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DAG task scheduling problems because of high adaptability of
these algorithms. In addition, these algorithms usually generate
output schedules of better quality than those generated by con-
structive heuristic-based ones([21][22][23]). However, the compu-
tation cost of these algorithms is higher than that of constructive
heuristic algorithms due to the poor search efficiency and frequent
solutions evaluation. According to ”No Free Lunch” theorem [29],
a single search methodology to achieve better performance for
all kinds of applications and situations is impossible. However,
this theorem does not postulate that a search methodology that
can improve performance in special applications or situations can-
not be developed. Automatically selecting appropriate scheduling
strategy for different situations may be a good choice to improve
the search efficiency of scheduling algorithm. Moreover, the time
complexity must be reduced in the search and evaluation of
solution spaces for these approaches on the basis of guided search
techniques.
In our paper, power-performance tradeoff problem in DVS-
enabled HMCSs is defined as energy-constrained performance
optimization (P ro1) and performance-constrained energy opti-
mization (P ro2). In order to tackle the two problems, a algorithm,
named quantum-inspired hyper-heuristics algorithm (QHA), is
proposed. This algorithm does not employ complex search strategy
to search the solution space directly; rather, it introduces the hyper-
heuristic framework [30] to manage reduced low-level heuristics.
In our approach, low-level heuristics are effectively designed for
various specific situations or objectives. Moreover, a quantum-
inspired high-level strategy that improves on the quantum-inspired
evolution algorithm [31] is developed to automatically manage
such low-level heuristics. Furthermore, a fast solution evaluation
technique is established to reduce the computation cost of the
algorithm. The main contributions of this study are as follows:
•
Problem Modeling. The power-performance tradeoff
problem in DVS enabled HMCSs for precedence-
constrained parallel applications scheduling is defined as
energy-constrained performance optimization (P ro1) and
performance-constrained energy optimization (P ro2) to
manage the energy consumption flexibly.
•
Hyper-heuristic framework is introduced and a reduced
low-level heuristics set established. To the best of our
knowledge, this framework is the first one introduced to
scheduling problem in HMCSs.
•
Quantum-inspired Hyper-heuristics Algorithm (QHA). To
improve the performance of hyper-heuristic framework,
a quantum-inspired high-Level learning strategy is de-
signed to evaluate the current performance of the low-level
heuristics more accurately than the traditional high-level
heuristic strategy can. This strategy can also maintain the
diversity of low-level selected probability.
•
Fast Solution Evaluation Technique. The technique can
avoid double counting while evaluating solutions.The ex-
perimental result shows that the proposed method average
improved the search speed by 38% to traditional solution
evaluation method.
The rest of this paper is organized as follows: in the following
section, the works related to our research is introduced. In section
3, the mathematical models of the problem are proposed. In
section 4, our methodology is described in detail. In section 5,
we demonstrate the workability of QHA through evaluations of
simulation experiments. In section 6, the conclusion of this study
is drawn.
2 RELATED WORK
2.1 Task scheduling and energy-aware scheduling
Static scheduling on MCSs has been researched extensively. The
proposed algorithms can be classified into: list-based, clustering
based, duplication-based, and guided random search-based. List-
based algorithm involves the task priority list building and tasks
mapping [21] [32]. The performance of these algorithms usually
varies according to the different rules of each task priority list
and task mapped. Cluster-based and duplication-based scheduling
algorithms typically reduce communication overheads among in-
tercommunication tasks, which prefer to communication-intensive
application scheduling [33][34]; Guided random search-based
scheduling algorithms are popular in DAG scheduling [25]-[28].
These algorithms use guided search strategy that is inspired by
biological evolution or biobehavioral to search the problem space
directly. These algorithms usually generate output schedules of
better quality than those produced by other algorithm categories.
However, the scheduling time of guided random search-based
scheduling algorithms is also higher than those of others because
of poor search efficiency and solution evaluation.
Energy-aware scheduling and resource allocation is one of
most promising approaches to saving energy in MCSs, and DVS
techniques has been widely used in energy-aware scheduling
(e.g.,[1]-[8] [12] [13][35][36]). The proposed algorithms can be
classified as follows according to different optimization objective
models: energy efficiency ratio optimization algorithm, energy-
constrained performance or performance-constrained energy op-
timization algorithm, multi-objective optimization algorithm. In
an energy efficiency ratio optimization algorithm(e.g.,[5][6][8]),
a schedule is first generated, and then scrutinize the schedule, if
changes to the schedule can reduce energy consumption, a new
schedule is produced. Thus, the algorithm can improve energy ef-
ficiency ratio significantly, but it cannot manage energy consump-
tion flexibly; In energy-constrained performance optimization or
performance-constrained energy optimization algorithm, the target
system and the task models of most algorithm do not consider
heterogeneous systems and dependent tasks simultaneously. For
instance, the target system model is composed of homogeneous
multiprocessor systems in [2][4]. In [16][17] the target task
model is composed of independent tasks; The multi-objective
optimization-based algorithm is another way to manage energy
consumption flexibly[7][18]. However, the Pareto optimal solution
set must be determined for the algorithm, and the computation
cost of this process is high because of the non-dominated solution
sorting operation. From the above knowable, flexibly Managing
of energy consumption in DVS-enabled heterogeneous multipro-
cessor or multi-computer systems is challenging for scheduling
dependent tasks.
2.2 Hyper-heuristic
Different heuristics have varying capabilities that may change over
the search space. In other words, no heuristic can perform ideally
in all situations[29]. Hyper-heuristics are intended to provide a
method to automatically managing low-level heuristics sets, as
opposed to searching the solution space directly. This frame-
work increases the generalizability of an algorithm with higher