Difference: ParametersInAMPL (9 vs. 10)

Revision 102018-07-29 - MichaelOSullivan

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META TOPICPARENT	name="AMPLSyntax"

<-- Ready to Review -->

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Defining 2-Dimensional Parameters

In a similar way to 2-dimensional sets, there are three different ways to define 2-dimensional parameters.

Changed:

<
<

Using a List For any parameter values that don't take the default value, you list the set element and value for that parameter.

model; param Min {ARCS} integer, default 0; data; param Min := Youngstown 'Kansas City' 1000 Pittsburgh 'Kansas City' 2000 Cincinnati Albany 1000

Using a Table To define parameter data in a table format you use the param keyword and the parameter's name followed by the : operator, a list of the second index set elements followed by the := operator, then rows of the table with an element of the first index set followed by the values corresponding to the second index set's element in that column.
```
param : ... := ... ... ... ; 
```
If the element does not exist or the default value is correct then place a . in the table. Otherwise, put the parameter value.
```
param Cost: Cincinnati 'Kansas City' Chicago Albany Houston Tempe Gary := Youngstown 350 450 375 500 . . . Pittsburgh 350 450 400 . . . 450 Cincinnati . . . 350 550 . . 'Kansas City' . . . . 375 650 . Chicago . . . . . 600 120 ; 
```
You can also define parameter data in a transposed table using almost the same syntax, but with the (tr) keyword and reversing the indexing sets
```
param (tr) : ... := ... ... ... ; 
```
Using an Array You define a list of column indices and values for each row index.
```
param Cost := [Youngstown, *] Cincinnati 350 'Kansas City' 450 ... ... [Chicago, *] ... Gary 120 ; 
```
Note The row indices have [=} and =] around them (as opposed to ( and ) for sets).

>
>

Using a List For any parameter values that don't take the default value, you list the set element and value for that parameter.

model;
param Min {ARCS} integer, default 0;
data;
param Min :=
Youngstown 'Kansas City' 1000
Pittsburgh 'Kansas City' 2000
Cincinnati Albany 1000

Using a Table To define parameter data in a table format you use the param keyword and the parameter's name followed by the : operator, a list of the second index set elements followed by the := operator, then rows of the table with an element of the first index set followed by the values corresponding to the second index set's element in that column.

param : ... := ... ... ... ;

If the element does not exist or the default value is correct then place a . in the table. Otherwise, put the parameter value.

param Cost:
Cincinnati 'Kansas City' Chicago Albany Houston Tempe Gary :=
Youngstown 350 450 375 500 . . .
Pittsburgh 350 450 400 . . . 450
Cincinnati . . . 350 550 . .
'Kansas City' . . . . 375 650 .
Chicago . . . . . 600 120 ;

You can also define parameter data in a transposed table using almost the same syntax, but with the (tr) keyword and reversing the indexing sets

param (tr) : ... := ... ... ... ;

Using an Array You define a list of column indices and values for each row index.

param Cost :=
[Youngstown, *] Cincinnati 350 'Kansas City' 450 ... ...
[Chicago, *] ... Gary 120 ;

Note The row indices have [=} and =] around them (as opposed to ( and ) for sets).

Defining Multi-Dimensional Parameters

Since we have multi-dimensional sets, we might need multi-dimensional parameters, e.g., Cost {TIME_ARCS} has four dimensions. We can define these parameters in a similar way to multi-dimensional sets:

Changed:

<
<

Using a List

param Cost := Youngstown April Albany April 0.5 # = 500 / 1000 Youngstown April Youngstown May 0.015 # = 15 / 1000 ... ;

Using a Table

param Cost := [*, May, *, May] Cincinnati 'Kansas City' Albany ... := Youngstown 0.35 0.45 0.5 ... Pittsburgh 0.35 0.45 . ... ... ;

Notice the [ ] around *, May, *, May as opposed to the ( ) for sets!

>
>

Using a List

param Cost :=
Youngstown April Albany April 0.5 # = 500 / 1000
Youngstown April Youngstown May 0.015 # = 15 / 1000 ... ;

Using a Table

param Cost :=
[*, May, *, May] Cincinnati 'Kansas City' Albany ... :=
Youngstown 0.35 0.45 0.5 ...
Pittsburgh 0.35 0.45 . ... ... ;

Notice the [ ] around *, May, *, May as opposed to the ( ) for sets!

Using an Array

set TIME_ARCS := (*, May, *, May) (Youngstown, Cincinnati) 0.35 ... ;

set TIME_ARCS := (Youngstown, May, *, May) Cincinnati 0.35 'Kansas City' 0.45 ... ... ;

Defining Multiple Parameters

Changed:

<
<

Using the : operator, multiple parameters may be defined at once. Simply state the names of the parameters and the := operator. Then list the set elements and values on the following rows.

param:             ... :    ...    ...  ;

If a parameter is not defined or the default value is sufficient, use the . operator.

model;  # The lower and upper bounds on the requirements param Min {REQUIREMENTS} default -Infinity; param Max {REQUIREMENTS} default Infinity;  data; param:        Min Max:= PROTEIN      8.0     . FAT          6.0     . FIBRE          .   2.0 SALT           .   0.4  ;

This approach also works for 2-dimensional parameters and lists, for the American Steel problem this allows us to "cut-and-paste" the list of arc properties

>
>

Using the : operator, multiple parameters may be defined at once. Simply state the names of the parameters and the := operator. Then list the set elements and values on the following rows.

param:             ... :    ...    ...  ;

If a parameter is not defined or the default value is sufficient, use the . operator.

model;
 # The lower and upper bounds on the requirements
param Min {REQUIREMENTS} default -Infinity;
param Max {REQUIREMENTS} default Infinity;

data;
param:        Min Max:=
PROTEIN      8.0     .
FAT          6.0     .
FIBRE          .   2.0
SALT           .   0.4  ;

This approach also works for 2-dimensional parameters and lists, for the American Steel problem this allows us to "cut-and-paste" the list of arc properties

From node	To node	Cost	Minimum	Maximum
Youngstown	Albany	500	-	1000

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etc

becomes

Changed:

<
<

param:                   Cost  Min  Max:= Youngstown Cincinnati     350    0 3000 Youngstown 'Kansas City'  450 1000 5000 ... Chicago    Gary           120    0 4000  ;

>
>

param:                   Cost  Min  Max:=
Youngstown Cincinnati     350    0 3000
Youngstown 'Kansas City'  450 1000 5000
...
Chicago    Gary           120    0 4000  ;

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Parameter values are accessed by specifying the indices of the parameter you want to access within [ and ].

Examples

Changed:

<
<

See Cost and Contributes below.

# Objective: minimise the cost per (100g) can minimize TotalCost: sum {i in INGREDIENTS} Cost[i] * Amount[i];  # Constraints: Meet the nutritional requirements  subject to MeetRequirement {r in REQUIREMENTS}:   Min[r] <= sum {i in INGREDIENTS} Contributes[i, r] * Amount[i] <= Max[r];

>
>

See Cost and Contributes below.

# Objective: minimise the cost per (100g) can
minimize TotalCost: sum {i in INGREDIENTS} Cost[i] * Amount[i];

# Constraints: Meet the nutritional requirements

 subject to MeetRequirement {r in REQUIREMENTS}:
   Min[r] <= sum {i in INGREDIENTS} Contributes[i, r] * Amount[i] <= Max[r];

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