International Journal of Emerging
Technology & Research
Volume 1, Issue 4, May-June, 2014
(www.ijetr.org)
ISSN (E): 2347-5900 ISSN (P): 2347-6079
Dynamic Multi Processor Task Scheduling using
Hybrid Particle Swarm Optimization with Fault Tolerance
Gayathri V S1, Sandhya S2, Hari Prasath L3
1, 2
Student, Department of Information Technology, Anand Institute of Higher Technology, Chennai
3
Assistant Professor, Department of Information Technology, Anand Institute of Higher Technology,
Chennai.
Abstract-The problem of task assignment in
heterogeneous computing systems has been
studied for many years with many variations. PSO
[Particle Swarm Optimization] is a recently
developed population based heuristic optimization
technique. The hybrid heuristic model involves
Particle Swarm Optimization (PSO) algorithm
and Simulated Annealing (SA) algorithm. The
PSO/SA algorithm has been developed to
dynamically schedule heterogeneous tasks on to a
heterogeneous processor in a distributed setup.
PSO with dynamically reducing inertia is
implemented which yields better result than fixed
inertia.

Task mitigation – dynamic reassignment of
tasks to processor in response to changing
loads on the processors and communication
network
Dynamic allocation technique can be applied to large
sets of real – world application that are able to be
formulated in a manner which allows for
deterministic execution. Some advantages of the
dynamic technique over static technique are that,
static technique should always have a prior
knowledge of all the tasks to be executed but
dynamic techniques do not require that.
2. RELATED WORK
Keywords: GA, HPSO, Inertia, PSO, TAP, Distributed
System, Simulated Annealing.
1.INTRODUCTION
The problem of scheduling a set of dependent or
independent task in a distributed computing system is
a well – studied area. In this paper, the dynamic task
allocation methodology is examined in a
heterogeneous computing environment.
 Task definition – the specification of the
identity and the characteristic of a task force
by the user, the compiler and based on
monitoring of the task force during
execution.
 Task assignment – the initial placement of
tasks on processors.
 Task scheduling – local CPU scheduling of
the individual tasks in the task force with
the consideration of overall progress of the
task force as a whole.
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Several research works have been carried out in Task
Assignment Problem [TAP]. The traditional methods
such as branch and bound, divide and conquer, and
dynamic programming gives the global optima, but it
is often time consuming or do not apply for solving
typical real – world problems.
The research [2,5,12] have derived optimal task
assignment to minimize the sum of task execution
and communication cost with the branch and bound
methods. Traditional methods used in optimizations
are deterministic, fast and give exact answer but often
get stuck on local optima. Consequently another
approach is needed when traditional methods cannot
be applied for modern heuristic are general purpose
optimization algorithms. Multiprocessor scheduling
methods can be divided into list heuristics, meta
heuristics. In list heuristics, the tasks are maintained
in a priority queue, in decreasing order of priority.
The tasks are assigned to the few processors in the
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(www.ijetr.org) ISSN (E): 2347-5900 ISSN (P): 2347-6079
𝑛
FIFO manner. A meta heuristic is a heuristic method
for solving a very general class of computational
problems by combining user-given black-box
procedures, usually heuristics themselves, in a
hopefully efficient way.
Xik --> set to 1 if task ‘i’ is assigned to
Available meta heuristics included SA algorithm [9],
Genetic Algorithm [2,6], Hill climbing, Tabu Search,
Neural networks, PSO and Ant Colony Algorithm.
PSO yields faster convergence when compared to
Genetic Algorithm, because of the balance between
exploration and exploitation in the search space. In
this paper a very fast and easily implemented
dynamic algorithm is presented based on Particle
Swarm Optimization [PSO] and its variant. Here a
scheduling strategy is presented which uses PSO to
schedule heterogeneous tasks on to heterogeneous
processors to minimize total execution cost. It
operates dynamically, which allows new tasks, to
arrive at any time interval. The remaining of the
paper is organised as follows. Section 3 deals with
problem definition, section 4 illustrates PSO
algorithm. The proposed methodologies are
explained Section 5.
