On parallel Branch and Bound frameworks for Global Optimization

Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity

Parallel Branch-and-Bound in Multi-core Multi-CPU Multi-GPU Heterogeneous Environments

International audienceWe investigate the design of parallel B&B in large scale heterogeneous compute environments where processing units can be composed of a mixture of multiple shared memory cores, multiple distributed CPUs and multiple GPUs devices. We describe two approaches addressing the critical issue of how to map B&B workload with the different levels of parallelism exposed by the target compute platform. We also contribute a throughout large scale experimental study which allows us to derive a comprehensive and fair analysis of the proposed approaches under different system configurations using up to 16 GPUs and up to 512 CPU-cores. Our results shed more light on the main challenges one has to face when tackling B&B algorithms while describing efficient techniques to address them. In particular, we are able to obtain linear speed-ups at moderate scales where adaptive load balancing among the heterogeneous compute resources is shown to have a significant impact on performance. At the largest scales, intra-node parallelism and hybrid decentralized load balancing is shown to have a crucial importance in order to alleviate locking issues among shared memory threads and to scale the distributed resources while optimizing communication costs and minimizing idle time