chapter 6 proposed parallel improved particle...

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CHAPTER 6

PROPOSED PARALLEL IMPROVED PARTICLE SWARM

OPTIMIZATION FOR MULTIPROCESSOR SCHEDULING

The present chapter proposes, two parallel approaches, Parallel

Synchronous and Parallel Asynchronous of Improved Particle Swarm

Optimization (IPSO) for multiprocessor task scheduling, with two cases

namely static independent tasks scheduling and dynamic task scheduling with

and without load balancing, to speed up the convergence and to reduce the

total execution cost of the entire schedule.

6.1 INTRODUCTION

In the growing scenario, the development of parallel optimization

algorithms are motivated by the high computational cost of complex

engineering optimization problems, in which many calculations are carried

out simultaneously. Parallel optimization works on the principle that large

problems can often be divided into smaller ones, which are then solved

simultaneously. To obtain an improved computational throughout and global

search capability, the parallelization of an increasingly popular global search

method is exploited, namely, the Parallel Particle Swarm Optimization

(PPSO) algorithm.

In view of improving the efficiency and performance in dynamic

environment, more effort is still required. Hence, the present chapter aims at

developing a new Parallel approach of Improved Particle Swarm

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Optimization to solve the multiprocessor scheduling problem. Parallel

synchronous Improved Particle Swarm Optimization (PSIPSO) and Parallel

Asynchronous Improved Particle Swarm Optimization (PAIPSO)

methodologies are tested for the multiprocessor scheduling problem. The

performances of the parallel Improved PSO (PSIPSO and PAIPSO)

approaches are better than that of the Parallel Synchronous Particle Swarm

Optimization (PSPSO) and Parallel Asynchronous Particle Swarm

Optimization (PAPSO) when applied to the multiprocessor task scheduling

problem.

6.2 REVIEW OF LITERATURE

Nicol and O’Hallaron (1991) extended the work on the problem of

mapping pipelined or parallel computations onto linear array, shared memory

and host-satellite systems. Results show that these problems can be solved

more efficiently when computation module execution times and inter module

communication times are bounded, and the processors satisfy certain

homogeneity constraints. Run-time complexity is reduced further with

parallel mapping algorithms based on these improvements, which run on the

architecture for which they create mappings.

Lee and Lee (1996) proposed new Parallel Simulated Annealing

algorithms which allow multiple Markov chains to be traced simultaneously

by Processing Elements which may communicate with each other. Both

synchronous and asynchronous algorithms implementation have been

considered. Their performance have been analysed in detail and also verified

by extensive experimental results. The proposed parallel simulated annealing

schemes for graph partitioning can find a solution of equivalent or even better

quality up to an order of magnitude faster than the conventional parallel

schemes. Among the proposed schemes, the one where Processing Elements

exchange information dynamically (not with a fixed period) performs best.

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Ahmad and Kwok (1999) dealt with the problem of parallelizing

the multiprocessor scheduling problem. A parallel algorithm is introduced

that is guided by a systematic partitioning of the task graph to perform

scheduling using multiple processors. The algorithm schedules both the tasks

and messages, and is suitable for graphs with arbitrary computation and

communication costs, and is applicable to systems with arbitrary network

topologies using homogeneous and heterogeneous processors. The algorithm

is implemented on the Intel Paragon processor and is compared with three

closely related algorithms. The experimental results indicated that the

proposed algorithm yields higher quality solutions while using an order of

magnitude smaller scheduling times. The algorithm also exhibited an

interesting trade-off between the solution quality and speedup while scaling

well with the problem size.

Alba and Troya (2001) analyzed the importance of the synchronism

in the migration step of various parallel distributed Genetic Algorithms.

Results have proved that parallel Genetic Algorithms almost always

outperform sequential Genetic Algorithms, and also asynchronous algorithms

always outperform their equivalent synchronous counterparts in real-time.

Van Soest and Casius (2003) enumerated the merits of a Parallel

Genetic Algorithm in solving hard optimization problems. A Parallel Genetic

Algorithm for optimization is outlined, and its performance on both

mathematical and biomechanical optimization problems is compared to a

sequential quadratic programming algorithm, a downhill simplex algorithm

and a Simulated Annealing Algorithm. The authors claim that the key

advantage of the genetic is that it can easily be parallelized at negligible

overhead.

