chapter 4 proposed hybrid intelligent approch for multiprocessor...

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CHAPTER 4

PROPOSED HYBRID INTELLIGENT APPROCH FOR

MULTIPROCESSOR SCHEDULING

The present chapter proposes a hybrid intelligent approach

(IPSO-AIS) using Improved Particle Swarm Optimization (IPSO) with

Artificial Immune System (AIS) for multiprocessor task scheduling problem

with two cases, namely, static task scheduling and dynamic task scheduling

with and without load balancing.

4.1 INTRODUCTION

The drawback in the hybrid approach IPSO-SA is that it slightly

slower in convergence due to the slow speed of SA. To conquer the drawback

of the hybrid algorithm IPSO-SA’s slow convergence, the search is guided

towards untried regions in the solution space and also to improve further, an

immune based intelligent approach is thought of. An Immune system is a

naturally occurring event response system that can quickly adapt to the

changing situations. In AIS, the models of vaccination and receptor editing

are designed to improve the immune performance.

The combined effect of IPSO with AIS directs to a promising

result. The basic idea of combining IPSO with AIS is to combine the good

features of both the algorithms.

In the present chapter, a new hybrid intelligent algorithm is

developed using IPSO with AIS to achieve better solutions.

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4.2 REVIEW OF LITERATURE

Luh and Liu (2004) developed a Reactive Immune Network (RIN)

for mobile robot learning navigation strategies within unknown environments.

In their approach, a modified virtual target method is integrated to solve the

local minima problem.

Wojtyla et al (2006) proposed an efficient method of extracting

knowledge when scheduling parallel programs onto processors using AIS.

The author’s proposed approach reorders the nodes of the program according

to the optimal execution order on one processor, which works in either

learning or production mode. In the learning mode an immune system to

optimize the allocation of the tasks to individual processors was used. In the

production mode the optimization module is not invoked, only the stored

allocations are used. The proposed approach gives similar results to the

optimization by a Genetic Algorithm (GA) but requires only a fraction of

function evaluations.

Fu et al (2007) proposed a hybrid artificial immune network which

uses the swarm learning of Particle Swarm Optimization to speed up the

convergence of the artificial immune system.

Yu (2008) developed an algorithm based on AIS to schedule for

heterogeneous computing environments. Empirical studies on bench mark

task graphs show that this algorithm significantly outperforms a deterministic

algorithm.

Lin and Ying (2012) developed an algorithm based on revised AIS

and Simulated Annealing effect (RAIS) to minimize the makespan of

blocking flow shop. The proposed algorithm is evaluated and compared with

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well-known bench mark problems of taillard used. The results show that the

proposed algorithm outperforms the state-of-art algorithms on the same bench

mark problems.

Engin et al (2004) used a computational method based on the

principle of clonal selection and affinity maturation mechanism of the

immune response. The objective is to minimize the makespan of the

scheduling problem. The operating parameters of meta-heuristics play an

important role. He presents a genetric systematic procedure which is based on

a multi-step experimental design approach for determining the optimum

system parameters of AIS and tested with benchmark problems. Results infer

that an AIS based algorithm is effective to solve hybrid flow shop problems.

Lin et al (2011) presented a Hybrid Taguchi-Immune Algorithm

(HTIA) to deal with the unit commitment problem, which integrates Taguchi

method and traditional immune algorithm and provides a powerful global

exploration capability. The proposed algorithm shows better performance

compared with the other methods published before. The test results reveal that

the proposed method is feasible and robust and more effective.

Bagheri et al (2010) proposed an artificial based on integrated

approach to solve the flexible job shop scheduling to minimize makespan.

The algorithm uses several strategies for selecting the individuals for

reproduction and also different mutation operators used for reproducing new

individuals. The proposed approach is validated with benchmark problems,

and computational results show the quality.

Zandieh et al (2006) used an immune algorithm to tackle complex

problems of a Sequence Dependent Setup Times (SDST) and produce a

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reasonable manufacturing schedule within an acceptable time. Results were

compared with the Random Key Genetic Algorithm (RKGA) presented

previously. From the results, it is known that IA outperformed RKGA.

