By Matteo Fischetti (auth.), Andrea Lodi, Michela Milano, Paolo Toth (eds.)
This e-book constitutes the refereed lawsuits of the seventh overseas convention on Integration of AI and OR concepts in Constraint Programming for Combinatorial Optimization difficulties, CPAIOR 2010, held in Bologna, Italy, in June 2010. The 18 revised complete papers and 17 revised brief papers offered including the prolonged abstracts of three invited talks have been rigorously reviewed and chosen from seventy two submissions. The papers are taken with either theoretical and functional, application-oriented matters and current present learn with a different concentrate on the combination and hybridization of the techniques of constraint programming, man made intelligence, and operations study applied sciences for fixing huge scale and intricate actual lifestyles combinatorial optimization difficulties.
Read Online or Download Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems: 7th International Conference, CPAIOR 2010, Bologna, Italy, June 14-18, 2010. Proceedings PDF
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Additional info for Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems: 7th International Conference, CPAIOR 2010, Bologna, Italy, June 14-18, 2010. Proceedings
Example text
Xi+1 then s(xi , v) ≥ s(xi+1 , v). Proof. t. t. s(xi+1 , w) ≥ s(xi+1 , v) then s(xi , v) > s(xi+1 , v). Otherwise, s(xi , v) = s(xi+1 , v). Ordering on Values. The two following properties establish the links between the natural ordering of values in D(xi ) and the minimum and maximum number of stretches in the sub-sequence starting from xi . Property 4. Let X = [x0 , x1 , . . , xn−1 ] be a sequence of variables and let i ∈ [0, n−1] be an integer. ∀v, w ∈ D(xi ) two well-ordered values, v ≤ w ⇒ s(xi , v) ≤ s(xi , w) + 1.
Cip−1 is initial (resp. final) if ci = 0 whenever s is not the initial (resp. a final) state of A. The number of states of # AR is the number of ordered partitions of p, and thus exponential in p. However, it is possible to have a compact encoding via constraints. Toward this, we use K + 1 sequences of p decision variables Sik in the domain {0, 1, . . , R} to encode the states of an arbitrary path of length K (the number of k columns) in # AR . For k ∈ {1, . . , K}, the sequence S0k , S1k , .
Proof. t. Increasing Nvalue. Otherwise, p(xi , v) is the exact minimum number of stretches among well-ordered instantiations I[x0 , . . , xi ] such that I[xi ] = v and s(xi , v) is the exact minimum number of stretches among well-ordered instantiations I[xi , . . , xn−1 ] such that I[xi ] = v. Thus, by construction p(xi , v) + s(xi , v)−1 is the exact minimum number of stretches among well-ordered instantiations I[x0 , x1 , . . , xn−1 ] such that I[xi ] = v. Let Dv ⊆ D be the set of domains such that all domains in Dv are equal to domains in D except D(xi ) which is reduced to {v}.