Higginson et al (2004) analyzed the importance of simulated

parallel annealing within a neighbourhood for optimization of bio-mechanical

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systems. A portable parallel version of a simulated annealing algorithm is

designed for solving optimization problems in biomechanics. The algorithm

for Simulated Parallel Annealing (SPA) within a neighborhood is designed to

minimize inter-processor communication time and closely retain the heuristics

of the serial Simulated Annealing algorithm. The computational speed of the

SPAN algorithm scaled linearly with the number of processors on different

computer platforms for a simple quadratic test problem and for a more

complex forward dynamic simulation of human pedalling.

Schutte et al (2004) discussed the parallelization of an increasingly

popular global search method, the Particle Swarm Optimization (PSO)

algorithm in detail to obtain enhanced throughput and global search capacity.

The parallel PSO algorithm’s robustness and efficiency are demonstrated

using a biomechanical system identification problem containing several local

minima and numerical or experimental noise. The problem involves finding

the kinematic structure of an ankle joint model that best matches experimental

movement data. For synthetic movement data generated from realistic ankle

parameters, the algorithm correctly recovered the known parameters and

produced identical results to a synchronous serial implementation of the

algorithm. When numerical noise is added to the synthetic data, the algorithm

found parameters that reduced the fitness value below that of the original

parameters. When applied to experimental movement data, the algorithm

found parameters consistent with previous investigations and demonstrated an

almost linear increase in throughput for up to 30 nodes in a computational

cluster. Parallel PSO provides a new option for global optimization of large-

scale engineering problems.

Ho et al (2004) proposed two Intelligent Evolutionary Algorithms

(IEA) and Intelligent Multiobjective Evolutionary Algorithms (IMOEA)

using a novel Intelligent Gene Collector (IGC) to solve single and

multiobjective large parameter optimization problems. IGC is the main phase

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in an intelligent recombination operator of IEA and IMOEA. Based on

orthogonal experimental design, IGC uses a divide-and-conquer approach.

IMOEA utilises a novel generalized Pareto-based scale-independent fitness

function for efficiency finding a set of Pareto-optimal solutions to a

multiobjective optimization problem. The IEA and IMOEA algorithms have

high performance in solving benchmark functions comprising of several

parameters, as compared with the existing Evolutionary Algorithms.

Chang et al (2005) presented a Parallel version of the Particle

Swarm Optimization (PPSO) algorithm together with three communication

strategies which can be used according to the independence of the data. The

first strategy is designed for solution parameters that are independent or are

only loosely correlated, such as the Griewank function. In cases where the

properties of the parameters are unknown, a third hybrid communication

strategy can be used. Experimental results demonstrated the usefulness of the

proposed PPSO algorithm.

Kwok and Ahmad (2005) proposed optimal algorithms for static

scheduling of task graphs with arbitrary parameters to multiple homogeneous

processors. The first algorithm is based on the A*search technique and uses a

computationally efficient cost function for guiding the search with reduced

complexity. Additionally, a number of effective state-pruning techniques are

proposed to reduce the search space. For further lowering the complexity, an

efficient parallelization of the search algorithm is proposed. Parallelization of

the algorithm is carried out with reduced inter processor communication as

well as with static and dynamic load balancing schemes to evenly distribute

the search states to the processors. An approximate algorithm is also proposed

that guarantees a bounded deviation from the optimal solution but executes in

a considerably shorter time. Based on an extensive experimental evaluation of

the algorithms, it is concluded that the parallel algorithm with pruning

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techniques is an efficient scheme for generating optimal solutions of

reasonably large problems.

Venter and Sobieszcanski Sobieski (2005) tested both the

synchronous and asynchronous parallel PSO algorithms for the optimization

of typical transport aircraft wing parameters. The result infers that the

asynchronous PSO algorithm performs better than the synchronous PSO in

terms of parallel efficiency.

Koh et al (2006) implemented an asynchronous parallel PSO

algorithm for analytical and biomechanical test problems. The asynchronous

PSO is 3.5 times faster than the synchronous PSO algorithm.

Waintraub et al (2009) developed several different PPSO

algorithms exploring the advantages of enhanced neighborhood topologies

implemented by communication strategies in multiprocessor architectures.

The proposed PPSOs have been applied to two complex and time consuming

nuclear engineering problems, namely, reactor Core Design (CD) and Fuel

Reload (FR) optimization. After exhaustive experiments, it has been

concluded that, PPSO still improves solutions after many thousands of

iterations, making prohibitive the efficient use of serial (non-parallel) PSO in

such a kind of real world problems and PPSO with more elaborated

communication strategies is demonstrated to be more efficient and robust than

the master-slave model. Advantages and peculiarities of each model are

carefully discussed in the present research.