King et al (2001) described an intelligent agent for task allocation

in a heterogeneous computing environment. It exploits some of the

functionalities in designing agent-based parallel control systems.

Sun and Yang (2008) presents a new hybrid optimization algorithm

which combines the strong global search ability of Artificial Immune System

(AIS) with a strong local search ability of External Optimization (EO)

algorithm. The algorithm tested with benchmark problems with makespan

criterion, and results show that the proposed method is effective.

Ebrahimi Moghaddam et al (2012) an Immune based Genetic

Algorithm (IGA) is proposed which reduces the search space of

Multiprocessor Task Scheduling Problem(MTSP), and effectively influences

the convergence speed of the optimization process and guarantees the validity

of the solutions by using crossover and mutation operators. Experimental

results showed that the proposed algorithm uses less number of iterations to

find the solution, when applied to the benchmark problems.

Kahraman et al (2009) proposed a new artificial immune system

algorithm to solve multi objective fuzzy flow shop scheduling problem, in

which fuzzy sets are used to model processing times and due dates. The

objective of the algorithm is to minimize the average tardiness and number of

tardy jobs. The effectiveness are tested by comparing it with genetic

algorithms. The outcome tells that the proposed algorithm is more effective.

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Zelenka (2011) compared two approaches for Job Shop Scheduling

Problem (JSSP) in real manufacturing system. The first approach is based on

the mechanisms inspired by biological evolution and the immune system. The

second stochastic optimization algorithm is based on social simulation

models.

4.3 HYBRID INTELLIGENT ALGORITHM

The main objective of the hybridization is to integrate different

learning and adaptation techniques to overcome individual limitations and to

achieve synergetic effects through the combination of these techniques.

Biological immune systems can be viewed as a powerful

distributed information processing systems, capable of learning and self-

adaptation. AIS is rapidly emerging, which is inspired by theoretical

immunology and observed immune functions, principles and models.

The efficient mechanisms of immune system, including clonal

selection, learning ability, memory, robustness and flexibility make AISs

useful in many applications. AIS appear to offer powerful and robust

information processing capabilities for solving complex problems. Hence, a

hybrid intelligent algorithm IPSO-AIS is developed to improve the

performance of the multiprocessor scheduling problem.

4.3.1 Basic AIS-Based Scheduling Algorithm

The brief outline of the proposed algorithm based on AIS can be

described as follows (Ge et al 2008).

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Step 1 : Initialize pop_size antibodies as an initial population, where

pop_size denotes the population size.

Step 2 : Select m antibodies from the population by the proportional

selection model and clone them to a clonal library.

Step 3 : Perform the mutation operation for each of the antibodies in the

clonal library.

Step 4 : Randomly select‘s’antibodies from the clonal library to perform

the operation of vaccination.

Step 5 : Replace the worst‘s’antibodies in the population by the

best‘s’antibodies from the clonal library.

Step 6 : Perform the operation of receptor editing if there is no

improvement of the highest affinity degree for a certain number

of generations.

Step 7 : Stop if the termination condition is satis ed; else, repeat Steps 2

to 7.

4.4 PROPOSED HYBRID INTELLIGENT ALGORITHM

(IPSO-AIS)

The steps involved in the proposed hybrid algorithm (Improved

PSO with Artificial Immune System is as follows,

Step 1 : Initialize Population size of the antibodies as PSA.

Step 2 : Initialize the number of particles N and its value may be generated

randomly. Initialize swarm with random positions and velocities.

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Step 3 : Compute the finishing time for each and every particle using the

objective function and also find the “pbest “. If current fitness of

particle is better than “ pbest” the set “ pbest” to current value. If

“pbest” is better than “gbest then set “gbest” to current particle

fitness value.

Step 4 : Select particles individual “pworst” value, that means particle

moving away from the solution point.

Step 5 : Update the velocity and position of particle as per Equation (2.1)

and (2.2).

Step 6 : If best particle is not changed over a period of time,

a) Select ‘m’ antibodies out of the population PSA by the

proportional selection model and clone them to a colonal

library.

Step 7 : Perform the mutation operation for each of the antibodies in the

clonal library.

