Parameter
Declaration and Attributes
Declaration and attributes
There are four parameter types in AIMMS that can hold data of the following four data types:
Parameter
for numeric values,StringParameter
for strings,ElementParameter
for set elements, andUnitParameter
for unit expressions.
Prior to declaring a parameter in the model editor you need to decide on its data type. In the model tree parameters of each type have their own icon. The attributes of parameters are given in this table.
Attribute 
Valuetype 
See also page 


indexdomain 


range 


constantexpression 


unitexpression 






numericstorageproperty 


string 


comment string 
The Text and Comment attributes, The Text and Comment attributes 

expression 


data enumeration 


expression 
The Uncertainty and Region attributes, The Uncertainty attribute 

expression 


expression 
Basic examples
The following declarations demonstrate some basic parameter declarations
Parameter Population {
IndexDomain : i;
Range : [0,inf);
Unit : [ 1000 ];
Text : Population of city i in thousands;
}
Parameter Distance {
IndexDomain : (i,j);
Range : [0,inf);
Unit : [ km ];
Text : Distance from city i to city j in km;
}
ElementParameter cityWithLargestPopulation {
Range : cities;
Definition : argMax( i, Population( i ) );
}
StringParameter emergencyMessage {
InitialData : "Warning";
}
Quantity Currencies {
BaseUnit : dollar;
Conversions : euro > dollar : # > # * 1.3;
}
UnitParameter selectedCurrency {
InitialData : [euro];
}
The IndexDomain
attribute
For each multidimensional identifier you need to specify its dimensions
by providing a list of index bindings at the IndexDomain
attribute.
Identifiers without an IndexDomain
are said to be scalar. In the
index domain you can specify default or local bindings to simple sets.
The totality of dimensions of all bindings determine the total dimension
of the identifier. Any references outside the index domain, either
through execution statements or from within the graphical user interface
are skipped.
Domain condition
You can also use the IndexDomain
attribute to specify a logical
expression which further restricts the valid tuples in the domain.
During execution, assignments to tuples that do not satisfy the domain
condition are ignored. Also, evaluation of references to such tuples in
expressions will result in the value zero. Note that, if the domain
condition contains references to other data in your model, the set of
valid tuples in the domain may change during a single interactive
session.
Example
Consider the sets ConnectedCities
with default index cc
and
DestinationCitiesFromSupply(i)
from the previous chapter. The
following statements illustrate a number of possible declarations of the
twodimensional identifier UnitTransportCost
with varying index
domains.
Parameter UnitTransportCost {
IndexDomain : (i,j);
}
Parameter UnitTransportCostWithCondition {
IndexDomain : (i,j) in ConnectedCities;
}
Parameter UnitTransportCostWithIndexedDomain {
IndexDomain : (i, j in DestinationCitiesFromSupply(i));
}
Explanation
The identifiers defined in the previous example will behave as follows.
The identifier
UnitTransportCost
is defined over the full Cartesian productCities
\(\times\)Cities
by means of the default bindings of the indicesi
andj
. You will be able to assign values to every pair of cities (i
,j
), even though there is no connection between them.The identifier
UnitTransportCostWithCondition
is defined over the same Cartesian product of sets. Its domain, however, is restricted by an additional condition(i,j) in ConnectedCities
which will exclude assignments to tuples that do not satisfy this condition, or evaluate to zero when referenced.Finally, the identifier
UnitTransportCostWithIndexedDomain
is defined over a subset of the Cartesian productCities
\(\times\)Cities
. The second elementj
must lie in the subsetDestinationCities(i)
associated withi
. AIMMS will produce a domain error if this condition is not satisfied.
The Range
attribute
With the Range
attribute you can restrict the values to certain
intervals or sets. The Range
attribute is not applicable to a
StringParameter
nor to a UnitParameter
. The possible values for
the Range
attribute are:
one of the predefined ranges
Real
,Nonnegative
,Nonpositive
,Integer
, orBinary
,any one of the interval expressions
[
\(a,b\)]
,[
\(a,b\))
,(
\(a,b\)]
, or(
\(a,b\))
, where a square bracket implies inclusion into the interval and a round bracket implies exclusion,any enumerated integer set expression, e.g.
{
\(a\)..
\(b\)}
covering all integers from \(a\) until and including \(b\),a set reference, if you want the values to be elements of that set. For set elementvalued parameters this entry is mandatory.
The values for \(a\) and \(b\) can be a constant number,
inf
, inf
, or a parameter reference involving some or all of the
indices on the index domain of the declared identifier.
Example
Consider the following declarations.
Parameter UnitTransportCost {
IndexDomain : (i,j);
Range : [ UnitLoadingCost(i), 100 ];
}
Parameter DefaultUnitsShipped {
IndexDomain : (i,j);
Range : {
{ MinShipment(i) .. MaxShipment(j) }
}
}
Set States {
Index : s;
}
Set adjacentStates {
SubsetOf : States;
IndexDomain : s;
}
ElementParameter nextState {
IndexDomain : s;
Range : adjacentStates(s);
}
It limits the values of the identifier UnitTransportCost(i,j)
to an
interval from UnitLoadingCost(i)
to 100. Note that the lower bound
of the interval has a smaller dimension than the identifier itself. The
integer identifier DefaultUnitsShipped(i,j)
is limited to an integer
range through an enumerated integer range inside the set brackets.
The Default
attribute
In AIMMS, parameters that have not been assigned an explicit value are
given a default value automatically. You can specify the default value
with the Default
attribute. The value of this attribute must be a
constant expression. If you do not provide a default value for the
parameter, AIMMS will assume the following defaults:
\(0\) for numbers,
\(1\) for unitvalued parameters,
the empty string
""
for strings, andthe empty element
"
for set elements.
The Definition
attribute
The Definition
attribute of a parameter can contain a valid
