A Multi-core Parallel Branch-and-Bound Algorithm Using Factorial Number System

Many real-world problems in different industrial and economic fields are permutation combinatorial optimization problems. Solving to optimality large instances of these problems, such as flowshop problem, is a challenge for multi-core computing. This paper proposes a multi-threaded factoradic-based branch-and-bound algorithm to solve permutation combinatorial problems on multi-core processors. The factoradic, called also factorial number system, is a mixed radix numeral system adapted to numbering permutations. In this new parallel algorithm, the B&B is based on a matrix of integers instead of a pool of permutations, and work units exchanged between threads are intervals of factoradics instead of sets of nodes. Compared to a conventional pool-based approach, the obtained results on flowshop instances demonstrate that our new factoradic-based approach, on average, uses about 60 times less memory to store the pool of subproblems, generates about 1.3 times less page faults, waits about 7 times less time to synchronize the access to the pool, requires about 9 times less CPU time to manage this pool, and performs about 30,000 times less context switches.