Subbaraj et al (2010) presented an advanced Parallelized Particle

Swarm Optimization algorithm with modified stochastic acceleration factors

(PSO-MSAF) to solve large scale Economic Dispatch (ED) problems. The

proposed algorithm prevents premature convergence and achieves better

speed up, especially for large scale ED problems, mitigating the burden of

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multimodality and heavy computation. To improve the performance of the

proposed algorithm, penalty parameter-less constraint handling scheme is

employed to handle power balance, prohibited operating zones and ramp-rate

limits. The proposed architecture effectively controls the local search ability,

thereby leading to better convergence towards the true optimal solution.

Mussi et al (2011) proposed possible approaches to parallelizing

PSO on graphics hardware within the Compute Unified Device Architecture

(CUDA™), a GPU programming environment by nVIDIA™ which supports

the company’s latest cards. In the proposed method, the author explored and

evaluated two different ways of exploiting GPU parallelism and compared the

execution speed of the two parallel algorithms, on functions which are

typically used as benchmarks for PSO, with a standard sequential

implementation of PSO (SPSO), as well as with the recently published results

of other parallel implementations.

The review of literature presents the details of parallel approaches

and hybrid parallel approaches to various problems. It also reveals that the

parallel approaches provide better results.

6.3 PARALLEL PARTICLE SWARM OPTIMIZATION

There are different types of parallelism namely Bit-level,

Instruction level, Data parallelism and Task parallelism. The present research

work uses Data Parallelism. Parallel computing has the advantages of less

time consumption, and faster rate of solving complex problems.

The Parallel Particle Swarm Optimizers (PPSO) are classified into

three categories namely Global PSO, Migration PSO and Diffusion PSO (Belal

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Master

Receive individual

Send globalvalue

Slaves

and EI-Ghazawi 2004). The next three sub-sections describe the mechanism of

each model.

6.3.1 Global PSO model (Master/ Slave)

In the global PSO model, finding the global optimal is done in a

master processor, while evaluation of the objective function and the

modifying particles velocities are executed in the slaves. In this model, the

communication overhead is linearly proportional to the folk size and the

computational gain obtained in master/slave model is reduced due to the large

communication overhead, as shown in Figure 6.1. The main feature is that

finding the global optimal is done on the total folk, hence the global

information about the optimal is available for each node.

Figure 6.1 Global PSO model (Master/Slave)

6.3.2 Migration PSO Model (Island)

In the migration PSO model, the folk is divided into sub-folks, each

of which is placed on one Processing Element (PE), each PE runs a PSO

algorithm on its sub-folks. Choosing the optimal value and modifying

individuals’ velocities is local to only its sub-folk. Similarly, after a finite

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Send best

Receivebest value

Sub-folk onsingle PE

number of iterations or migration intervals, the best solution of each PE is

migrated to the neighbouring processors, as shown in Figure 6.2. In migration

PSO model, two modules are involved namely, a first module for sending and

receiving messages from other neighbours, and the second for updating the

individuals velocities based on the local optimal found on each node. The first

module can run at separate time interval or by interrupts.

Figure 6.2 Migration PSO model

6.3.3 Diffusion PSO Model

Diffusion PSO depends on the locality concept. Each individual is a

separate breeding unit and all the evaluations of the objective function is

performed locally. The distributed algorithm is different in its functionality

from the sequential one. In a distributed algorithm, the locality of information

is assumed for each agent. Each agent does not know much about what the

currently global best value is at each iteration, and moves towards its best

value in its neighbourhood. At first, each node considers its value is the best

value so far. Also, in each step, every node will get the neighbour’s best value

so far. If any of their values are less than its best value so far, this value will

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The starting node

The first neighbour

The second neighbour

The third neighbour

Send MY best value

Receive neighbour best value

then replace its current value and will be sent to its neighbours as shown in

Figure 6.3.

Figure 6.3 Diffusion Model

Determining the best value in each node neighbourhood means that

each node broadcasts its current value to all its neighbours and it then

modifies its best value so far to be the best of all its own value and its

neighbours’ value. This would help in searching all areas and not escaping

from local minima and maxima. The effectiveness of this model depends on

the connectivity of the model, ranging from ring topology. This model

exploits the use of distributed learning, since each agent inspects for the

solution and cooperates with its neighbours to exchange information.

