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Published byCamden Mustain Modified over 3 years ago

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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 ordering Choose time slot that can accept least classes (sdf) Value ordering What 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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BMS paper is well worth a look

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IF S[i] = c THEN for 0 j m O[i][j] = o[c][j] The Link Constraint m is # options

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IF S[i] = c THEN 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] = c THEN 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] = c THEN 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 to propagation some O[i][j] is set? P Q and Q is false?

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IF S[i] = c THEN 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 these constraints 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?

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