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results are presented and discussed in Section 5.
2 RELATED WORKS
The paper presents the scheduling problem of peri-
odic non preemptive tasks that implement a recon-
figurable embedded system while minimizing the en-
ergy consumption. There are many papers in the liter-
ature on algorithms providing approximating results
for this NP-complete problem. In (Heilmann, 2003),
the author presented an exact solution for the gen-
eral resource-constrained project scheduling problem
to determine a mode and a start time for each activity
such that all constraints are respected and the dura-
tion of the project is minimized. The solution method
is a depth-first search based branch&bound proce-
dure. The work in (Xu, 1993) presented a branch and
bound approach to solve allocation problem commu-
nicating periodic tasks. In another work (GAUJAL
and al, 2003), Gauja presented an algorithm based
on finding the shortest path in a graph to solve the
same problem. In (Hladik and al, 2008), the au-
thors presented Integer Linear Programming (ILP) for
scheduling problem with dependent tasks in a multi-
processor homogeneous system. (Kuei-Tang and al,
2013) applied DVFS techniques to mobile computing
platforms where performance constraints, such as task
deadlines. They try the problem in a linear program
and solve the problem by the simplex algorithm. The
objective function is to make the trade-off between
the total weighted tardiness and the power cost. A
scheduling based on constraint programming multi-
objective (multi-criteria optimization) is proposed in
(Hladik and al, 2008). In (Majazi and Ghorbanali.,
2012), the authors focused on the multi-objective flex-
ible job-shop scheduling problem with parallel pro-
cessors and maintenance cost. Two meta-heuristic
algorithms, an hybrid genetic algorithm. Based on
DVS technology, Jeannenot proposed in (Jeannenot
and al,2004) a set of algorithms under periodic real-
time tasks in a processor with dynamic variable speed.
The authors seek to determine the suitable speeds exe-
cution for each task to minimize the total energy con-
sumption from a real-time feasible embedded system.
Although the cited works are interesting and im-
portant, they do not address reconfigurable systems
that can dynamically change their behaviors at run-
time. We expose in the current paper the problem
of reconfigurable systems by using Integer program-
ming and simulated annealing. The goal is to compute
the frequency processor and the execution sequence
of tasks with a good performance in terms of energy
cost and execution time.
3 PROBLEM AND NOTATION
We detail the problem in this section and present a
terminology to be followed in the current paper. We
assume a reconfigurable real-time system to be com-
posed of periodic independent tasks that we assume
synchronous. A reconfiguration scenario is any run-
time operation allowing the addition-removal-update
of tasks to adapt the system to its environment. Nev-
ertheless, the application of a scenario can increase
the energy consumption or push some tasks (new or
old) to violate corresponding deadlines. Our goal is
to provide some solutions that will optimize the en-
ergy consumption and guarantee the respect of dead-
lines after each reconfiguration scenario. We propose
two approaches Integer Programming IP Model and
Simulated Annealing SA to find the required solution
by changing the processor speed. We want also to
compare these two approaches to find the optimal and
best solution. The integer programming approach is
based on a mathematical model including the objec-
tive function and the constraints in relation, the sim-
ulated annealing heuristic is inspired from a process
used in metallurgy, many parameters will be fixed to
turn this heuristic and to give the expected solution
such as the initial solution with which it must start,
the initial temperature and the maximum number of
iterations.
Notation:
We consider a set of n periodic tasks T
i
, i = 1 . . . n.
Each task i is classically characterized by four
parameters. Firstly by its release (or arrival) time r
i
,
i.e each task T
i
cannot begin execution before time
r
i
. Secondly by its absolute deadline constraint d
i
,
i.e. each task should finish before time d
i
. Thirdly
by its computation time at the normalized processor
frequency C
ni
. Finally by its period which is equal to
the deadline (Liu and Layland, 1973).
We denote respectively by f
n
and V
n
the normalized
frequency and voltage of the system. We assume
that there’re usually proportional. We suppose that
each task T
i
is executed at frequency F
i
and at voltage
V
i
. We denote by η
i
the reduction factor of voltage
when T
i
is executed, V
i
=
V
n
η
i
. So C
i
= C
ni
η
i
. In
general, when the system is running at frequency F
and voltage V, the power consumption is
P = CV
2
F where C is a constant related to the circuit
type of processor (Chuan and al, 2012). If the system
is running over x times, the energy consumption is:
E = Px.
The problem is then to allow low-power and real-time
optimal scheduling of reconfigurable tasks after each
reconfiguration scenario.
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