Step 8 : Randomly select ’s’ antibodies from the clonal library to perform

the operation of vaccination.

Step 9 : Replace the worst’s’ antibodies in the population by the best‘s’

antibodies from the clonal Library

Step 10 : Terminate the process if maximum number of iterations reached

or optimal value is obtained, else go to step 3.

The flow chart for the hybrid algorithm is shown in Figure 4.1

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Start

Initialize population size of Antibodies

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

D

Compute the objective function

Invoke Hybrid algorithm

If E < best ‘E’ (Pbest) so far

For each generation

For each particle

Search is terminatedoptimal solution

reached

B

Current value = new p best

Choose the minimum F of all particles as the g best

Calculate particle velocity using Equation (2.1)

A

No

Yes

Figure 4.1 Flowchart for the proposed hybrid intelligent approachIPSO-AIS

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Calculate particle position using (2.2)

Update memory of each particle

If the best particle is notchanged over a period of time

Select ‘m’ antibodies from the population and clonethem to clonal library

Perform mutation operation to the antibodies

No

Perform vaccination operation on randomly selected‘s’ antibodies

C

B

Yes

A

Replace the worst antibodies by best antibodies

Figure 4.1 (Continued)

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Perform receptor editing operation

If improvement inhighest affinity degree

Yes

No

Yes

No

End

End

If stopping conditionreached

Stop

B

D

C

Figure 4.1 (Continued)

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4.5 SIMULATION PROCEUDRE

The details of the simulation carried out for implementing theproposed hybrid algorithm is given in the present section.

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, such as 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 hybrid algorithm,

the proposed approach is run with 30 independent trials with different values

of random seeds and control parameters. The optimal result is obtained for

following the parameter settings

Artificial Immune System

Number of generations : 200

Mutation rate : 0.1

Sampling rate : 0.1

Antibodies : Twice the number of tasks

Improved Particle Swarm Optimization

The initial solution is generated randomly

C1g, C1b and C2 : 2,2 and 2

Population size : Twice the number of tasks

(Salman et al 2002)

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Wmin - Wmax : 0.5

Max. Iteration : 500

The proposed hybrid approach IPSO-ACO is developed using

MATLAB R2009 and executed in a PC with Intel core i3 processor with

3 GB RAM and 2.13 GHz speed.

4.6 STATIC SCHEDULING

The tasks considered are independent. Hence, the tasks can be

executed in any order in any processor. The objective function is the same as

specified in the Equations (2.4) to (2.9). The application of intelligent hybrid

algorithm (IPSO-AIS) for scheduling multiprocessor tasks is shown in the

present chapter.

4.6.1 Results and Discussion

The proposed hybrid approach IPSO-AIS is tested for static task

scheduling problem with the datasets specified in the simulation procedure

and the results achieved are shown in Table 4.1.

Table 4.1 Total finishing time and average waiting time using theproposed hybrid intelligent approach IPSO-AIS

No of Processors No of jobsProposed IPSO-AIS

AWT TFT2 20 22.16 52.643 20 38.65 48.373 40 34.26 61.204 30 23.92 65.474 50 25.96 67.835 45 27.56 64.965 60 30.19 69.01

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The proposed hybrid approach IPSO-AIS is tested with various

randomly generated datasets. For the dataset 3 processors with 40 tasks,

IPSO-AIS produces total finishing time 61.20s and average waiting time

34.26s, for dataset 4 processors with 50 tasks 67.83s as total finishing time

and 25.96s as average waiting time and for dataset 5 processors with 60 tasks

30.19 s as average waiting time and 69.01s as total finishing time.

4.6.2 Performance Comparison

In order to validate the performance of the proposed hybrid

intelligent approach IPSO-AIS, comparisons have been made with the

approaches IPSO, IPSO-SA with the same datasets, and are reported in

Table 4.2. These results reveal that the proposed hybrid approach IPSO-AIS

is comparatively better than the other approaches.

