Combinatorial Approaches for Low-power and Real-time Adaptive
Reconfigurable Embedded Systems
Hamza Chniter
1
, Fethi Jarray
2
and Mohamed Khalgui
1
1
INSAT Institute - University of Carthago, Tunis, Tunisia
FST faculty - University of Elmanar, Tunis, Tunisia
2
ISI Institute, Mednine, Tunisia
Keywords:
Embedded System, Reconfiguration, Real-Time and Low-Power Scheduling, Mixed-Integer Linear Program-
ming, Simulated Annealing.
Abstract:
This paper describes an optimisation-oriented approach to dynamic reconfiguration of embedded systems
with real-time and power consumption constraints. A reconfiguration scenario is assumed to be any run-time
operation allowing the addition-removal-update of OS tasks to adapt the system to its environment under
well-defined conditions. The problem is that any reconfiguration can lead the system to an unfeasible state
where temporal properties are violated or the energy consumption is well-increased. Two methods, integer
programming and simulated annealing, are used to that purpose. The methods have been validated using
analysis tools to evaluate the whole contribution.
1 INTRODUCTION
Nowadays, embedded systems (ES) are integrated
in larger architectures to interact continuously with
their environment under functional and temporal con-
straints (GAUJAL and al, 2003). These ES gen-
erally include both software and hardware compo-
nents which offer today many advantages like the run-
time reconfiguration of the system. A reconfiguration
is any operation allowing the adaptation of the sys-
tem to its environment under well-defined constraints
(Quadri and al, 2012). The embedded systems are
characterized also by their dedicated function and the
high requirements on reliability and correctness. In
fact, it will be able to react with the environment
and meet various functional and extra-functional (e.g.
temporal) constraints. These systems run often under
power constraints that can be violated after particu-
lar reconfiguration scenarios (addition of heavy OS
tasks). Consequently, some processor technologies
are used to make the trade-off between time execu-
tion, speed and energy consumption. One of the new
technologies called DVS (Dynamic Voltage Scaling)
(GRUIAN, 2002) is integrated into processors to dy-
namically change the execution speed of tasks. It aims
to change the operating frequency of the processor
during execution from a set of available speeds.
We assume in the paper a system of n synchronous
periodic tasks which meet the corresponding dead-
lines to be described in user requirements. If tasks
are asynchronous, we can transform them to syn-
chronous. We assume a run-time reconfiguration sce-
nario to add m new tasks in order to adapt the system
to its environment under well-defined constraints. We
assume that the new system of (n+m) tasks is not fea-
sible where some deadlines are violated and the en-
ergy consumption increases. The problem is how can
we compute a new processor frequency in order to ob-
tain a new feasible system after this reconfiguration?
To solve the problem, we propose two combinato-
rial approaches: integer programming and simulated
annealing. These two approaches have been used to
minimize the energy consumption after any reconfig-
uration scenario by determining the suitable proces-
sor frequency to satisfy also the temporal properties.
We prove in particular the performance of the integer
programming to the simulated annealing. Some ex-
perimentations are applied at the end of the paper to
evaluate the whole contribution.
The remainder of this paper is organized as fol-
lows. We discuss in Section 2 the originality of this
paper by studying the state of the art. Section 3 ex-
poses the problem. We present in Section 4 some ter-
minologies and the contribution dealing with integer
program formulation and a simulated annealing for
reconfigurable embedded systems. Finally, numerical
151
Chniter H., Jarray F. and Khalgui M..
Combinatorial Approaches for Low-power and Real-time Adaptive Reconfigurable Embedded Systems.
DOI: 10.5220/0004752701510157
In Proceedings of the 4th International Conference on Pervasive and Embedded Computing and Communication Systems (PECCS-2014), pages
151-157
ISBN: 978-989-758-000-0
Copyright
c
 2014 SCITEPRESS (Science and Technology Publications, Lda.)