6.4 PROPOSED PARALLEL APPROACH

Advancement and the recent trends in the computer and network

technologies have direct towards the developments of parallel optimization

algorithms. PSIPSO method is proposed for the task scheduling problem,

which requires a synchronization point at the end of each optimizer iteration

before continuing to the next iteration. The PSO algorithm is well suited for a

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coarse grained parallel implementation on a parallel or distributed computing

network.

The present research uses Master-Slave model. The parallelism is

carried out using master-slave approach.

6.5 PROPOSED PARALLEL SYNCHRONOUS IMPROVED

PARTICLE SWARM OPTIMIZATION APPROACH

(PSIPSO)

The procedure for PSIPSO is as follows,

1. Configure the master slave environment.

2. The initial swarm is generated and initialized by the master.

3. The master sends the initial swarm to all the salves.

4. The slaves evaluate the initial swarm using the fitness function

and select the personal best and global best of the swarm.

5. Each of the slaves calculates the fitness function, and then

updates the velocity and position and sends each of its optimal

solution to the master after the specified number of iteration is

completed.

6. The master decides the best solution after receiving the results

from all the slaves based on the objective function after the

maximum number of iterations specified is completed.

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Initialize the population Input number of processors,number of jobs and population size

Compute the objective function

The master sends the unique combination of differentparticles to the slaves

Start

Invoke IPSO

Slave 1 Slave 2Slav

Slave 3 Slave n

The master receives the updated best particle form all the slaves afterpre-determined number of iterations is completed

The master decides the global best value

A

Figure 6.4 Flowchart for the proposed PSIPSO algorithm

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A

Choose the minimum ‘F’ of all particles as the gbest

If E < best ‘E’ (Pbest) so far

Search isterminated

optimal solutionreached

For each generation

For each particle

Current value = new pbest

No

Yes

Calculate particle velocity

Calculate particle position

Update memory of each particle

End

End

Return by using IPSO

Stop

Figure 6.4 (Continued)

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6.6 PROPOSED PARALLEL ASYNCHRONOUS IMPROVED

PARTICLE SWARM OPTIMIZATION APPROACH (PAIPSO)

The weakness of the proposed PSIPSO algorithm is that, the

schedule for the next iteration is analysed after the current iteration is

completed. This can be overcome by considering a parallel asynchronous

algorithm. The goal is to have no idle processors as one moves from one

iteration to the next. To implement a PAIPSO algorithm is to separate the update

actions coupled with each sequence and those linked with the entire swarm.

PAIPSO is implemented using a maser-slave approach. The master

processor holds the queue of feasible particles to be sent to the slave

processors. The master performs all decision making processes such as

velocity updation, position updation and convergence checks. The slaves

perform the function evaluations for the particles sent to them. The tasks

performed by the master and slave are as follows, (Koh et al 2006)

Master Processor

1. Initialize all optimization parameters and particle positions

and velocities.

2. Holds a queue of particles for the slave processors to evaluate

3. Updates the particle positions and velocities based on the

currently available information.

4. Sends the next particle in the queue to an available slave

processor

5. Receives cost function values from the slave processors.

6. Checks convergence.

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Check Convergence

Update

Master initializes

Xf Xf Xf

No of Particles

No

of It

erat

ions

CheckConvergence and

Update

Initialize

Xf

Xf

Xf

Xf

Xf

Xf

No of Particles

Slave Processor

1. Receives the particle from the master processor.

2. Evaluates the objective function of the particle sent to all

the slaves.

3. Sends the cost function value to the master processor.

Figure 6.5 Block diagram of parallel synchronous IPSO approach

Figure 6.6 Block diagram of parallel asynchronous IPSO approach

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Block diagrams for parallel synchronous and parallel asynchronous

IPSO algorithms are shown in Figures 6.5 and 6.6. In which Grey boxes

indicate the first set of particles evaluated by each algorithm.

After completion of initialization step by the master processor,

particles are sent to the slave processors to evaluate the objective (analysis)

function. The initial step of the optimization is identical to that of the PSIPSO

algorithm. After initialization, the PAIPSO algorithm uses a first-in-first-out

centralized task queue to determine the order in which the particles are sent to

the slave processors.

Whenever a slave processor completes a function evaluation, it

returns the cost function value and the corresponding particle number to the

master processor, which places the particle number at the end of the task

queue. Since the order in which particles report their results, vary,

randomness in the particle order occurs.

Once a particle reaches the front of the task queue, the master

processor updates its position and velocity and sends it to the next available

slave processor. If the number of slave processors is the same as the number

of particles, the next available processor will then always be the same

processor that handled the particle initially. If the number of slave processors

is less than the number of particles, the next available processor will then be

the processor which happens to be free when the particle reaches the front of

the task queue. Even with heterogeneity in tasks and/or computational

resources, the task queue ensures that each particle performs approximately

the same number of function evaluations over the course of an optimization.

