SUMMARYIn this paper, we address the design and implementation of graphical processing unit (GPU)-accelerated branch-and-bound algorithms (B&B) for solving flow-shop scheduling optimization problems (FSP). Such applications are CPU-time consuming and highly irregular. On the other hand, GPUs are massively multithreaded accelerators using the single instruction multiple data model at execution. A major issue that arises when executing on GPU, a B&B applied to FSP is thread or branch divergence. Such divergence is caused by the lower bound function of FSP that contains many irregular loops and conditional instructions. Our challenge is therefore to revisit the design and implementation of B&B applied to FSP dealing with thread divergence. Extensive experiments of the proposed approach have been carried out on wellknown FSP benchmarks using an Nvidia Tesla (C2050 GPU card (http://www.nvidia.com/docs/IO/43395/ NV_DS_Tesla_C2050_C2070_jul10_lores.pdf)). Compared with a CPU-based execution, accelerations up to 77.46 are achieved for large problem instances.

On the road to exascale, coprocessors are increasingly becoming key building blocks of High Performance Computing platforms. In addition to their energy efficiency, these many-core devices boost the performance of multi-core processors. In this paper, we revisit the design and implementation of Branch-and-Bound (B&B) algorithms for multi-core processors and Intel Xeon Phi coprocessors considering the offload mode as well as the native one. In addition, two major parallel models are considered: the master-worker and the work pool models. We address several parallel computing issues including processor-coprocessor data transfer optimization and vectorization. The proposed approaches have been experimented using the Flow-Shop scheduling problem (FSP) and two hardware configurations equivalent in terms of energy consumption: Intel Xeon E5-2670 processor and Intel Xeon Phi 5110P coprocessor. The reported results show that: (1) the proposed vectorization mechanism reduces the execution time by 55.4% (resp. 30.1%) in the many-core (resp. multi-core) approach ; (2) the offload mode allows a faster execution on MIC than the native mode for most FSP problem instances ; (3) the many-core approach (offload or native) is in average twice faster than the multi-core approach ; (4) the work pool parallel model is more suited for many/multi-core B&B applied to FSP than the master-worker model because of its irregular nature.

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In many optimal design searches, the function to optimise is a simulator that is computationally expensive. While current High Performance Computing (HPC) methods are not able to solve such problems efficiently, parallelism can be coupled with approximate models (surrogates or meta-models) that imitate the simulator in timely fashion to achieve better results. This combined approach reduces the number of simulations thanks to surrogate use whereas the remaining evaluations are handled by supercomputers. While the surrogates' ability to limit computational times is very attractive, integrating them into the overarching optimization process can be challenging. Indeed, it is critical to address the major trade-off between the quality (precision) and the efficiency (execution time) of the resolution. In this article, we investigate Evolution Controls (ECs) which are strategies that define the alternation between the simulator and the surrogate within the optimization process. We propose a new EC based on the prediction uncertainty obtained from Monte Carlo Dropout (MCDropout), a technique originally dedicated to quantifying uncertainty in deep learning. Investigations of such uncertainty-aware ECs remain uncommon in surrogateassisted evolutionary optimization. In addition, we use parallel computing in a complementary way to address the high computational burden. Our new strategy is implemented in the context of a pioneering application to Tuberculosis Transmission Control. The reported results show that the MCDropout-based EC coupled with massively parallel computing outperforms strategies previously proposed in the field of surrogate-assisted optimization.

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