Car Sequencing Problem
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Transcript of Car Sequencing Problem
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Car Sequencing Problem
An update
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How to certify output
Standard output
The Certificate class
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Easy Problems
We have a directory of easy problems
How were these made?
Why do we need easy problems?
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Heuristics
Variable orderingChoose time slot that can accept least classes (sdf)
Value orderingWhat class should we put in that slot? - class with least options? - class where product of (nonzero) options is low? - class of least demand?
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And so on
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And so on
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BMS paper is well worth a look
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IF S[i] = cTHEN for 0 ≤ j ≤ m O[i][j] = o[c][j]
The Link Constraint
m is # options
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IF S[i] = cTHEN for 0 ≤ j ≤ m O[i][j] = o[c][j]
The Link Constraint
Using ifOnlyIf
ifOnlyIf(S[i] = c, and(O[i][0] =o[c][0], …, O[i][m]=o[c][m]))
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IF S[i] = cTHEN for 0 ≤ j ≤ m O[i][j] = o[c][j]
The Link Constraint
Using implies
implies(S[i] = c, O[i][0]=o[c][0])...implies(S[i] = c, O[i][m]=o[c][m])
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IF S[i] = cTHEN for 0 ≤ j ≤ m O[i][j] = o[c][j]
The Link Constraint
Using implies
implies(S[i] = c, O[i][0]=o[c][0])...implies(S[i] = c, O[i][m]=o[c][m])
What happens if due topropagation some O[i][j] is set?
P Qand Q is false?
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IF S[i] = cTHEN for 0 ≤ j ≤ m O[i][j] = o[c][j]
How big is the model?
Using implies
implies(S[i] = c, O[i][0]=o[c][0])...implies(S[i] = c, O[i][m]=o[c][m])
How many of theseconstraints are there?
How big is the model?
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Have a look at the p/q constraint
How big is the model?
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Two models linked?
One has S, a sequence of classes
The other has an array of cars allocated positions
This might allow better heuristics
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Channeling
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Questions?