The proposed parallel synchronous and asynchronous algorithms

are experienced with multiprocessor task scheduling. Static and dynamic

(with and without load balancing) task scheduling problems.

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6.7 SIMULATION PROCEUDRE

The present section provides the details of the simulation carried

out for implementing the proposed parallel approaches PSIPSO and PAIPSO.

Benchmark datasets are taken from EricTailard’s site for dynamic

task scheduling. Two datasets are taken for simulation. Data set 1involves

50 tasks and 20 processors. Data set 2 involves 100 tasks with 20 processors.

The data for the static scheduling is randomly generated, i.e., 2 processors

with 20 tasks, 3 processors with 20 tasks, 3 processors with 40 tasks, 4

processors with 30 tasks, 4 processors with 50 tasks, 5 processors with 45

tasks and 5 processors with 60 tasks.

To demonstrate the effectiveness of the proposed parallel

approaches PSIPSO and PAIPSO, the proposed approaches are run with 30

independent trials with different values of random seeds and control parameters.

The optimal result is obtained for the following parameter settings.

Improved Particle Swarm Optimization:

1. The initial solution is generated randomly

2. C1g, C1b and C2 = 2,2 and 2

3. Population size = Twice the number of tasks (Salman et al

2002)

4. Wmin - Wmax = 0.5

5. Iteration = 500

The proposed hybrid approaches PSIPSO and PAIPSO are

developed using MATLAB R2009 and executed in a PC with Intel core i3

processor with 3 GB RAM and 2.13 GHz speed.

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6.8 STATIC SCHEDULING

In this method, the tasks are considered as independent of one

another. Hence, the tasks can be executed in any order. The objective function

is the same as specified in the Equations (2.4) to (2.9).

The proposed parallel algorithms PSIPSO and PAIPSO are applied

to static task scheduling and the results achieved are tabulated and shown in

Table 6.1.

6.8.1 Results and Discussion

The proposed parallel approaches PSIPSO and PAIPSO are tested

with the datasets specified in the simulation procedure for multiprocessor

static independent task scheduling problem. The obtained results have been

tabulated and is shown in Table 6.1.

Table 6.1 Total finishing time and average waiting time using theproposed PSIPSO and proposed PAIPSO

No ofprocessors

No of jobsProposedPSIPSO

ProposedPAIPSO

AWT TFT AWT TFT2 20 17.79 48.90 16.08 42.49

3 20 34.56 47.01 30.64 44.92

3 40 29.73 57.02 24.96 56.28

4 30 20.65 61.96 18.92 57.92

4 50 23.79 67.34 20.61 56.74

5 45 26.07 59.87 22.67 56.06

5 60 28.12 62.83 25.47 60.32

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The proposed parallel approach PSIPSO produces total finishing

time for the dataset 2 processors with 20 tasks, as 48.90s and average waiting

time as 17.79s. For the same dataset, the parallel approach PAIPSO produces

total finishing time as 42.49s and average waiting time as 16.08s, which is

better compared with the parallel approach PSIPSO. For the dataset 4

processors with 50 tasks, PSIPSO produces total finishing time as 67.34s and

average waiting time as 23.79s. For the same dataset, PAIPSO produces total

finishing time as 56.74s and average waiting time as 20.61s.

Thus, the results achieved using the parallel approaches for the

static task scheduling problem, PAIPSO yields better results than the parallel

approach PSIPSO. The behavioural and convergence characteristics of the

proposed parallel approach PAIPSO provides a better solution.

6.8.2 Performance Comparison

In order to validate the performance of the Parallel approaches

PSIPSO and PAIPSO, comparisons have made with the hybrid heuristic

approach IPSO-ACO for the same problem with same datasets are shown in

Table 6.2.

For the dataset 2 processors with 20 tasks, IPSO-ACO produces

average waiting time as 18.02s, total finishing time as 48.92s, the proposed

PSIPSO produces average waiting time as 17.79s and total finishing time as

48.90s as total finishing time. The proposed PAIPSO produces average

waiting time as 16.08s and total finishing time as 42.49s. For the dataset 5

processors with 45 tasks, IPSO-ACO produces 26.21s as average waiting

time, 60.87s as total finishing time, the proposed PSIPSO produces 26.07s as

the average waiting time and 59.87s as the total finishing time, and the

proposed PAIPSO produces 22.67s as average waiting time and 56.06s as

total finishing time. For the dataset 5 processors with 60 tasks, IPSO-ACO

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produces average waiting time as 28.42s, total finishing time as 64.26s, the

proposed PSIPSO produces 28.12s as the average waiting time and 62.83s as

the total finishing time. The proposed PAIPSO produces 25.47s as average

waiting time and 60.32 as the total finishing time.

