, bounds=(0,1e+15), initialize=0)
m.i12 = Var(within=Integers, bounds=(0,1e+15), initialize=0)
m.i13 = Var(within=Integers, bounds=(0,1), initialize=0)

m.obj = Objective(sense=minimize, expr= 5 * m.i1 * m.i1 + 5 * m.i1 + 5 * m.i2
    * m.i2 - 5 * m.i2 + 5 * m.i3 * m.i3 + 5 * m.i3 + 5 * m.i4 * m.i4 + 5 *
    m.i4 + 9 * m.i10 * m.i10 - m.i10 - m.i5 + m.i6 - m.i7 - m.i8 - m.i9 - m.i11
    - m.i12 - m.i13)

m.e1 = Constraint(expr= 2 * m.i1 + 2 * m.i2 + m.i10 + m.i11 <= 10)
m.e2 = Constraint(expr= 2 * m.i1 + 2 * m.i3 + m.i10 + m.i12 <= 10)
m.e3 = Constraint(expr= 2 * m.i2 + 2 * m.i3 + m.i11 + m.i12 <= 10)
m.e4 = Constraint(expr= -8 * m.i1 + m.i10 <= 0)
m.e5 = Constraint(expr= -8 * m.i2 + m.i11 <= 0)
m.e6 = Constraint(expr= -8 * m.i3 + m.i12 <= 0)
m.e7 = Constraint(expr= -2 * m.i4 - m.i5 + m.i10 <= 0)
m.e8 = Constraint(expr= -2 * m.i6 - m.i7 + m.i11 <= 0)
m.e9 = Constraint(expr= -2 * m.i8 - m.i9 + m.i12 <= 0)
m.e10 = Constraint(expr= m.i13 <= 1)