GPU上两阶段负载调度问题的建模与近似算法

随着硬件功能的不断丰富和软件开发环境的逐渐成熟,GPU(graphics processing unit)越来越多地被应用到通用计算领域,并对诸多计算系统(尤其是嵌入式系统)性能的显著提升起到了至关重要的作用.在基于GPU的计算系统中,大规模并行负载同时进行数据传输和加载的情况时常发生,数据传输延时在系统性能全局最优化中变得不容忽视.综合考虑负载的传输时间和执行时间,以总负载makespan最小化作为系统性能的全局优化目标,研究了GPU上负载“传输-执行”联合调度问题.首先,将负载的时间信息和并行任务数与矩形域的二维空间联系起来,建立了负载的2D双层矩形域模型;然后,将GPU上负载调度问题归结为一类Strip-Packing问题;最后,基于贪婪策略给出了近似度为3的多项式时间近似算法,算法复杂度为O(nlogn).该近似算法的核心是对数据传输阶段进行负载排序调度.这从理论层面上证明了GPU系统采取“传输-执行”两阶段调度的有效性,即,在数据传输阶段采取负载排序调度,在负载执行阶段采取先来先服务(first-come-first-serve,简称FCFS)调度,能够使GPU 性能达到全局最优或近似最优.     

Hybrid simulated annealing and reduced variable neighbourhood search for an aircraft scheduling and parking problem

Aircraft stands and runways at airports are critical airport resources for aircraft scheduling and parking. Making use of limited apron and runway resources to improve airport efficiency is becoming increasingly important. In this paper, we study a realistic Aircraft Scheduling and Parking Problem (ASPP) with the goal of simultaneously determining the takeoff and landing time of each aircraft with consideration for wake vortex effect constraints and parking positions in the limited parking apron at a target airport. The objective of the ASPP is to minimise the total service time for aircraft. We developed a mixed-integer linear programme formulation for the ASPP. A novel improved bottom-left/right strategy is applied to construct solutions and a Hybrid Simulated Annealing and Reduced Variable Neighborhood Search (HSARVNS) is proposed to identify near-optimal solutions. Numerical experiments on randomly generated ASPP instances and on a large set of benchmarks for a reduced version of the ASPP (i.e. the classical Two-Dimensional Strip-Packing Problem (2D-SPP)) demonstrate the effectiveness and efficiency of the proposed approach. For the ASPP, HSARVNS can find optimal solutions for small instances in a fraction of a second and can find high-quality solutions for instances with up to 250 aircraft within a reasonable timeframe. For the 2D-SPP, the HSARVNS can find optimal solutions for 32 of 38 tested benchmarks within 90 s on average.