Table 6.2 Comparison of job total finishing time and average waitingtime using proposed parallel approaches PSIPSO andPAIPSO with hybrid approach IPSO-ACO

No ofprocessors

No ofjobs

IPSO-ACO ProposedPSIPSO

ProposedPAIPSO

AWT TFT AWT TFT AWT TFT2 20 18.02 48.92 17.79 48.90 16.08 42.49

3 20 35.12 48.00 34.56 47.01 30.64 44.92

3 40 30.16 57.32 29.73 57.02 24.96 56.28

4 30 21.87 62.45 20.65 61.96 18.92 57.92

4 50 24.63 67.45 23.79 67.34 20.61 56.74

5 45 26.21 60.87 26.07 59.87 22.67 56.06

5 60 28.42 64.26 28.12 62.83 25.47 60.32

It is empirically proved that the proposed parallel algorithms,

PSIPSO and PAIPSO simultaneously reduces the total finishing time and

average waiting time in comparison with hybrid heuristic approach IPSO-

ACO. This has been achieved by the introduction of bad experience and good

experience component in the velocity updation equation and also parallel

computation.

Thus, based on the results, it can be observed that the proposed

parallel algorithm PAIPSO achieves better results than the hybrid heuristic

approach IPSO-ACO.

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The variations in total finishing time and waiting time using

different approaches IPSO-ACO, PSIPSO and PAIPSO are shown from

Figures 6.7 to 6.13

Figure 6.7 Total finishing time and average waiting time for 2 processorswith 20 jobs using IPSO-ACO, PSIPSO and PAIPSO


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Figure 6.11 Total finishing time and average waiting time for 4 processorswith 50 jobs IPSO-ACO, PSIPSO and PAIPSO


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It has been proven that the proposed parallel approach PAIPSO

determines reasonable quality solutions much faster than the other

approaches. The inclusion of the worst component along with the best

component and the parallel approach tends to simultaneously minimize the

average waiting time and the total finishing time.

At the outset, the results infer that the parallel Asynchronous

Enhanced Particle Swarm Optimization (PAIPSO) yields an improvement in

the performance when compared to the other hybrid PSO approaches.

6.9 DYNAMIC TASK SCHEDULING WITHOUT LOAD

BALANCING

The foremost goal of dynamic task scheduling problem is to reduce

the makespan. Hence, to minimize the total execution time the objective

function is the same as represented in the Equations (2.10) to (2.12).

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The proposed parallel approaches PSIPSO and PAIPSO are tested

for the dynamic tasks scheduling problem with datasets specified in the

simulation procedure. The results obtained are shown in Table 6.3.

Table 6.3 Best cost, worst cost, average cost and convergence time usingIPSO–ACO, PSIPSO and PAIPSO for dynamic taskscheduling without load balancing

Method IPSO -ACOProposedPSIPSO

ProposedPAIPSO

Number of tasks 50 100 50 100 50 100Best Cost 2131 4226 2126 4196 2126 4196

Worst Cost 2853 4793 2792 4751 2786 4703Average Cost 2492 4509.5 2459 4473.5 2456 4506.9

Convergence Timein seconds 5.9822 8.1236 3.4862 4.4642 1.8674 2.5691

Parallelization of the Improved Particle Swarm Optimization is

proposed to speed up the execution and to provide concurrence. The obtained

results, best, average and worst cost for dynamic task scheduling using the

parallel algorithms PSIPSO and PAIPSO have been compared with that of the

hybrid algorithm IPSO-ACO. The results show that the best cost achieved using

PAIPSO is 2126 for data set 1 and 4196 for data set 2 and is shown in Table 6.3.

When compared to the other methods, the average cost obtained is also better in

the case of the proposed algorithm. The convergence time is drastically reduced

for the proposed parallel algorithm PAIPSO compared with hybrid approach

IPSO-ACO, and is 1.86s for dataset1 and 2.56 s for dataset 2.

Thus it is inferred from the result that the Asynchronous version of

IPSO performs better than the Synchronous parallel version of IPSO. PAIPSO

is (4 to 6s) faster than the hybrid approach IPSO-ACO.

