Alias: Multiple Names for a Set

Sometimes it is necessary to have more than one name for the same set, for example, in models that deal with the interactions of elements within the same set. For instance, in input-output models, each commodity may be used in the production of all other commodities and it is necessary to have two names for the set of commodities to specify the problem without ambiguity. Example:

from gamspy import Container, Set, Alias

m = Container()
i = Set(m, name="i", records=[f"i{i}" for i in range(5)])
ip = Alias(m, name="ip", alias_with=i)

A second name ip for the set i is established that can be used instead of the original set name i.

Note

The newly introduced set name may be used as an alternative name for the original set; the associated set will always contain the same elements as the original set. If the alias name is not provided, it will be autogenerated.

Besides using the Alias() constructor directly, one can also use the gamspy.Container.addAlias() method of the Container class (which internally calls Alias()):

h = Set(m, name="h", records=range(1, 6))
hp = m.addAlias(name="hp", alias_with=h)

It is possible to create an alias from another alias object. In this case a recursive search will be performed to find the root parent set – this is the set that will ultimately be stored as the alias_with property. We can see this behavior in the following example:

from gamspy import Container, Set, Alias

m = Container()
i = Set(m, name="i", records=[f"i{i}" for i in range(5)])
ip = Alias(m, name="ip", alias_with=i)
ipp = Alias(m, "ipp", ip)

In [1]: ip.alias_with.name
Out[1]: 'i'

In [2]: ipp.alias_with.name
Out[2]: 'i'

Warning

If an alias is to be used for the universal set, the UniverseAlias class has to be used. More about this in The Universal Set: * as Set Identifier.

Typical examples for the usage of aliases are problems where transportation costs between members of one set have to be modeled. Example:

from gamspy import Container, Set, Alias, Parameter, SpecialValues

m = Container()
i = Set(m, "i", description="plant locations")

tran = Parameter(
    m,
    description="transport cost for interplant shipments (us$ per ton)",
    domain=[i, i],
    domain_forwarding=True,
    records=[
        ("pto-suarez", "palmasola", 87.22),
        ("potosi", "palmasola", 31.25),
        ("potosi", "pto-suarez", 55.97),
        ("baranquill", "palmasola", 89.80),
        ("baranquill", "pto-suarez", 114.56),
        ("baranquill", "potosi", 70.68),
        ("cartagena", "palmasola", 89.80),
        ("cartagena", "pto-suarez", 114.56),
        ("cartagena", "potosi", 70.68),
        ("cartagena", "baranquill", 5.00),
    ],
)
tran[i, i] = SpecialValues.EPS

The parameter tran is two-dimensional and both indices are the set i. The data for the transport cost between the plants is given in this symbol; note that the transport costs are given only for one direction; for instance, costs are specified from pto-suarez to palmasola but not vice versa:

In [1]: tran.pivot(fill_value=SpecialValues.NA)
Out[1]:
            pto-suarez  potosi  baranquill  cartagena  palmasola
pto-suarez       -0.00     NaN         NaN        NaN      87.22
potosi           55.97   -0.00         NaN        NaN      31.25
baranquill      114.56   70.68        -0.0        NaN      89.80
cartagena       114.56   70.68         5.0       -0.0      89.80
palmasola          NaN     NaN         NaN        NaN      -0.00

The following alias statement introduces ip as another name for the set i. The parameter mui is also two-dimensional and both indices refer to the set i, but this time the alias ip is used in the second position. The parameter mui is defined to contain the transport costs from one plant location to the other, in both directions.

ip = Alias(m, name="ip", alias_with=i)
mui = Parameter(m, domain=[i, ip], description="transport cost: interplant shipments (us$ per ton)")

mui[i, ip] = tran[i, ip] + tran[ip, i]

In [1]: mui.pivot()
Out[1]:
            pto-suarez  potosi  baranquill  cartagena  palmasola
pto-suarez       -0.00   55.97      114.56     114.56      87.22
potosi           55.97   -0.00       70.68      70.68      31.25
baranquill      114.56   70.68       -0.00       5.00      89.80
cartagena       114.56   70.68        5.00      -0.00      89.80
palmasola        87.22   31.25       89.80      89.80      -0.00

Please note that the domain in the declaration of mui could be also [i, i]. Only the assignment statement to mui requires the alias ip to represent an assignment over all possible pairs. The assignment tran[i, i] = SpecialValues.EPS assigns EPS (a sticky 0) to the diagonal of the tran parameter.