from pyomo.environ import *
from pyomo.opt import SolverStatus, TerminationCondition
def create_relaxation():
## Create Pyomo Model
m = ConcreteModel()
## Declare variables (all continous for now)
m.x = Var(domain=NonNegativeReals)
m.y1 = Var(bounds=(0,1))
m.y2 = Var(bounds=(0,1))
m.y3 = Var(bounds=(0,1))
## Declare constraints
def con1_rule(m):
return -1.0*m.x + 3.0*m.y1 + 2.0*m.y2 + m.y3 <= 0
m.con1 = Constraint(rule=con1_rule)
def con2_rule(m):
return -5.0*m.y1 - 8.0*m.y2 - 3.0*m.y3 <= -9
m.con2 = Constraint(rule=con2_rule)
## Declare objective
def obj_rule(m):
return m.x + m.y1 + 3*m.y2 + 2*m.y3
m.obj = Objective(rule=obj_rule,sense=minimize)
return m
def solve_print(m,verbose=False):
# Solve the model
opt = SolverFactory('cbc')
results = opt.solve(m, tee=verbose)
if (results.solver.status == SolverStatus.ok) and (results.solver.termination_condition == TerminationCondition.optimal):
# Print solution when the solution is optimal
print("x = ",value(m.x))
print("y1 = ",value(m.y1))
print("y2 = ",value(m.y2))
print("y3 = ",value(m.y3))
print("Z = ",value(m.obj))
elif (results.solver.termination_condition == TerminationCondition.infeasible):
print("Infeasible.")
else:
# Something else is wrong
print('Solver Status:',result.solver.status)
# m.pprint()
Full LP relaxation.
m = create_relaxation()
solve_print(m,False)
x = 2.6 y1 = 0.2 y2 = 1.0 y3 = 0.0 Z = 5.800000000000001
m = create_relaxation()
m.y1.fix(0.0)
solve_print(m,False)
x = 2.3333333 y1 = 0.0 y2 = 1.0 y3 = 0.33333333 Z = 5.999999959999999
m = create_relaxation()
m.y1.fix(1.0)
solve_print(m,False)
x = 4.0 y1 = 1.0 y2 = 0.5 y3 = 0.0 Z = 6.5
m = create_relaxation()
m.y1.fix(0.0)
m.y3.fix(0.0)
solve_print(m,False)
WARNING: Loading a SolverResults object with a warning status into
model.name="unknown";
- termination condition: infeasible
- message from solver: <undefined>
Infeasible.
m = create_relaxation()
m.y1.fix(0.0)
m.y3.fix(1.0)
solve_print(m,False)
x = 2.5 y1 = 0.0 y2 = 0.75 y3 = 1.0 Z = 6.75
m = create_relaxation()
m.y1.fix(1.0)
m.y2.fix(0.0)
solve_print(m,False)
WARNING: Loading a SolverResults object with a warning status into
model.name="unknown";
- termination condition: infeasible
- message from solver: <undefined>
Infeasible.
m = create_relaxation()
m.y1.fix(1.0)
m.y2.fix(1.0)
solve_print(m,False)
x = 5.0 y1 = 1.0 y2 = 1.0 y3 = 0.0 Z = 9.0
m = create_relaxation()
m.y1.fix(0.0)
m.y3.fix(1.0)
m.y2.fix(0.0)
solve_print(m,False)
WARNING: Loading a SolverResults object with a warning status into
model.name="unknown";
- termination condition: infeasible
- message from solver: <undefined>
Infeasible.
m = create_relaxation()
m.y1.fix(0.0)
m.y3.fix(1.0)
m.y2.fix(1.0)
solve_print(m,False)
x = 3.0 y1 = 0.0 y2 = 1.0 y3 = 1.0 Z = 8.0