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Figures 6.14 and 6.15 depicts the best cost obtained using the

proposed parallel method PSIPSO and PAIPSO for data set 1 and data set2.

Figure 6.14 Best cost for 50 tasks and 20 processors using IPSO-ACO,PSIPSO and PAIPSO


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The Parallel approach PAIPSO is faster and performs better than

with all other algorithms proposed in the present research.

6.9.2 Performance comparison

The performance of the proposed parallel approach PAIPSO is

compared with the previously proposed (Visalakshi and Sivanandam 2009)

approaches PSPSO and PAPSO for the same datasets and for multiprocessor

dynamic task scheduling.

Table 6.4 Performance comparison of PAIPSO with parallel PSOapproaches

MethodPSPSO

(Visalakshi andSivanandam 2009)

PAPSO(Visalakshi and

Sivanandam 2009)

ProposedPAIPSO

Number of tasks 50 100 50 100 50 100

Best cost 2186 4496 2186 4496 2126 4196

Worst cost 2983 4968 2888 4712 2786 4703

Average cost 2594.5 4768.9 2477.6 4526.3 2456 4506.9

Convergence timein seconds

3.4256 4.4648 1.9619 2.7571 1.8674 2.5691

The PSPSO produces the best cost for dataset 1 as 2186, PAPSO

produces best cost as 4496 and the proposed PAIPSO produces 2126 as best

cost for dataset 1 and 4196 as the best cost for dataset 2. Comparing the

convergence time, the proposed PAIPSO is faster than the parallel approaches

PSPSO and PAPSO.

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This comparison reveals that the proposed parallel approach

PAIPSO achieves better results and also that there is a significant difference

in the convergence time, when tested for the multiprocessor task scheduling

problem.

6.10 DYNAMIC TASK SCHEDULING WITH LOAD BALANCING

In order to improve the processor performance and utilization, load

balancing of tasks have to be considered. Therefore the concept of load

balancing is dealt, in which the objective function is the same as represented

in the Equations (2.13) to (2.16).


Table 6.5 shows, the best cost, worst cost, average cost and

convergence time for the hybrid algorithms, IPSO-ACO, PSIPSO and

PAIPSO for dynamic task scheduling with load balancing.

Table 6.5 Best cost, worst cost, average cost and convergence time usingIPSO–ACO, PSIPSO and PAIPSO for dynamic taskscheduling with balancing

MethodIPSO -ACO

Proposed

PSIPSO

Proposed

PAIPSO

Number of tasks 50 100 50 100 50 100

Best Cost 13.0582 22.1531 13.0942 22.1644 13.0942 22.1644

Worst Cost 11.4922 20.9624 11.4983 20.9761 12.4386 21.9982

Average Cost 12.2752 21.5576 12.2964 21.5703 12.1528 22.0814

ConvergenceTime in seconds 7.5695 10.6314 4.8964 5.7687 2.1032 2.8712

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The best cost obtained for dataset 1 using the parallel hybrid

approach IPSO-ACO is 13.0582, using the proposed parallel approach

PSIPSO is 13.0942 and using the proposed parallel approach PAIPSO is

13.0942. For dataset 2, IPSO-ACO produces 22.1531 as the best cost, the

proposed PSIPSO produces 22.1644 as the best cost and the proposed

PAIPSO produces 22.1644 as the best cost. The convergence time for the

hybrid approach is 7.6s, 10.63s for dataset1 and dataset2. The proposed

parallel approaches PSIPSO and PAIPSO produces convergence time as

4.89s, 2.1s for dataset 1 and 5.76s, 2.87s for dataset 2 respectively. Thus, the

convergence time achieved reveals that the proposed parallel approach

PAIPSO produces better results faster than PSIPSO and the hybrid approach

IPSO-ACO.

The best cost achieved using the proposed parallel approaches

PSIPSO and PAIPSO are compared with the hybrid approach IPSO-ACO for

data set 1 and data set2 and are shown in Figures 6.16 and 6.17.


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The PAIPSO converges faster than the PSIPSO because the idle

time of the processors is considerably reduced.

6.10.2 Performance Comparison

The performance of the proposed parallel approaches PSIPSO and

PAIPSO are compared with the previously proposed ((Visalakshi and

Sivanandam 2009) parallel methods PSPSO and PAPSO for the same datasets

and for multiprocessor dynamic task scheduling.

