Algorithms for Hierarchical and Semi-Partitioned Parallel Scheduling

We propose a model for scheduling jobs in a parallel machine setting that takes into account the cost of migrations by assuming that the processing time of a job may depend on the specific set of machines among which the job is migrated. For the makespan minimization objective, the model generalizes classical scheduling problems such as unrelated parallel machine scheduling, as well as novel ones such as semi-partitioned and clustered scheduling. In the case of a hierarchical family of machines, we derive a compact integer linear programming formulation of the problem and leverage its fractional relaxation to obtain a polynomial-time 2-approximation algorithm. Extensions that incorporate memory capacity constraints are also discussed

A GPU-accelerated Branch-and-Bound Algorithm for the Flow-Shop Scheduling Problem

Branch-and-Bound (B&B) algorithms are time intensive tree-based exploration methods for solving to optimality combinatorial optimization problems. In this paper, we investigate the use of GPU computing as a major complementary way to speed up those methods. The focus is put on the bounding mechanism of B&B algorithms, which is the most time consuming part of their exploration process. We propose a parallel B&B algorithm based on a GPU-accelerated bounding model. The proposed approach concentrate on optimizing data access management to further improve the performance of the bounding mechanism which uses large and intermediate data sets that do not completely fit in GPU memory. Extensive experiments of the contribution have been carried out on well known FSP benchmarks using an Nvidia Tesla C2050 GPU card. We compared the obtained performances to a single and a multithreaded CPU-based execution. Accelerations up to x100 are achieved for large problem instances