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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The power P
i
to be consumed by task T
i
is :
P
i
= CV
i
2
F
i
= C
V
n
f
n
η
i
3
.
The energy E
i
consumed by the task T
i
is:
E
i
= P
i
C
i
= C
V
n
f
n
C
ni
η
i
2
= K
C
ni
η
i
2
where the constant
K = CV
n
F
n
.
So the total energy consumption of the system is:
E =
n
∑
i=1
E
i
= K
n
∑
i=1
C
ni
η
i
2
(1)
As a running example to be followed in the next sec-
tions, we assume a real-time embedded system to be
composed first of 5 tasks as depicted in table 1-page 3.
We assume a run-time reconfiguration scenario to add
3 new OS tasks in order to adapt the system under par-
ticular constraints. The problem is then to guarantee
the feasibility of these eight tasks after this scenario
while satisfying also the energy constraints.
Table 1: Current system configuration
Tasks Release time WCET deadline period
T
1
0 13 80 80
T
2
0 6 70 70
T
3
0 39 90 90
T
4
0 13 110 110
T
5
0 26 100 100
The current system is feasible and was tested
by the real-time scheduling simulator ’chaddar’
(Singhoff and al, 2004). The energy consumption is
equal to 2.328J = 2328mW and the CPU charge is
equal to 1.059. The CPU charge factor U was calcu-
lated by equation (2) and the energy by equation (1)
previously presented.
U =
n
∑
i=1
C
i
d
i
.
(2)
Where C
i
, d
i
are respectively the execution time and
the deadline of task i and n denotes the number of
tasks in the system. We assume a reconfiguration sce-
nario by adding 3 additional tasks in table ??-page 3
to the current system, so the new system becomes in-
feasible because we have some tasks that miss their
deadlines(T
5
, T
8
, T
4
) and the CPU charge increases to
1.427. The energy consumption is also increased and
becomes 3, 168J = 3168mW .
We propose as a possible solution to modify the
processor speed by using integer programming model
or simulated annealing to meet the corresponding
deadlines and to optimize the energy consumption.
Table 2: New system configuration.
Tasks Release time WCET deadline period
T
1
0 13 80 80
T
2
0 6 70 70
T
3
0 39 90 90
T
4
0 13 110 110
T
5
0 26 100 100
T
6
0 10 85 85
T
7
0 11 94 94
T
8
0 14 105 105
4 CONTRIBUTION: FEASIBLE
RECONFIGURATION FOR
EMBEDDED SYSTEM
We define in this section the two solutions that we
propose for the modification of the processor speed
after any reconfiguration scenario.
4.1 Integer Programming Model
We seek to minimize the total energy consumption of
the system under various operating constraints, the
energy is defined as above:
E =
n
∑
i=1
E
i
= K
n
∑
i=1
C
ni
η
i
2
(3)
We introduce the starting time t
i
to denote the effec-
tive starting time of task T
i
. Our goal to minimize
the total consumed energy under the following
constraints:
a) No simultaneously executed tasks
To ensure a single executed task in a time, we
should have either t
j
−t
i
−C
i
≥ 0 or t
i
−t
j
−C
j
≥ 0
or for every pair of tasks T
i
and T
j
. This condition
can be rewritten as t
i
− t
j
≥ C
n j
η
j
− Mα
i j
and
t
j
− t
i
≥ C
ni
η
i
− M(1 − α
i j
) where α
i j
is a binary
variable and M is a big constant. α
i j
= 1 means
that T
j
is executed before T
i
.
b) Deadline of each task should be respected
t
i
+C
ni
η
i
≤ d
i
(4)
c) The the release time should be respected,
t
i
≥ r
i
∀ i. Thus the basic model is the following
CombinatorialApproachesforLow-powerandReal-timeAdaptiveReconfigurableEmbeddedSystems
153

P





























Minimize K
n
∑
i=1
C
ni
η
i
2
s.t.
t
i
−t
j
≥ C
n j
η
j
− Mα
i j
t
j
−t
i
≥ C
ni
η
i
− M(1 − α
i j
)
t
i
+C
ni
η
i
≤ d
i
∀ i
t
i
≥ r
i
∀ i
t
i
≥ 0 ∀ i
α
i j
∈ {0, 1} ∀ i < j
η
i
≥ 0 ∀ i
(5)
It is easy to incorporate into P the finish time of the
system ’T ’ by adding the following constraint:
T ≥ t
i
+C
ni
η
i
∀ i. The extended program is:
PE





























Minimize K
n
∑
i=1
C
ni
η
i
2
+ T
t
i
−t
j
≥ C
n j
η
j
− Mα
i j
t
j
−t
i
≥ C
ni
η
i
− M(1 − α
i j
)
t
i
+C
ni
η
i
≤ d
i
∀ i
t
i
≥ r
i
∀ i
T ≥ t
i
+C
ni
η
i
∀ i
t
i
≤ 0 ∀ i
α
i j
∈ {0, 1} ∀ i < j
η
i
≥ 0 ∀i
(6)
Since the objective function is fractional and the con-
straints are linear, its not possible to solve the program
P or PE by any solver thus we simplify this program
by maximizing the min of the reduction factor η
i
. The
non-linearity of the program PE is due to the fact that
the computation time of tasks is proportional to the
reduction factor whereas the energy consumption is
inversely proportional to the reduction factors. The
simplified program is:
PS









































