We present a coarse-grain (outer-loop) parallel implementation of RLT1/2/3 (Level 1, 2, and 3 Reformulation and Linearization Technique—in that order) bound calculations for the QAP within a branch-and-bound procedure. For a search tree node of size S, each RLT3 and RLT2 bound calculation iteration is parallelized S ways, with each of S processors performing O(S5) and O(S3) linear assignment problem solution calculations, respectively. Our implementation is aware of memory usage and availability and uses this information to throttle parallelism as appropriate and to manage resources during the branch-and-bound search. Our new code succeeded in solving for the first time the Tai30b instance of the QAP.
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