processor ‘k’
n --> number of processor
r --> number of task
eik --> incurred execution cost if task ‘i’ is
executed on processor ‘k’
cij --> incurred communication cost if task
‘i’ & ‘j’ executed on different processor
mi --> memory requirement of task ‘i’
pi --> processor requirement of task ‘i’
Mk --> memory availability of processor ‘k’
Pk --> Processor capability of processor ‘k’
Q(x) --> objective function which combines
the total execution and communication cost
(2) --> says that each task should be
assigned exactly one processor
(3) & (4) --> are the constraints that to
assure the resource demand should never
exceed the resource capability
3. PROBLEM DEFINITION
This paper considers the TAP with the following
scenario. The system consists of a set of
heterogeneous processors (n) having different
memory and processing resources, which implies that
tasks (r) executed on different processors encounters
different execution cost. The communication links
are assumed to be identical however communication
cost between tasks will be encountered when
executed on different processors. A task will make
use of the resources from its execution processor.
The objective is to minimize the total execution and
communication cost encountered by task assignment
subject to the resource constraints. To achieve
minimum cost for the TAP, the function is
formulated as
𝑟
𝑛
𝑟−1
𝑟
𝑛
𝑀𝑖𝑛 𝑄(𝑥) = ∑ ∑ 𝑒𝑖𝑘 𝑥𝑖𝑘 + ∑ ∑ 𝑐𝑖𝑗 (1 − ∑ 𝑥𝑖𝑘 𝑥𝑗𝑘 ) −
𝑖=1 𝑘=1
𝑖=1 𝑗=𝑖+1
𝑛
𝑛
∀ 𝑖 = 1,2, … . , 𝑟−→ (2)
𝑘=1
∑ 𝑚𝑖 𝑥𝑖𝑘 ≤ 𝑀𝑘
∀ 𝑘 = 1,2, … . , 𝑛−→ (3)
𝑘=1
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𝑘=1
∀ 𝑘 = 1,2, … . , 𝑛−→ (4)
𝑥𝑖𝑘 ∈ {0,1}
∀𝑖, 𝑘−→ (5)
4. PARTICLE SWARM
OPTIMIZATION
PSO is a stochastic optimization technique which
operates on the principle of social behaviour like bird
flocking or fish schooling. In a PSO system, a swarm
of individuals (called particles) flow through the
swarm space. Each particle represents the candidate
solution to the optimization problem. The position of
a particle is influenced by the best particle in its
neighbourhood (ie) the experience of neighbouring
particles. When the neighbourhood of the particle of
the entire swarm, the best position in the
neighbourhood is referred to as the global best
particle and the resulting algorithm is referred to as
‘gbest’ PSO.
When the smaller neighbourhood
are used, the algorithm is generally referred to as the
‘lbest’ PSO. The performance of each particle is
measured using a fitness function that varies
depending on the optimization problem.
𝑘=1
→ (1)
∑ 𝑥𝑖𝑘 = 1
∑ 𝑝𝑖 𝑥𝑖𝑘 ≤ 𝑃𝑘
Each particle in the swarm is represented by the
following characteristics ,xij - the current position of
the particle, vij - the current velocity of the particle,
pbestij – personal best position of the particle. The
personal best position of the particle ‘i’ is the best
position visited by particle ‘i’ so far. There are two
versions for keeping the neighbour best vector
namely ‘lbest’ and ‘gbest’. In the local version each
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Volume 1, Issue 4, May-June, 2014
(www.ijetr.org) ISSN (E): 2347-5900 ISSN (P): 2347-6079
particle keeps track of the best vector ‘lbest’ attained
by its local topological neighbourhood of particles.
For the global version, the best ‘gbest’ is determined
by all particles in the entire swarm. Hence the ‘gbest’
model is a special case of the ‘lbest’ model.