Maximize x
s.t.
t
i
−t
j
≥ C
n j
η
j
− Mα
i j
t
j
−t
i
≥ C
ni
η
i
− M(1 − α
i j
)
t
i
≤ M ∀ i
t
i
+C
ni
η
i
≤ d
i
∀ i
t
i
≥ r
i
∀ i
x ≤ η
i
∀ i
0 ≤ η
i
∀ i
x ≤ η
i
∀ i
t
i
≥ 0 ∀ i
α
i j
∈ {0, 1} ∀ i < j
C
ni
≥ 0 ∀ i
(7)
Case study:
Our model was applied to the system recently pre-
sented to resolve the non feasibility problem. It com-
putes for each task, start time, finish time and new
the WCET after changing the reduction factor of the
processor speed. The results are presented in table 4.
Table 3: Applied model for WCET reconfiguration.
Tsks Release
time
Last
WCET
New
WCET
Reduction
factor
Start
time
Finish
time
deadline
T
1
0.00 13.00 9.105 0.70 0.00 9.105 80
T
2
0.00 6.00 4.202 0.70 9.105 13.307 70
T
3
0.00 39.00 27.316 0.70 13.307 40.623 90
T
4
0.00 13.00 9.105 0.70 40.623 49.729 110
T
5
0.00 26.00 18.210 0.70 49.729 67.939 100
T
6
0.00 10.00 7.004 0.70 67.939 74.944 85
T
7
0.00 11.00 7.704 0.70 74.944 82.648 94
T
8
0.00 14.00 9.805 0.70 82.648 92.454 105
4.2 Simulated Annealing Approach
We have also proposed simulated annealing approach
to proof its performance in a reconfigurable real-time
embedded system and to compare it to integer pro-
gramming and related works. The simulated anneal-
ing SA is based on neighborhood search. In local
search techniques, we generally start with a random
solution and try to improve it over the iterations.
Greedy heuristics always move from the current so-
lution to the best neighboring solution. In order to es-
cape local minima, simulated annealing allows uphill
moves in a controlled manner. At each step, we gener-
ate a perturbation, if the objective function decreased,
then, we accept the new state, else we accept the new
state with a probability related to this increase. We
have to choose an initial temperature and to ensure
the stop criteria.
Initial solution:
A solution should only respect the release times of
the tasks, i.e. we relax the rest of constraints. The ini-
tial solution can be computed by the following way:
1. Sort the tasks according to their release times.
2. If two tasks have the same release times, we
choose the one with the closest deadline.
3. Repeat the two steps until choosing all tasks.
Objective function:
The objective function is to minimize the sum of
the total energy consumption, the total execution time
and the number of tasks that miss their deadlines.
Neighborhood structure:
The neighborhood of a solution is a set of solu-
tions that can be reached from the solution by a sim-
ple operation (move). Given the current solution, rep-
resented by the set of tasks, their starting times and
effective frequencies, a neighbor solution is built by
either swapping the execution order of two randomly
selected tasks or changing the frequency of a random
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154

