A branch, bound, and remember algorithm for the 1|r _i |σt _i scheduling problem

This paper presents a modified Branch and Bound (B&B) algorithm called, the Branch, Bound, and Remember (BB&R) algorithm, which uses the Distributed Best First Search (DBFS) exploration strategy for solving the 1|r _i |σt _i scheduling problem, a single machine scheduling problem where the objective is to find a schedule with the minimum total tardiness. Memory-based dominance strategies are incorporated into the BB&R algorithm. In addition, a modified memory-based dynamic programming algorithm is also introduced to efficiently compute lower bounds for the 1|r _i |σt _i scheduling problem. Computational results are reported, which shows that the BB&R algorithm with the DBFS exploration strategy outperforms the best known algorithms reported in the literature.