Cat Swarm Optimization Task Scheduling Algorithm Based on Double Arbitration Mechanism and Taguchi Orthogonal Method
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摘要: 针对异构计算系统任务调度过程中通信冲突以及算法运行时间的问题，该文提出一种基于双仲裁机制和田口正交法的猫群优化任务调度算法。首先利用双仲裁机制对任务资源进行管理，动态判决任务的分配，有效避免通信冲突，再将田口正交法应用到猫群优化过程的跟踪模式中，降低算法运行时间，提高解的质量。实验结果表明，该算法运行速度明显高于其他算法至少约10%，算法在处理大量任务时的并行化效果最优，在异构环境中也体现出其相当大的优势。Abstract: To solve communication conflicts and algorithm running time problem in task scheduling process of heterogeneous computing system, a cat swarm optimization task scheduling algorithm is proposed based on double arbitration mechanism and Taguchi orthogonal method. Firstly, the double arbitration mechanism is used to manage the task resources, and the task assignment is dynamically decided to avoid effectively communication conflicts. Then, the Taguchi orthogonal method is applied to the tracking mode of the cat swarm optimization process to reduce the algorithm running time and improve the quality of the solution. Experimental results show that the algorithm runs at a rate of at least about 10% faster than other algorithms. The algorithm performs best in parallelism when dealing with a large number of tasks and has considerable advantages in heterogeneous environments.
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表 1 双仲裁映射判决算法
算法1 双仲裁映射判决算法 输入：TA, PLA, t, Tm 输出：有效的任务映射结果DAM(T) (1) if (( ${T_m} \cdot {t_a} \le t \le {T_m} \cdot {t_s}$) and ( ${T_m} \cdot s = {\rm IDLE}\parallel {\rm WAIT}$)) then
enQueue (Q, Tm)(2) Select Tm from Q where ${T_m} \cdot p$ is the highest (3) if (PLA=NULL) then (4) temp P·taskid $ \leftarrow {T_n} \cdot \rm{taskid}$;
temp P·pos $ \leftarrow {[(0},{0),(}{T_n} \cdot w,{T_n} \cdot h{)]}$;(5) ${T_n} \cdot s \leftarrow {\rm EXE}$;TA [i+1][0] $ \leftarrow {T_n} \cdot w$; TA [i+1][1] $ \leftarrow {T_n} \cdot h$; (6) insert node tempP into PLA; else (7) DAM(Tj, d); end if (8) end if 
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表 2 L8(27)正交阵列
实验序列号 考虑的因子 A B C D E F G 1 1 0 0 1 1 0 0 2 1 1 1 0 0 0 0 3 0 0 1 0 1 1 0 4 0 1 0 0 1 0 1 5 1 1 1 1 1 1 1 6 1 0 0 0 0 1 1 7 0 0 1 1 0 0 1 8 0 1 0 1 0 1 0
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表 3 预估计算时间矩阵
T0 T1 T2 T3 T4 T5 T6 P0 T0/P0 T1/P0 T2/P0 T3/P0 T4/P0 T5/P0 T6/P0 P1 T0/P1 T1/P1 T2/P1 T3/P1 T4/P1 T5/P1 T6/P1 P2 T0/P2 T1/P2 T2/P2 T3/P2 T4/P2 T5/P2 T6/P2 P3 T0/P3 T1/P3 T2/P3 T3/P3 T4/P3 T5/P3 T6/P3 P4 T0/P4 T1/P4 T2/P4 T3/P4 T4/P4 T5/P4 T6/P4 P5 T0/P5 T1/P5 T2/P5 T3/P5 T4/P5 T5/P5 T6/P5 P6 T0/P6 T1/P6 T2/P6 T3/P6 T4/P6 T5/P6 T6/P6 P7 T0/P7 T1/P7 T2/P7 T3/P7 T4/P7 T5/P7 T6/P7
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表 4 田口-猫群优化算法
算法2 田口-猫群优化算法 输入：猫的初始位置，初始速度，MR, SMP, SRD, CDC, SPC
输出：最优的任务调度结果(1) if (seeking flag← 1) //按照搜寻模式进行 (2) 生成第k只猫的y (y=SMP) 份副本Zqd (1 ≤ q ≤ Y, 1 ≤ d ≤ D) ; //D是解空间的维数 (3) 每当CDC对Zqd进行加或减的变异操作就随机改变猫的维度， 确定被改变的猫的适应度； (4) 从Y中随机选取候选值后发现并替换猫的最佳位置；else (5) 选取两级田口正交阵列 ${L_n}{(}{{2}^{n - {1}}}{),}\forall n \ge N + {1}$; //N表示任务数量 (6) 根据式(2)生成两组速度并根据任务数量N确定任务调度的维数； (7) 根据正交阵列 ${L_n}{(}{{2}^{n - {1}}}{)}$计算n次实验的适应度值； (8) end if 选取当前最优个体 ${x_l}$和最佳位置 ${x_p}$； (9) if ( ${x_l} > {x_g}$) ${x_l} = {x_g}$; ${x_p} = {G_b}$; //当前最佳位置即全局最佳位置 (10) 根据式(4)，式(5)计算并更新当前速度和位置； (11) if (达到最终条件) 输出最佳的任务调度顺序； (12) else 重新计算每只猫的适应度值；end if (13) end if
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表 5 DTCSO算法参数设置
参数 值 猫的数量 100 最大迭代次数 1000 权重w 0.5 c1 1 r1 [0,1] MR 0.5 SMP 3 N {10,20,30,40,50,60,70,80,90,100,200,300,400,500} den {0.2,0.5,0.8} fat {0.1,0.4,0.8} reg {0.2,0.5,0.8} jump {1,2,4} CCR {0.1,0.2,0.5,0.8,1.0,2.0,5.0,8.0,10.0} $\beta $ {0.1,0.2,0.5,1.0,2.0} Q {2,4,8,16,32}
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表 6 调度算法优良比较(%)
HGAAP CSO HPSO-GA ACO-GA DTCSO算法 更好 100 98.6 93.62 86.7 相同 0 0 0.08 0.6 更差 0 1.4 6.3 12.7
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