(indexed) numerical expression. Whenever a defined parameter is
referenced inside your model, AIMMS will, by default, recompute the
associated data if (data) changes to any of the identifiers referenced
in its definition make its current data outofdate. In the definition
expression you can refer to any of the indices in the index domain as if
the definition was the righthand side of an assignment statement to the
parameter at hand (see also Assignment Statements).
Example
The following declaration illustrates an indexed Definition
attribute.
Parameter MaxTransportFrom {
IndexDomain : i;
Definition : Max(j, Transport(i,j));
}
Care when used in loops
Whenever you provide a definition for an indexed parameter, you should carefully verify whether and how that parameter is used in the context of one of AIMMS’ loop statements (see also Flow Control Statements). When, due to changes in only a slice of the dependent data of a definition during a previous iteration, AIMMS (in fact) only needs to evaluate a single slice of a defined parameter during the actual iteration, you should probably not be using a defined parameter. AIMMS’ automatic evaluation scheme for defined identifiers will always recompute the data for such identifiers for the whole domain of definition, which can lead to severe inefficiencies for highdimensional defined parameters. You can find a more detailed discussion on this issue in Dependency is symbolic.
The Unit attribute
By associating a unit to every numerical identifier in your model, you can let AIMMS help you check your model’s consistency. AIMMS also uses the Unit attribute when presenting data and results in both the output files of a model and the graphical user interface. You can find more information on the use of units in Units of Measurement.
The Property
attribute
The Property
attribute can hold various properties of the identifier
at hand. The allowed properties for a parameter are NoSave
or one of
the numerical storage properties Integer
, Integer32
,
Integer16
, Integer8
or Double
, in addition to the properties
Stochastic
, Uncertain
, Random
which are discussed in
Properties and Attributes for Uncertain Data.
The property
NoSave
indicates whether the identifier values are stored in cases. It is discussed in detail in The Property attribute.By default, the values of numeric parameters are stored as double precision floating point numbers. By specifying one of the storage properties
Integer
,Integer32
,Integer16
,Integer8
, orDouble
AIMMS will store the values of the identifier as (signed) integers of default machine length, 4 bytes, 2 bytes or 1 byte, or as a double precision floating point number respectively. These properties are only applicable to parameters with an integer range.
The Property
statement
During execution you can change the properties of a parameter through
the Property
statement. The syntax of the Property
statement and
examples of its use can be found in The OPTION and PROPERTY Statements.
The Text
attribute
With the Text
attribute you can provide one line of descriptive text
for the enduser. If the Text
string of an indexed parameter or
variable contains a reference to one or more indices in the index
domain, then the corresponding elements are substituted for these
indices in any display of the identifier text.
Properties and Attributes for Uncertain Data
Stochastic programming and robust optimization
The AIMMS modeling language allows you to specify both stochastic programs and robust optimization models. Both methodologies are designed to deal with models involving data uncertainty. In stochastic programming the uncertainty is expressed by specifying multiple scenarios, each of which can define scenariospecific values for certain parameters in your model. Stochastic programming is discussed in full detail in Stochastic Programming. For robust optimization, parameters can be declared to not have a single fixed value, but to take their values from an userdefined uncertainty set. Robust optimization is discussed in Robust Optimization.
Properties
The following Parameter
properties are available in support of
stochastic programming and robust optimization models.
The property
Stochastic
indicates that the identifier can hold stochastic event data for a stochastic model. It is discussed in detail in Stochastic Parameters and Variables.The property
Uncertain
indicates that the identifier can hold uncertain values from an uncertainty set specified through theUncertainty
and/orRegion
attributes. Uncertain parameters are used in AIMMS’ robust optimization facilities, and are discussed in detail in Uncertain Parameters and Uncertainty Constraints.The property
Random
indicates that the identifier can hold random values with respect to a distribution with characteristics specified through theDistribution
attribute. Random parameters are used in AIMMS’ robust optimization facilities, and are discussed in detail in Chance Constraints.
The Uncertainty
and Region
attributes
The Uncertainty
and Region
attributes are available if the
parameter at hand has been declared uncertain using the Uncertain
property. Uncertain parameters are used by AIMMS’ robust optimization
framework, and are discussed in full detail in
Uncertain Parameters and Uncertainty Constraints. With the Region
attribute you can
specify an uncertainty set using one of the predefined uncertainty sets
Box
, ConvexHull
or Ellipsoid
. The Uncertainty
attribute
specifies a relationship between the uncertain parameter at hand, and
one or more other (uncertain) parameters in your model. The
Uncertainty
and Region
attributes are not exclusive, i.e., you
are allowed to specify both, in which case AIMMS’ generation process of
the robust counterpart will make sure that both conditions are satisfied
by the final solution.
The Distribution
attribute
The Distribution
attribute is available if the parameter at hand has
been declared random using the Random
property. Random parameters
are used by AIMMS’ robust optimization framework, and are discussed in
full detail in Chance Constraints. With the Distribution
attribute you can declare that the values for the random parameter at
hand adhere to one of the predefined distributions discussed in
Chance Constraints.