An Adaptative Multi-GPU based Branch-and-Bound. A Case Study: the Flow-Shop Scheduling Problem
This work addresses the computational bottleneck in exact optimization for scheduling problems, offering significant speedups for researchers and practitioners in operations research, though it is incremental as it builds on existing GPU-based B&B methods.
The authors tackled the challenge of solving permutation-based combinatorial optimization problems like the Flow-Shop Scheduling Problem (FSP) exactly using Branch-and-Bound (B&B) algorithms by designing an adaptive multi-GPU approach with dynamic parameter tuning, achieving accelerations up to 105 times compared to CPU-based execution for large instances.
Solving exactly Combinatorial Optimization Problems (COPs) using a Branch-and-Bound (B&B) algorithm requires a huge amount of computational resources. Therefore, we recently investigated designing B&B algorithms on top of graphics processing units (GPUs) using a parallel bounding model. The proposed model assumes parallelizing the evaluation of the lower bounds on pools of sub-problems. The results demonstrated that the size of the evaluated pool has a significant impact on the performance of B&B and that it depends strongly on the problem instance being solved. In this paper, we design an adaptative parallel B&B algorithm for solving permutation-based combinatorial optimization problems such as FSP (Flow-shop Scheduling Problem) on GPU accelerators. To do so, we propose a dynamic heuristic for parameter auto-tuning at runtime. Another challenge of this work is to exploit larger degrees of parallelism by using the combined computational power of multiple GPU devices. The approach has been applied to the permutation flow-shop problem. Extensive experiments have been carried out on well-known FSP benchmarks using an Nvidia Tesla S1070 Computing System equipped with two Tesla T10 GPUs. Compared to a CPU-based execution, accelerations up to 105 are achieved for large problem instances.