Table 4.2 Comparison of job finishing time and average waiting timeusing IPSO, IPSO-SA and the proposed IPSO-AIS

No ofProcessors

No ofjobs

IPSO IPSO-SAProposedIPSO-AIS

AWT TFT AWT TFT AWT TFT2 20 29.12 57.34 25.61 54.23 22.16 52.643 20 45.00 54.01 40.91 50.62 38.65 48.373 40 41.03 69.04 38.45 65.40 34.26 61.204 30 29.74 70.97 26.51 66.29 23.92 65.474 50 30.06 70.62 28.34 68.01 25.96 67.835 45 33.65 68.04 30.12 66.43 27.56 64.965 60 36.56 72.31 32.76 69.13 30.19 69.01

For the dataset 3 processors with 40 tasks, IPSO produces average

waiting time 41.03s, hybrid approach IPSO-SA produces as 38.45s and the

proposed hybrid intelligent approach IPSO-AIS produces as 34.26s. For the

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same dataset, total finishing time produced by IPSO is 69.04s, by hybrid

approach IPSO-SA is 65.40s and by the proposed intelligent approach is

61.20s. For the dataset 5 processors with 60 tasks, IPSO produces average

waiting time as 36.56s and total finishing time as 72.31s, IPSO-SA produces

average waiting time as 32.76s and total finishing time as 69.13s and the

proposed hybrid intelligent algorithm IPSO-AIS produces 30.19s as average

waiting time and total finishing time as 69.01s. It is empirically proved that

the proposed hybrid approach IPSO-AIS simultaneously reduces both Total

finishing time and average waiting time.

Thus, based on the results, it is inferred that the proposed hybrid

intelligent algorithm IPSO-AIS produces better results than the conventional

methodologies LPT, SPT, GA, standard PSO, and hybrid approach IPSO-SA.

The variations found in the total finishing time and average waiting

time using different approaches namely, using IPSO, IPSO-SA and IPSO-AIS

are shown from Figures 4.2 to 4.8.

Figure 4.2 Total Finishing Time and Average waiting time for 2processors with 20 jobs using IPSO, IPSO-SA and IPSO-AIS

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Figure 4.7 Total finishing time and average waiting time for 5processors with 45 jobs using IPSO, IPSO-SA and IPSO-AIS

Figure 4.8 Total finishing time and average waiting time for 5processors with 60 jobs using IPSO, IPSO-SA and IPSO-AIS

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Thus, the results reveal that the proposed IPSO-AIS produce an

improvement in the performance, when compared to the standard PSO and

hybrid approach IPSO-SA.

4.7 DYNAMIC TASK SCHEDULING WITHOUT LOAD

BALANCING

In the dynamic task scheduling problem, reducing the total

completion time of processors is a major issue. Hence, to minimize the

makespan of the entire schedule, the objective function is represented in

Equations (2.10) to (2.12).


The obtained results have been tabulated and shown in Table 4.3,

which represents the cost and convergence time comparison of IPSO, IPSO-

SA and Intelligent Hybrid Algorithm. The results reveal that the IPSO-AIS

performs better than the other algorithms.

Table 4.3 Best cost, worst cost, average cost and convergence timeusing IPSO, IPSO-SA and the proposed hybrid intelligentapproach IPSO-AIS for dynamic task scheduling withoutload balancing

Method IPSO IPSO-SAProposedIPSO-AIS

Number of tasks 50 100 50 100 50 100

Best Cost 2374 4527 2156 4376 2136 4309

Worst Cost 3136 5213 2901 4908 2886 4856

Average Cost 2755 4870 2528.5 4624 2511 4582.5

Convergence Time 4.0521 5.7112 4.2156 5.8428 4.9124 7.4682

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Comparisons have been made based on the algorithms with IPSO,

IPSO-SA and the proposed hybrid intelligent approach IPSO-AIS on the best,

average and worst cost achieved for dynamic task scheduling. For dataset 1,

IPSO achieves the best cost as 2374, IPSO-SA achieves the best cost as 2156

and the proposed hybrid intelligent approach IPSO-AIS achieves the best cost

as 2136. For dataset 2, IPSO produces best cost 4527, IPSO-SA produces the

best cost as 4376 and the proposed hybrid intelligent approach IPSO-AIS

produces the best cost as 4309. The proposed hybrid approach IPSO-AIS

produces better results compared with other algorithms, but the convergence

time for the proposed hybrid algorithm IPSO-AIS is higher (app 1.16 times)

than IPSO-SA, because of the extra calculation involved in the immunization.

