Difference: SetsInAMPL (13 vs. 14)

Revision 142010-09-16 - MichaelOSullivan

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META TOPICPARENT name="AMPLSyntax"
<-- Ready to Review - done - Lauren-->

Sets in AMPL

Line: 36 to 36
 
  1. Use a logical expression (after the :) to indicate if an element (or pair of elements, or “tuple” of elements) should be included in the set.

Generic Set Expression

Changed:
<
<
{  in , [ in ,  in , …] :   } 
>
>
{ <e> in <S>, [<f> in <T>, <g> in <U>, …] :   <logical expression involving e [f, g, …]>} 
  Set expressions may also involve one or more set operators:
Line: 54 to 54
  Sets are usually defined in a data file:
Changed:
<
<
set NODES := Youngstown Pittsburgh Cincinnati 'Kansas City' Chicago              Albany Houston Tempe Gary ; 
>
>
set NODES := Youngstown Pittsburgh Cincinnati 'Kansas City' Chicago
             Albany Houston Tempe Gary ;
  although they may be defined during declaration using either an explicit set literal or using a set expression:
Changed:
<
<
set KIND := {'HOST', 'DEVICE', 'SWITCH', 'HUB', 'LINK', 'SUPERLINK'};  set COMPONENT := {C in CLASSES : (kind[C] = 'HOST'  ) or              (kind[C] = 'DEVICE') or              (kind[C] = 'HUB'   ) or              (kind[C] = 'SWITCH')};  set FABRIC := NODE union LINK; 
>
>
set KIND := {'HOST', 'DEVICE', 'SWITCH', 'HUB', 'LINK', 'SUPERLINK'};
set COMPONENT := {C in CLASSES : (kind[C] = 'HOST'  ) or
                                 (kind[C] = 'DEVICE') or
                                 (kind[C] = 'HUB'   ) or
                                 (kind[C] = 'SWITCH')};
set FABRIC := NODE union LINK;
  and sets may also be defined dynamically:
Changed:
<
<
set SEARCH within VERTICES; let SEARCH := {v in VERTICES: (v, w) in EDGES}; 
>
>
set SEARCH within VERTICES;
let SEARCH := {v in VERTICES: (v, w) in EDGES};
 

Defining 2-Dimensional Sets

There are three different ways to define 2-dimensional sets. The "best" way to use depends on the set.

Changed:
<
<
  1. Using a List You simply list the elements in the set. This is good for sparse sets.

    model; set ARCS within NODES cross NODES; data; set ARCS := (Youngstown, Albany), (Youngstown, Cincinnati), ... ; 
  2. Using a Table You give a table using the first index set for the rows and the second index set for the columns, then you place a + where an element exists and a - where there is no element. This is good for dense sets.
    set ARCS: Cincinnati 'Kansas City' Chicago Albany Houston Tempe Gary := Youngstown + + + + - - - Pittsburgh + + + - - - + Cincinnati - - - + + - - 'Kansas City' - - - - + + - Chicago - - - - - + + ; 
  3. Using an Array You define a list of column indices for each row index. This is a good for sets with a few elements for each row.
    set ARCS := (Youngstown, *) Cincinnati ‘Kansas City’ Chicago Albany (Pittsburgh, *) Cincinnati ‘Kansas City’ Chicago Gary (Cincinnati, *) Albany Houston ... 
>
>
  1. Using a List You simply list the elements in the set. This is good for sparse sets.

       model;
       set ARCS within NODES cross NODES;
       data;
       set ARCS := (Youngstown, Albany), (Youngstown, Cincinnati), ... ;
       
  2. Using a Table You give a table using the first index set for the rows and the second index set for the columns, then you place a + where an element exists and a - where there is no element. This is good for dense sets.
set ARCS:
              Cincinnati 'Kansas City' Chicago Albany Houston Tempe Gary :=
Youngstown    +           +            +       +      -       -     -
Pittsburgh    +           +            +       -      -       -     +
Cincinnati    -           -            -       +      +       -     -
'Kansas City' -           -            -       -      +       +     -
Chicago       -           -            -       -      -       +     +
 ;
  1. Using an Array You define a list of column indices for each row index. This is a good for sets with a few elements for each row.
set ARCS :=
(Youngstown, *) Cincinnati ‘Kansas City’ Chicago Albany
(Pittsburgh, *) Cincinnati ‘Kansas City’ Chicago Gary
(Cincinnati, *) Albany Houston ...
  Return to top
Line: 82 to 117
  AMPL will put the elements in this set in the order they appear in the data file (or let statement). AMPL also understands the following operations for ordered sets:
Changed:
<
<
ord(e, ORD_SET)   # The position of e in ORD_SET first(ORD_SET)    # The first element in ORD_SET last(ORD_SET)     # The last element in ORD_SET prev(e, ORD_SET)  # The element before e in ORD_SET next(e, ORD_SET)  # The element after e in ORD_SET member(i, ORDSET) # The element at position i in ORD_SET 
>
>
ord(e, ORD_SET)   # The position of e in ORD_SET
first(ORD_SET)    # The first element in ORD_SET
last(ORD_SET)     # The last element in ORD_SET
prev(e, ORD_SET)  # The element before e in ORD_SET
next(e, ORD_SET)  # The element after e in ORD_SET
member(i, ORDSET) # The element at position i in ORD_SET
  Return to top
Line: 90 to 132
  Consider the following AMPL statement from the The American Steel Planning Problem. We use ord in the creation of TIME_ARCS:
Changed:
<
<
# The set of time-staged arcs set TIME_ARCS within TIME_NODES cross TIME_NODES :=    { (m, t) in TIME_NODES, (n, u) in TIME_NODES :      ( ( (m, n) in ARCS) and (t = u) ) or # The transportation arcs      ( (m = n) and (ord(t, MONTHS) + 1 = ord(u, MONTHS)) )}; # The storage arcs 
>
>
# The set of time-staged arcs
set TIME_ARCS within TIME_NODES cross TIME_NODES :=
  { (m, t) in TIME_NODES, (n, u) in TIME_NODES :
    ( ( (m, n) in ARCS) and (t = u) ) or # The transportation arcs
	( (m = n) and (ord(t, MONTHS) + 1 = ord(u, MONTHS)) )}; # The storage arcs
  There are many concepts within this one statement, let's look at them one at a time.
Line: 99 to 147
 There are many operations we can perform on sets (see Set Expressions). We have seen that cross creates all pairs of two sets, so TIME_NODES cross TIME_NODES creates a set of all pairs of TIME_NODES.

Some set operations may be looped over indexing sets. For example, to generate all the transportation arcs in the time-staged network you could use the following statement:

Changed:
<
<
set TRANSPORT_ARCS := union {t in MONTHS} (union {(m, n) ARCS} {(m, t, n, t)}); 
or you could loop over MONTHS and ARCS simultaneously:
set TRANSPORT_ARCS := union {t in MONTHS, (m, n) in ARCS} {(m, t, n, t)}; 
>
>
set TRANSPORT_ARCS := union {t in MONTHS} (union {(m, n) ARCS} {(m, t, n, t)});
or you could loop over MONTHS and ARCS simultaneously:
set TRANSPORT_ARCS := union {t in MONTHS, (m, n) in ARCS} {(m, t, n, t)};
 

Set Membership and Subsets

 
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