The following equations are used for the velocity
updation and the position updation
𝑣𝑖𝑗 = 𝑤 ∗ 𝑣𝑖𝑗 + 𝑐1 ∗ 𝑟𝑎𝑛𝑑1(𝑝𝑏𝑒𝑠𝑡𝑖𝑗 − 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑖𝑗 ) + 𝑐2
∗ 𝑟𝑎𝑛𝑑2(𝑔𝑏𝑒𝑠𝑡𝑖𝑗 − 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑖𝑗 )−→ (6.1)
If we consider it for local best version then the above
equation can be rewritten as
𝑣𝑖𝑗 = 𝑤 ∗ 𝑣𝑖𝑗 + 𝑐1 ∗ 𝑟𝑎𝑛𝑑1(𝑝𝑏𝑒𝑠𝑡𝑖𝑗 − 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑖𝑗 ) + 𝑐2
∗ 𝑟𝑎𝑛𝑑2(𝑙𝑏𝑒𝑠𝑡𝑖𝑗 − 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑖𝑗 )−→ (6.2)
Equation (6.1) & (6.2) is followed by
Here c1 & c2 are cognitive co-efficient and
rand1&rand2 are the two random variables drawn
from U(0,1). Thus the particle flies through potential
situation towards pbesti and gbestin a navigated way
while still exploring new areas by the stochastic
mechanism to escape from local optima. If c1=c2
each particle attracts to the average of pbest and
gbest. Since c1 expresses how much particle trusts its
own past experience it is called the cognitive
parameter and c2 expenses how much it trusts the
swarm called the social parameter. Most
implementations use a setting with c1 roughly equal
to c2. The inertia weight ‘w’ controls the momentum
of the particle. The inertia weight can be dynamically
varied by applying an annealing scheme for the wsetting of the PSO where ‘w’ decreases over the
whole run. In general the inertia weight is set
according to the equation (8).
𝑤𝑚𝑎𝑥 − 𝑤𝑚𝑖𝑛
∗ 𝑖𝑡𝑒𝑟−→ (8)
𝑖𝑡𝑒𝑟𝑚𝑎𝑥
A significant performance improvement is seen by
varying inertia.
5. PROPOSED METHODOLOGY
This section discusses the proposed dynamic task
scheduling using PSO. Table1 shows an illustrative
example where each row represents the particle
which corresponds to the task assignment that assigns
five tasks to three processors. [Particle3, T4] = P1
means that in particle 3, the task 4 is assigned to
processor 1. This section discusses simple PSO,
hybrid PSO. In PSO, each particle corresponds to a
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Particle Number
Particle1
Particle2
Particle3
Particle4
Particle5
T1
P3
P1
P1
P2
P2
T2
P2
P2
P3
P1
P2
T3
P1
P3
P2
P2
P1
T4
P2
P1
P1
P3
P3
T5
P2
P1
P2
P1
P1
Table 1: Representation of Particles
𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑖𝑗 = 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑖𝑗 + 𝑣𝑖𝑗 −→ (7)
𝑤 = 𝑤𝑚𝑎𝑥 −
candidate solution of the underlying problem. In the
proposed method each particle represents a feasible
solution for the task assignment using a vector of ‘r’
element and each element is an integer value between
1 to n. The below table shows an illustrative example
where each row represents the particle which
correspond to a task assignment that assigns the five
task to three processors
In a hybrid version hybridisation is done by
performing simulated annealing at the end of an
iteration of simple PSO. Generally TAP assigns ‘n’
tasks to ‘m’ processors. So that the load is shared and
also balanced. The proposed system calculates the
fitness value of each assignment and selects the
optimal assignment from the set of solutions. The
system compares the memory and processing
capacity of the processor with the memory and
processing requirements of the task assigned, else the
penalty is added to the calculated fitness value.
The algorithm is used for dynamic task scheduling.
The particles are generated based on the number of
processors used, number of tasks that have arrived at
a particular point of time and population size is
specified. Initially particles are generated at random
and the fitness is calculated which decides the
goodness of the schedule. The pbest and gbest values
are calculated. Then the velocity updation and
position updation are done. The same procedure is
repeated for maximum number of iterations specified.
The global solution which is the optimal solution is
obtained. When a new task arrives it is compared
with the tasks that are in the waiting queue and a new
schedule is obtained thus a sequence keeps on
changing with time based on the arrival of new tasks.
Each particle corresponds to a candidate solution of
the underlying problem. Thus each particle represents
a decision for task assignment using a vector of ‘r’
elements and each element is an integer value
between 1 to n. The algorithm terminates when the
maximum number of iterations is reached. The near
optimal solution is obtained by using Hybrid PSO.