The PSPSO produces the best cost for dataset 1 as 12.982, PSPSO

produces 12.982 and the proposed parallel approach PAIPSO produces

13.0942. For dataset 2, PSPSO produces best cost as 21.998, PAPSO

produces 21.998 and the proposed parallel approach PAIPSO produces

22.1644. The convergence time for the dataset 1 using PSPSO is 3.98s, using

PAPSO is 2.3s and using the proposed PAIPSO is 2.1s.

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Table 4.6 Performance comparisons of PAIPSO with Parallel PSOapproaches

MethodPSPSO

(Visalakshi andSivanandam 2009)

PAPSO(Visalakshi and

Sivanandam 2009)

ProposedPAIPSO

Number of tasks 50 100 50 100 50 100

Best cost 12.982 21.998 12.982 21.998 13.0942 22.1644

Worst cost 10.863 19.429 12.348 21.008 12.4386 21.9982

Average cost 11.789 21.032 12.215 21.816 12.1528 22.0814

Convergencetime in seconds 3.9831 5.1956 2.3041 3.1553 2.1032 2.8712

The proposed parallel approach PAIPSO converges very fast when

compared with the other parallel approaches PSPSO and PAPSO. Thus, the

result reveals that the proposed parallel approach PAIPSO outperforms the

other parallel approaches PSPSO and PAPSO, because of the inclusion of the

bad experience particles in the velocity equation of IPSO which plays a major

role along with parallelization concept, improves the results to near optimal

solution when applied to the task assignment problem with dynamic tasks.

6.11 CONCLUSION

The present chapter proposed parallel approaches PSIPSO and

PAIPSO to solve different types of task scheduling problems such as static

and dynamic task scheduling with and without load balancing. The proposed

parallel approaches locate the optimum solution iteratively from the initial

randomly generated search space. The performance of the proposed PAIPSO

is tested using random and bench mark data sets.

The proposed approach yields better results for both the static and

dynamic task scheduling problem. The proposed parallel approach PAIPSO

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reduces simultaneously both average waiting time and total finishing time

when applied to static independent task scheduling. For the dataset 5

processors with 45 tasks, IPSO-ACO produces total finishing time as 60.87s

and average waiting time as 26.21s, PSIPSO produces average waiting time

as 26.07s, total finishing time as 59.87s and the proposed PAIPSO produces

average waiting time as 22.67s and total finishing time as 56.06s. Based on

the results obtained, it is observed that the proposed parallel approach

PAIPSO provides better results.

The proposed parallel approach PAIPSO is applied to dynamic task

scheduling without load balancing. The results achieved by the proposed

parallel approach PAIPSO is compared with parallel approaches proposed

earlier namely PSPSO and PAPSO. For dataset1, the best cost achieved by

PSPSO is 2186, PAPSO achieves best cost as 2186 and the proposed parallel

approach PAIPSO achieves the best cost as 2126 which is better than

approaches compared. The proposed parallel approach PAIPSO is 5.5s faster

than the hybrid heuristic approach IPSO-ACO for dataset 2 and 4.11s faster

than the result produced by the hybrid approach IPSO-ACO for dataset 1.The

proposed parallel approach have been compared with the other previously

proposed parallel approaches namely PSPSO and PAPSO and the comparison

results concludes that the proposed parallel approach is 0.18s faster than

PAPSO and 1.89s faster than PSPSO for dataset2.

The proposed parallel approaches PSIPSO and PAIPSO are applied

to dynamic task scheduling with load balancing. The results achieved by the

proposed approaches are compared with parallel approaches proposed earlier

namely PSPSO and PAPSO. For dataset 2, the best cost achieved by PSPSO

is 21.998, the best cost achieved by PAPSO is 21.998 and the best cost

achieved by the proposed parallel approach PAIPSO is 22.1644. The

proposed parallel approach PAIPSO converges 1.8799s faster than PSPSO,

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0.2s faster than PAPSO for dataset 1. For dataset 2, PAIPSO is 2.3244 times

faster than PSPSO, 0.2841s faster than PAPSO. The proposed parallel

approach yields better results for both static and dynamic task scheduling

problem.

From the results of simulation, it is observed that the proposed

parallel approach PAIPSO rapidly increases the performance of the solution

and prevents trapping to a local optimal value. Further, the proposed PAIPSO

enhances the probability to find the global best solution, thereby allowing

faster convergence for all the data sets. Thus, the proposed parallel approach

PAIPSO produced significant result than GA, standard PSO and hybrid

approaches (IPSO-SA, IPSO-AIS and IPSO-ACO).

chapter 6 proposed parallel improved particle...

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