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analyze the best trade-off solutions defined as the nearest to the (normalized)
ideal objective vector [5] for each problem instance, which corresponds to an
ideal solution that equally weights power, temperature, and QoS.
The results in Table 2 demonstrate that NSGA-II+BFH computes the best
power-aware solutions, up to 77.8% better than the BAU strategy, and NSGA-
II+BD obtains the best temperature results, up to 85.8% over the BAU strategy.
However, those solutions have a significant impact on the other objectives. Ac-
curate QoS values are obtained using NSGA-II+BD when admitting reasonable
temperature deviations, for both non-deferrable and deferrable workloads.
Regarding the best trade-off solutions, NSGA-II+EFT accounts for the lower
impacts on QoS (in average, 8.4% for non-deferrable workloads, and 10.0% for
deferrable workloads), while achieving important improvements on energy (be-
tween 38-62% ) and temperature (up to 49% ) when compared against the BAU
strategy. NSGA-II+BD is an acceptable second option. The results also indicate
that no significant differences on the objective function values are obtained when
considering deferrable and non-deferrable tasks using the proposed schedulers.
The reported results indicate that NSGA-II+ETF is a promising technique for
datacenter controlling, to decide the most appropriate trade-off between objec-
tives (e.g., during short periods of very high electricity price, it might be useful
to drop power demand at the expense of QoS and temperature).
Fig. 3 presents examples of Pareto fronts computed for two different (repre-
sentative) problem instances. The figures show that a good coverage of trade-off
solutions is obtained, correctly sampling the region of (equally-weighted) best
compromise solutions for the problem. When comparing the three schedulers,
we see that NSGA-II+EFT generally outperforms NSGA-II+BSD and NSGA-
II+BFH in terms of QoS. For example, for power profile A, EFT (blue) delivers
solutions with very low QoS impact all across the Pareto front, making the front
almost a 2D curve of trade-off between temperature and power violations.
Solution analysis . Fig. 4 presents four illustrative solutions from the Pareto
front obtained using NSGA-II+EFT for a problem instance with 75 tasks and
power profile A. Figs. 4(a)-4(c) show the extremes of the Pareto front. Fig. 4(a)
NSGA−II+BFH
NSGA−II+BD
NSGA−II+EFT
NSGA−II+BFH
NSGA−II+BD
NSGA−II+EFT
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(b) 50 tasks, power profile B
Fig. 3. Sample Pareto fronts computed by NSGA-II+EFT for representative instances
(a) 50 tasks, power profile A
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