Page - 189 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 76 thenstrategiesexceptRandandOPTIwouldhavesufficedwithaprobabilityof1. Figure5bdisplays results forLigoworkflows. Here, PHEFTandOHEFTwere thebest strategies, followedbyOPTI andPESS. Figure 6 shows cpw performance profiles of six strategies forMontage andLigoworkflows considering τ = [1. . .1.2]. In both cases, PHEFThad the highest probability of being the better strategyforcpwoptimization. Theprobability that itwasthewinneronagivenproblemwithinfactors of1.1of thebest solutionwasclose to0.85and1forMontageandLigo, respectively. (a) (b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 1.02 1.04 1.061.08 1.1 1.12 1.14 1.16 1.18 1.2 ʏ Rand BC PESS OPTI PHEFT OHEFT 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2 ʏ Rand BC PESS OPTI PHEFT OHEFT Figure6. cpwperformanceprofile,τ=[1. . .1.2]. (a)Montage; (b)Ligo. Figure7showsthemeanperformanceprofilesofallmetrics, scenariosandtest cases, considering τ=[1. . .1.2]. Therewerediscrepancies inperformancequality. Ifwewant toobtainresultswithin a factorof1.02of thebest solution, thenPHEFTgeneratedthemwithprobability0.8,whileRandwith aprobabilityof0.47. Ifwechoseτ=1.2, thenPHEFTproducedresultswithaprobabilityof0.9,and Randwithaprobabilityof0.76. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14 1.16 1.18 1.2 ʏ Rand BC PESS OPTI PHEFT OHEFT Figure7.Meanperformanceprofileoverallmetricsandtest cases,τ=[1. . .1.2]. 7.Conclusions Effective imageandsignalprocessingworkflowmanagementrequires theefficientallocationof tasks to limitedresources. In thispaper,wepresentedallocationstrategies that took intoaccountboth 189