CODEWITHSUNDEEP
optimizationpyomo
ulicious
ulicious

Reputation: 31

Pyomo: Unbounded objective function though bounded

I am currently implementing an optimization problem with pyomo and since now some hours I get the message that my problem is unbounded. After searching for the issue, I came along one term which seems to be unbounded. I excluded this term from the objective function and it shows that it takes a very high negative value, which supports the assumption that it is unbounded to -Inf.

But I have checked the problem further and it is impossible that the term is unbounded, as following code and results show:

model.nominal_cap_storage = Var(model.STORAGE, bounds=(0,None)) #lower bound is 0

#I assumed very high CAPEX for each storage (see print)
dict_capex_storage = {'battery': capex_battery_storage,
                      'co2': capex_co2_storage,
                      'hydrogen': capex_hydrogen_storage,
                      'heat': capex_heat_storage,
                      'syncrude': capex_syncrude_storage}

print(dict_capex_storage)
>>> {'battery': 100000000000000000, 'co2': 100000000000000000,
     'hydrogen': 1000000000000000000, 'heat': 1000000000000000, 'syncrude': 10000000000000000000}

From these assumptions I already assume that it is impossible that the one term can be unbounded towards -Inf as the capacity has the lower bound of 0 and the CAPEX is a positive fixed value. But now it gets crazy. The following term is has the issue of being unbounded:

model.total_investment_storage = Var()
def total_investment_storage_rule(model):
    return model.total_investment_storage == sum(model.nominal_cap_storage[storage] * dict_capex_storage[storage] \
                                                 for storage in model.STORAGE)
model.total_investment_storage_con = Constraint(rule=total_investment_storage_rule)

If I exclude the term from the objective function, I get following value after the optimization. It seems, that it can take high negative values.

>>>>
Variable total_investment_storage
-1004724108.3426505

So I checked the term regarding the component model.nominal_cap_storage to see the value of the capacity:

model.total_cap_storage = Var()
def total_cap_storage_rule(model):
    return model.total_cap_storage == sum(model.nominal_cap_storage[storage] for storage in model.STORAGE)
model.total_cap_storage_con = Constraint(rule=total_cap_storage_rule)

>>>>
Variable total_cap_storage
0.0

I did the same for the dictionary, but made a mistake: I forgot to delete the model.nominal_cap_storage. But the result is confusing:

model.total_capex_storage = Var()
def total_capex_storage_rule(model):
    return model.total_capex_storage == sum(model.nominal_cap_storage[storage] * dict_capex_storage[storage] \
                                             for storage in model.STORAGE)
model.total_capex_storage_con = Constraint(rule=total_capex_storage_rule)

>>>>
Variable total_capex_storage
0.0

So my question is why is the term unbounded and how is it possible that model.total_investment_storage and model.total_capex_storage have different solutions though both are calculated equally? Any help is highly appreciated.

Upvotes: 2

Views: 967

Answers (2)

ulicious
ulicious

Reputation: 31

I solved the problem by setting a lower bound to the term, which takes a negative value:

model.total_investment_storage = Var(bounds=(0, None)

I am still not sure why this term can take negative values but this solved at least my problem

Upvotes: 0

AirSquid
AirSquid

Reputation: 11903

I think you are misinterpreting "unbounded." When the solver says the problem is unbounded, that means the objective function value is unbounded based on the variables and constraints in the problem. It has nothing to do with bounds on variables, unless one of those variable bounds prevents the objective from being unbound.

If you want help on above problem, you need to edit and post the full problem, with the objective function, and (if possible) the error. What you have now is a collection of different snippets of different variations of a problem, which isn't really informative on the overall issue.

Upvotes: 1

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