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1.1Fitness Evaluation
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Generate the Initial Swarm
The initial population is generated randomly and
checked for the consistency. Then each particle must
be assigned with the velocities obtained randomly
and it lies in the interval [0,1]. Each solution vector
in the solution space is evaluated by calculating the
fitness value for each vector. The objective value of
Q(x) in (1) can be used to measure the quality of each
solution vector. In modern heuristics the feasible
solutions are also considered. Since they may provide
a valuable clue to targeting optimal solution. A
penalty function is only related to constraints (3) &
(4) and it is given by
Evaluate the Initial Swarm using the fitness
function
Find the personal best of each particle and the
global best of the entire swarm
Update the particle velocity using global best
Apply velocities to the particle positions
𝑟
𝑃𝑒𝑛𝑎𝑙𝑡𝑦(𝑥) = max (0, ∑ 𝑚𝑖 𝑥𝑖𝑘 − 𝑀𝑘 )
𝑖=1
𝑟
Evaluate new particle positions
+ max (0, ∑ 𝑝𝑖 𝑥𝑖𝑘 − 𝑃𝑘 ) −→ (9)
𝑖=1
The penalty is added to the objective function
wherever the resource requirement exceeds the
capacity. Hence the fitness function of the particle
vector can finally be defined as in equation
Re - evaluate the original swarm
G
L
O
B
A
L
B
E
S
T
P
S
O
Find the new personal best and global best
𝐹𝑖𝑡𝑛𝑒𝑠𝑠(𝑥) = (𝑄(𝑥) + 𝑃𝑒𝑛𝑎𝑙𝑡𝑦(𝑥))−1 −→ (10)
Hence the fitness value increases the total cost is
minimized which is the objective of the problem
Has the maximum
Iteration reached?
1.2 Simple PSO
As we have already seen in Section 2 Classical PSO
is very simple. There are two versions for keeping the
neighbours best vector namely ‘lbest’ and ‘gbest’.
The global neighbourhood ‘gbest’ is the most
inituitive neighbourhood. In the local neighbourhood
‘lbest’ a particle is just connected to a fragmentary
number of processes. The best particle is obtained
from, the best particle in each fragment.
1.2.1gbest PSO
In the global version, every particle has access to
fitness and best value soo far of all particles in the
swarm. Each particle compares with fitness value
with all other particles. It has exploitation of solution
spaces but exploration is weak. The implementation
can be depicted As a flow chart as shown in Fig. 1
Get the best individual from the last
Fig: Global best Pso
1.2.2lbest PSO
In the local version, each particle keeps tracts of best
vector lbest attained by its local topological
neighbourhood of particles. Each particle compares
with its neighbours decided based on the size of the
neighbourhood. The groups exchange information
about local optima. Here the exploitation of the
solution space is weakened and exploration becomes
stronger.
6. HYBRID PSO
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Modern meta-heuristics manage to combine
exploration and exploitation search. The exploration
seeks for new regions, and once it finds a good
region, the exploitation search kicks in.
The embedded simulated annealing heuristic
proceeds as follows. Given a particular vector, its r
elements are sequentially examined for updating. The
value of the examined element is replaced, in turn, by
each integer from 1 to n, and retains the best one that
Generate the Initial Swarm
Evaluate the Initial Swarm using the fitness
function
Initialize the personal best of each particle and
the global best of the entire swarm
Update the particle velocity using personal best
or local best
Apply velocities to the particle positions
Evaluate new particle positions
Re - evaluate the original swarm and find the
new personal best and global best
Improve solution quality using simulated
annealing
Has the maximum
Iteration reached?
Get the best individual from the last
Fig: Hybrid Best Pso
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H
Y
B
R
I
D
B
E
S
T
P
S
O
attains the highest fitness value among them. While
an element is examined, the values of the remaining
r-1 elements remain unchanged. A neighbour of the
new particle is selected. The fitness values for the
new particle and its neighbourhood is found. They
are compared and the minimum value is selected.