The best cost obtained using the proposed hybrid intelligent

approach IPSO-AIS for dataset 1 and dataset2 are shown in Figures 4.9 and

4.10.

Figure 4.9 Best costs for 50 tasks and 20 processors using IPSO,IPSO-SA and IPSO-AIS

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Figure 4.10 Best costs for 100 tasks 20 processors using IPSO, IPSO-SAand IPSO-AIS

The proposed hybrid intelligent approach IPSO-AIS performs

better than with the IPSO and the hybrid algorithm IPSO-SA.


The performance of the proposed hybrid approach IPSO-AIS is

compared with the previously proposed ((Visalakshi and Sivanandam 2009)

hybrid PSO algorithms PSO-HC and PSO-SA for the same datasets.

Table 4.4 Performance comparison of various PSO based hybridapproaches

MethodPSO-HC

(Visalakshi andSivanandam 2009)

PSO-SA(Visalakshi and

Sivanandam 2009)

ProposedIPSO-AIS

Number oftasks 50 100 50 100 50 100

Best cost 2322 4621 2186 4496 2136 4309Worst cost 2994 5449 2916 4948 2886 4856

Average cost 2658 5035 2551 4722 2511 4582.5Convergence

time in seconds 4.9636 7.3588 6.4311 8.7349 4.9124 7.4682

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For the dataset 1, PSO-HC produces the best cost as 2322, PSO-SA

produces the best cost as 2186 and the proposed hybrid approach IPSO-AIS

produces the best cost as 2136. For dataset 2, PSO-HC produces the best cost

as 4621, PSO-SA produces the best cost as 4496 and the proposed hybrid

approach IPSO-AIS produces the best cost as 4309. The proposed hybrid

intelligent approach IPSO-AIS performs better when compared with the other

previously proposed hybrid methods of PSO-HC and PSO-SA.

Thus, the result concludes that the proposed hybrid intelligent

approach IPSO-AIS performs better than the other hybrid approaches PSO-

HC and PSO-SA.

4.8 DYNAMIC TASK SCHEDULING WITH LOAD BALANCING

In order to improve the performance and utilization of

multiprocessor system, 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 4.5 illustrates the best cost, worst cost, average cost and

convergence time for, IPSO, hybrid algorithm IPSO-SA and the proposed

hybrid intelligent algorithm IPSO-AIS.

For dataset 1, the best cost achieved using IPSO is 12.0042, IPSO-

SA produces the best cost as 12.9961and the proposed hybrid intelligent

algorithm IPSO-AIS produces the best cost as 13.0014. For dataset 2, the best

cost produced by IPSO is 21.4291, IPSO-SA produces the best cost as

22.0223 and the proposed hybrid intelligent approach IPSO-AIS produces the

best cost as 22.132. The average cost is also improved in the proposed hybrid

intelligent algorithm IPSO-AIS. The convergence time for the proposed

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IPSO-AIS method is 6.2154s for dataset 1 and 8.3992s for dataset 2, which is

higher than the hybrid algorithm IPSO-SA.

Table 4.5 Best cost, worst cost, average cost and convergence time usingIPSO, IPSO-SA and the proposed hybrid intelligent approachIPSO-AIS for dynamic task scheduling with load balancing

Method IPSO IPSO-SAProposedIPSO-AIS

Number of tasks 50 100 50 100 50 100

Best Cost 12.0042 21.4291 12.9961 22.0223 13.0014 22.132

Worst Cost 10.9820 19.2103 11.4832 20.9313 11.4881 20.9474

Average Cost 11.4931 20.3197 12.2396 21.4768 12.2448 21.5397

Convergence Timein seconds 5.1176 6.9064 5.1284 6.9205 6.2154 8.3992

The best cost obtained using the intelligent hybrid algorithm

IPSO-AIS for data set 1 and data set2 are shown in Figures 4.11 and 4.12.


