Encodings, Consistency Algorithms and Dynamic Variable - Value Ordering Heuristics for Multiple Permutation Problems
We introduce a technique to model a given multiple permutation problem as a constraint satisfaction problem (CSP). Our modeling eliminates the explicit need for channeling constraints by ensuring that an assignment or domain reduction to a variable in one model immediately updates the domains of all of the effected variables in all of the redundant models of the problem. We develop a forward-checking algorithm and then an arc-consistency (AC) algorithm that is tailored towards our modeling. We also explore various optimization methods for our AC algorithm that reduce propagation redundancy and find local inconsistencies sooner. We show that our CSP modeling coupled with our AC algorithm perform better than other CSP modelings with a generic AC algorithm. We also explore heuristics that integrate dynamic variable and value ordering into an AC algorithm and compare their performance to the state of the art CSP solvers.
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