def three_objective_model():
model = ConcreteModel()
# Define variables
model.LIGN = Var(within=NonNegativeReals)
model.LIGN1 = Var(within=NonNegativeReals)
model.LIGN2 = Var(within=NonNegativeReals)
model.OIL = Var(within=NonNegativeReals)
model.OIL2 = Var(within=NonNegativeReals)
model.OIL3 = Var(within=NonNegativeReals)
model.NG = Var(within=NonNegativeReals)
model.NG1 = Var(within=NonNegativeReals)
model.NG2 = Var(within=NonNegativeReals)
model.NG3 = Var(within=NonNegativeReals)
model.RES = Var(within=NonNegativeReals)
model.RES1 = Var(within=NonNegativeReals)
model.RES3 = Var(within=NonNegativeReals)
# --------------------------------------
# Define the objective functions
# --------------------------------------
def objective1(model):
return 30 * model.LIGN + 75 * model.OIL + 60 * model.NG + 90 * model.RES
def objective2(model):
return 1.44 * model.LIGN + 0.72 * model.OIL + 0.45 * model.NG
def objective3(model):
return model.OIL + model.NG
# --------------------------------------
# Define the regular constraints
# --------------------------------------
def constraint1(model):
return model.LIGN - model.LIGN1 - model.LIGN2 == 0
def constraint2(model):
return model.OIL - model.OIL2 - model.OIL3 == 0
def constraint3(model):
return model.NG - model.NG1 - model.NG2 - model.NG3 == 0
def constraint4(model):
return model.RES - model.RES1 - model.RES3 == 0
def constraint5(model):
return model.LIGN <= 31000
def constraint6(model):
return model.OIL <= 15000
def constraint7(model):
return model.NG <= 22000
def constraint8(model):
return model.RES <= 10000
def constraint9(model):
return model.LIGN1 + model.NG1 + model.RES1 >= 38400
def constraint10(model):
return model.LIGN2 + model.OIL2 + model.NG2 >= 19200
def constraint11(model):
return model.OIL3 + model.NG3 + model.RES3 >= 6400
# --------------------------------------
# Add components to the model
# --------------------------------------
# Add the constraints to the model
model.con1 = Constraint(rule=constraint1)
model.con2 = Constraint(rule=constraint2)
model.con3 = Constraint(rule=constraint3)
model.con4 = Constraint(rule=constraint4)
model.con5 = Constraint(rule=constraint5)
model.con6 = Constraint(rule=constraint6)
model.con7 = Constraint(rule=constraint7)
model.con8 = Constraint(rule=constraint8)
model.con9 = Constraint(rule=constraint9)
model.con10 = Constraint(rule=constraint10)
model.con11 = Constraint(rule=constraint11)
# Add the objective functions to the model using ObjectiveList(). Note
# that the first index is 1 instead of 0!
model.obj_list = ObjectiveList()
model.obj_list.add(expr=objective1(model), sense=minimize)
model.obj_list.add(expr=objective2(model), sense=minimize)
model.obj_list.add(expr=objective3(model), sense=minimize)
# By default deactivate all the objective functions
for o in range(len(model.obj_list)):
model.obj_list[o + 1].deactivate()
return model