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Thus, the results conclude that the proposed hybrid intelligent

approach IPSO-AIS performs well when compared to the standard PSO, IPSO

and IPSO-SA for the dynamic task scheduling problem with load balancing

concept. However, the time taken for convergence is slightly (app 1.2 times)

higher than IPSO-SA.


The performance of the proposed IPSO is compared with the

previously proposed (Visalakshi and Sivanandam 2009) hybrid PSO

algorithms PSO-HC and PSO-SA for the same datasets.

For the dataset 1, PSO-HC produces the best cost as 12.008, PSO-

SA produces the best cost as 12.982 and the proposed hybrid approach IPSO-

AIS produces best cost as 13.0014. For dataset 2, PSO-HC produces best cost

as 21.114, PSO-SA produces 21.998 as the best cost and the proposed hybrid

approach IPSO-AIS produces 22.132 as the best cost. The proposed hybrid

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intelligent approach IPSO-AIS perform well when compared with the other

previously (Visalakshi and Sivanandam 2009) proposed hybrid methods PSO-

HC and PSO-SA.

Table 4.6 Performance comparison of various PSO based hybridapproaches

MethodPSO-HC

(Visalakshi andSivanandam 2009)

PSO-SA(Visalakshi and

Sivanandam 2009)

ProposedIPSO-AIS

Number of tasks 50 100 50 100 50 100

Best cost 12.008 21.114 12.982 21.998 13.0014 22.132

Worst cost 9.885 19.392 11.476 20.926 11.4881 20.9474

Average cost 10.9465 20.253 12.229 21.462 12.2448 21.5397

Convergencetime in seconds 6.2172 8.4994 7.6559 10.6415 6.2154 8.3992

Thus, the comparison reveals that the proposed hybrid approach

IPSO-AIS achieves better results than the other approaches.

4.9 CONCLUSION

The chapter four has thus dealt with the application of IPSO-AIS to

solve different types of multiprocessor task scheduling with two cases,

namely, static independent task scheduling and dynamic scheduling with and

without load balancing.

The proposed hybrid intelligent approach IPSO-AIS is tested with a

static task scheduling problem to reduce both the total finishing time and

average waiting time. For the dataset 5 processors with 60 tasks, IPSO

produces an average waiting time of 36.56s and the total finishing time of

72.31s, IPSO-SA produces average waiting time of 32.76s and the total

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finishing time of 69.13s. The proposed hybrid intelligent algorithm IPSO-AIS

produces 30.19s as average waiting time and the total finishing time as 69.01s

for the same dataset. Thus, IPSO-AIS reduce simultaneously both the total

finishing time and average waiting time.

The proposed hybrid intelligent approach IPSO-AIS is applied to

dynamic task scheduling without load balancing problem. For dataset 2, IPSO

produces the best cost as 4527, IPSO-SA produces the best cost as 4376 and

the proposed hybrid intelligent approach IPSO-AIS produces 4309.

The proposed hybrid intelligent approach IPSO-AIS is applied to

dynamic task scheduling with load balancing problem. For dataset 2, the best

cost produced by IPSO is 21.4291, IPSO-SA produces the best cost as

22.0223 and the proposed hybrid approach IPSO-AIS produces the best cost

as 22.132.

The proposed hybrid intelligent approach IPSO-AIS is compared

with the other hybrid approaches which were earlier proposed, namely,

PSO-HC and PSO-SA. The results infer that the proposed hybrid intelligent

approach IPSO-AIS improves the performance of the scheduling.

The proposed hybrid intelligent approach reduces the makespan for

both static and dynamic task scheduling problems, but there is slight increase

in the convergence time (app 1.15 times) when compared with IPSO-SA for

dynamic task scheduling. Hence, other hybrid technologies need to be tried so

that the convergence time is better than the methodologies tried out. Hence,

new hybrid algorithms are proposed in the subsequent chapters to further

refine the cost and the convergence time achieved, which is the main

objective of task scheduling. The next chapter deals with the hybrid

algorithm, Improved Particle Swarm Optimization with Ant Colony

Optimization.

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