task beyond its deadlines.
Simulated annealing parameters:
The main parameters of the simulated annealing
are the initial temperature, the temperature length, the
cooling ratio and the stopping criterion. The initial
temperature (90) must be high enough so that the fi-
nal solution to be independent of the starting one. The
temperature length (50) is the number of iterations at a
given temperatures. However the temperature length
may vary from temperature to temperature and it is
important to spend long time at lower temperatures
The cooling ratio (µ = 0.9) is the rate at which the
temperature is reduced. In our simulation, the simu-
lated annealing stops when the minimum value of the
temperature has been reached (5) or a certain number
of temperatures (4) has passed without acceptance of
a new solution or the number of total iterations (1000)
has been executed.
5 NUMERICAL RESULTS
The integer programming model was solved with
ILOG CPLEX 11.1 solver on a mono-processor core
2 duo , 1.2 Mhz and 1 Giga RAM. The simulated an-
nealing was implemented in C and executed in the
same machine.
Comparation with related work:
We note that the two approaches implemented in
this paper to solve the problem of non feasibility of
a reconfigurable real-time embedded system, give re-
sults close to those of (Jeannenot and al,2004). How-
ever the previous model developed does not guarantee
the feasibility of the system. In addition our model
allows to compute the feasibility more than the ex-
ecution sequence of tasks but also the start and the
finish time of each task. In our experimentation, we
have randomly generated instances with 10 to 400
jobs. The numerical results are depicted in the ta-
ble 4. The first column shows the size of the prob-
lem i.e the number of jobs. The sub-column labeled
”time” indicates the running time in seconds for each
method. The sub-column labeled ”Energy” gives the
total energy consumption. The sub-column labeled
”CPU charge” gives the total charge of the processor.
The sub-column labeled ”Fitness” gives the objective
function recently described. Finally, the sub-column
labeled ”D exceeded” reveals the number of tasks that
miss their deadlines.
Table 4 shows that the fitness function of the integer
program is lower than that of the simulated annealing.
The processor is less loaded in the integer program
than in the simulated annealing. However for the large
size instances, the simulated annealing is much faster.
We conclude that the integer programming is more
preferment than the simulated annealing algorithm for
the small and the medium instances. Moreover in-
teger program guarantees that all tasks are respected
due to the constraint of deadlines (c).
Figures 1 and 2 present a graphic Comparation
between simulated annealing and IP in term of CPU
charge and energy consumption. In figure 1, SA gives
a lower CPU charge than IP because the IP attempts
to exploit up the processor to fulfill the needs of tasks
and to meet all the deadlines. However, SA does not
sometimes meet all the deadlines.
Figure 1: Comparation between SA and IP from CPU
charge.
According to the energy consumption, we observe
in figure 2 that IP is more effective as the number of
instances increases because it allows to explore more
the search space of solutions and can give a fairly op-
timal solution.
Figure 2: Comparation between SA and IP from energy
consumption.
In figure 2, we compare the average CPU charge
for the two proposed approaches and those presented
as follows in (Jeannenot and al,2004) on instances of
5 to 15 tasks. Approaches marked with ’*’ correspond
to the SA and the IP proposed in this paper, others
CombinatorialApproachesforLow-powerandReal-timeAdaptiveReconfigurableEmbeddedSystems
155

Table 4: Comparation between integer programing and simulated annealing.
Simulated annealing Integer programming
basic system+added tasks Time Energy CPU charge Fitness D exceeded Time Energy CPU charge Fitness D exceeded
5+5 42ms 51.44 0,9743 64.04 1 2.52s 22.5 1 37.50 0
15+5 38ms 114.96 0,8929 134.76 1 8.03s 39 0,9999 64.99 0
20+10 50ms 169.96 0,99953 197.16 1 25.56s 55.5 1 92.50 0
30+10 45ms 255.61 0,9781 261.81 1 345.54s 75 0,8933 125.00 0
40+10 71ms 271.6 0,9716 315.19 0 1626.04s 147.75 1 215.99 0
45+15 69ms 353.43 0,9512 405.02 1 1623.3s 162.44 0,9215 247.03 0
50+20 84ms 358.06 0,9703 420.25 1 1624.68s 165.68 0,8629 259.18 0
60+20 52ms 448.67 0,8791 516.66 1 1621.42s 154.69 0,86452 252.75 0
70+20 67ms 469.64 0,9653 573.83 1 1621.63s 247.97 0,8913 251.69 0
80+20 68ms 561.13 0,9732 644.13 0 1708.29s 307.02 0,9283 453.98 0
150+50 278ms 1176.52 0,9892 1345.12 1 1880.57s 743,39 0,9711 513.05 0
250+50 659ms 1748.46 0,8908 2007.46 1 1950.89s 1230.76 0,8791 594.33 0
300+100 1s 2212.5 0,8996 2632.70 66 2226.04s 499.04 0,8839 753.61 0
refer to (Jeannenot and al,2004). Our approaches try
to exploit the flexibility of the processor speed to meet
the deadlines of tasks and to minimize the energy cost
because in our contribution approaches will work in
a reconfigurable real-time embedded system so that
feasibility constraint after a reconfiguration scenario
requires more resources of processors.
Figure 3: Average CPU charge from each approach.
6 CONCLUSIONS
The paper proposes two methods based on integer
programming and simulated annealing to solve the
non-feasibility scheduling problem while minimizing
the energy consumption of a reconfigurable real-time
embedded system. The numerical results show that
the integer programming model gives good results
and over performs the simulated annealing algorithm
to resolve the problem. Both approaches give results
close to those presented in (Jeannenot and al,2004)
but they take advantage of the fact that They deal with
reconfigurable real-time system and can ensure the
system feasibility after any scenario. However, their
effectiveness is not yet checked for other categories of
tasks such as sporadic and aperiodic. The proposed
model can be extended to include other constraints
such as multiprocessor systems and other objectives
such as minimization of the communication between
the tasks.
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