This minimum value is assigned to the personal best
of this particle. The heuristic is terminated if all the
elements of the particle have been examined for
updating and all the particles are examined. The
computation for the fitness value due to the element
updating and all the particles are examined. Since a
value change in one element affect the assignment of
exactly one task, we can save the fitness computation
by only recalculating the system costs and constraint
conditions related to the reassigned task. The flow is
shown in Fig. 3
7.DYNAMIC TASK
USING HYBRID PSO
SCHEDULING
Modern meta-heuristics manage to combine
exploration and exploitation search. The exploration
search seeks for new regions, and once it finds a good
region, the exploitation search kicks in. However,
since the two strategies are usually interwound, the
search may be conducted to other regions before it
reaches the local optima. As a result, many
researchers suggest employing a hybrid strategy,
which embeds a local optimizer in between the
iterations of the meta-heuristics. Hybrid PSO was
proposed in [24] which makes use of PSO and the
Hill Climbing technique and the author has claimed
that the hybridization yields a better result than
normal PSO. This paper uses the hybridization of
PSO and the Simulated Annealing Algorithm. PSO is
a stochastic optimization technique which operates
on the principle of social behavior like bird flocking
or fish schooling. PSO has a strong ability to find the
most optimistic result. The PSO technique can be
combined with some other evolutionary optimization
technique to yield an even better performance.
Simulated Annealing is a kind of global optimization
technique based on annealing of metal. It can find the
global optimum using stochastic search technology
from the means of probability. Simulated Annealing
(SA) algorithm has a strong ability to find the local
optimistic result. And it can avoid the problem of
local optimum, but its ability of finding the global
optimistic result is weak. Hence it can be used with
other techniques like PSO to yield a better result than
used alone.
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The HPSO shown in Fig 1 is an optimization
algorithm combining the PSO with the SA. PSO has
a strong ability in finding the most optimistic result.
Meanwhile, at times it has a disadvantage of local
optimum. SA has a strong ability in finding a local
optimistic result, but its ability in finding the global
optimistic result is weak. Combining PSO and SA
leads to the combined effect of the good global
search algorithm and the good local search algorithm,
which yields a promising result. The embedded
simulated annealing heuristic proceeds as follows.
Given a particle vector, its r elements are sequentially
examined for updating. The value of the examined
element is replaced, in turn, by each integer value
from 1 to n, and retains the best one that attains the
highest fitness value among them. While an element
is examined, the values of the remaining r -1
elements remain unchanged. A neighbor of the new
particle is selected. The fitness values for the new
particle and its neighbor are found. They are
compared and the minimum value is selected. This
minimum value is assigned to the personal best of
this particle. The heuristic is terminated if all the
elements of the particle have been examined for
updating and all the particles are examined. The
computation for the fitness value due to the element
updating can be maximized. The procedure for
Hybrid PSO is as follows,
1. Generate the initial swarm.
2. Initialize the personal best of each particle and the
global best of the entire swarm.
3. Evaluate the initial swam using the fitness
function.
4. Select the personal best and global best of the
swarm
5. Update the velocity and the position of each
particle using the equations (4 ) and (5 ).
6. Obtain the optimal solution in the initial stage.
7. Apply Simulated Annealing algorithm to further
refine the solution.
8. Repeat step 3- step 7 until the maximum number of
iterations specified.
9. Obtain the optimal solution at the end.
8.FAULT TOLERANCE
After the Scheduling is been done each and above
process is allowed to run on the respective processor
which was allotted after scheduling. After some time
if a new process comes at run time then automatically
an interrupt is raised as specified in the above steps.
Now at the time of execution if a processor has gone
failure then the task assigned to that task will leads to
failure.
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In order to overcome this problem we keep track of
the task execution at regular time interval.
The process of Fault tolerance is as follows
1. Task execution is done with the
respective allocated processor
2. A log is created with regular time
interval
3. If a processor gets failure then an
interrupt is raised and from log file
status of each task executed is collected
4. Then with the available details
rescheduling is done and process is
restarted
9.CONCLUSION
In many problem domains, the assignment of the
tasks of an application to a set of distributed
processors such that the incurred cost is minimized
and the system throughput is maximized. Several
versions of the task assignment problem (TAP) have
been formally defined but, unfortunately, most of
them are NPcomplete. In this paper, we have
proposed a particle swarm optimization/simulated
annealing (PSO/SA) algorithm which finds a nearoptimal task assignment with reasonable time. The
Hybrid PSO performs better than the local PSO and
the Global PSO.
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