In this paper, we describe the first parallel Branch-and-Bound (B&B) algorithm with a history-based domination technique. Although history-based domination substantially speeds up a B&B search, it makes parallelization much more challenging. Our algorithm is the first parallel exact algorithm for the Sequential Ordering Problem using a pure B&B approach. To effectively explore the solution space, we have developed three novel parallelization techniques: thread restart, parallel history domination, and history-table memory management. The proposed algorithm was experimentally evaluated using the SOPLIB and TSPLIB benchmarks on multi-core processors. Using 32 threads with a time limit of one hour, the algorithm gives geometric-mean speedups of 72x and 20x on the medium-difficulty SOPLIB and TSPLIB instances, respectively. On the hard instances, it solves 12 instances that the sequential algorithm does not solve, with geometric-mean speedups of 16x on SOPLIB and 32x on TSPLIB. Super-linear speedups up to 366x are seen on 16 instances.

In this paper, we describe a parallel Branch-and-Bound (B&B) algorithm with a history-based domination technique, and we apply it to the Sequential Ordering Problem (SOP). To the best of our knowledge, the proposed algorithm is the first parallel B&B algorithm that includes a history-based domination technique and is the first parallel B&B algorithm for solving the SOP using a pure B&B approach. The proposed algorithm takes a pool-based approach and employs a collection of novel techniques that we have developed to achieve effective parallel exploration of the solution space, including parallel history domination, history table memory management, and a thread restart technique. The proposed algorithm was experimentally evaluated using the SOPLIB and TSPLIB benchmarks. The results show that using ten threads with a time limit of one hour on the medium-difficulty instances, the proposed algorithm gives a geometric-mean speedup of 19.9 on SOPLIB and 10.23 on TSPLIB, with super-linear speedups up to 65x seen on 17 instances.