Difference: SetsInAMPL (8 vs. 9)

Revision 92008-03-11 - MichaelOSullivan

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META TOPICPARENT	name="AMPLSyntax"

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Sets in AMPL

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Efficient Generation of Sets

Changed:

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When creating models, generating sets by looping over all possibilities and removing those that don't fit some conditions (e.g., like the TIME_ARCS statement) can take a long time if there are many possibilities. This is time that could be spent solving the model! If possible you should try to create sets by building them up from smaller building block, rather than by creating an enormous set and pruning it. For example, instead of using this statement

# 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 arcs used for transportation     ( (m = n) and (ord(t, MONTHS) + 1 = ord(u, MONTHS)) )}; # The arcs used for storage

to create TIME_ARCS you could use these statement

set TRANSPORT_ARCS := union {t in MONTHS, (m, n) in ARCS} {(m, t, n, t)}; set STORAGE_ARCS := union {t in MONTHS, (m, n) in ARCS : t <> last(MONTHS)}   {(m, t, n, next(t, MONTHS)}; set TIME_ARCS within TIME_NODES cross TIME_NODES := TRANSPORT_ARCS union STORAGE_ARCS;

Rather than looping over all possibilities and only keeping those that are appropriate, the new statement only loops over smaller sets that can be used to build up the TIME_NODES set efficiently.

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-- MichaelOSullivan - 27 Feb 2008

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# 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 arcs used for transportation
     ( (m = n) and (ord(t, MONTHS) + 1 = ord(u, MONTHS)) )}; # The arcs used for storage

to create TIME_ARCS you could use these statements

set TRANSPORT_ARCS := union {t in MONTHS, (m, n) in ARCS} {(m, t, n, t)};
set STORAGE_ARCS := union {t in MONTHS, (m, n) in ARCS : t <> last(MONTHS)}
   {(m, t, n, next(t, MONTHS)};

set TIME_ARCS within TIME_NODES cross TIME_NODES := TRANSPORT_ARCS union STORAGE_ARCS;

Rather than looping over all possibilities and only keeping those that are appropriate, the new statement only loops over smaller sets that can be used to build up the TIME_NODES set efficiently.

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-- MichaelOSullivan - 27 Feb 2008

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