An Adaptative Multi-GPU based Branch-and-Bound. A Case Study: the Flow-Shop Scheduling Problem

TL;DR

This paper presents an adaptive multi-GPU branch-and-bound algorithm for solving the flow-shop scheduling problem, achieving significant acceleration over CPU implementations through dynamic parameter tuning and multi-GPU parallelism.

Contribution

It introduces a novel adaptive parallel B&B algorithm with runtime heuristic tuning and multi-GPU exploitation for permutation-based combinatorial optimization problems.

Findings

Achieves up to 105x speedup over CPU implementations.

Demonstrates the effectiveness of dynamic parameter tuning.

Shows scalability with multiple GPUs on benchmark instances.

Abstract

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.