1 A hybrid particle swarm optimization algorithm for optimal task assignment in distributed system Peng-Yeng Yin and Pei-Pei Wang Department of Information.

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A hybrid particle swarm optimization algorithm for optimal task assignment in distributed system

Peng-Yeng Yin and Pei-Pei WangDepartment of Information Management

National Chi Nan University

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Task assignment problem

The objective of task assignment is to find an optimal assignment of the task such that the total cost is minimized while at the same time, all the resource constraints are satisfied.

Task-interaction graph Processor-interaction graph

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Problem formulation

Integer quadratic programming

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Problem formulation

Integer linear programming

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Existing Methods for solving TAP Mathematical Programming

Integer linear programming, branch and bound Providing exact solutions but could be extremely

time-consuming for solving large scaled problems. Meta-heuristics:

Genetic algorithms. Simulated annealing. Proving approximate solution with reasonable time.

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Particle Swarm Optimization (PSO) Proposed by Kennedy and Eberhart in 1995

Metaphor: social dynamics of bird flocking. Positive feedback: each bird (particle) benefits from the

discoveries and experiences of its own and that of the other members of the entire swarm during food foraging.

Stochastic: each bird flies in the direction guided by the collective experiences (swarm intelligence) with additive randomness, facilitating a balance between exploitation and exploration searches and the ability to escape from local optima.

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Continuous PSO Algorithm each particle particlei is randomly positioned in the solution space and is

a candidate solution to the optimization problem each particle particlei remembers the best position it visited so far, referr

ed to as pbesti, and the best position by the entire swarm, referred to as gbest

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Proposed Hybrid PSO (HPSO) for solving TAP Particle representation：

Fitness evaluation：

r

ikiki

r

ikiki PxpMxmXPenalty

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,0max,0max

1 XPenaltyXQXFitness

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Our HPSO for solving TAP

Particle updating：

HPSO： Embedding a hill-climbing approach.

1,…,|V2|

the ith particle:

….

1,…,|V2|

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Experimental Results Optimal parameterization (HPSO)

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Experimental Results Optimal parameterization (GA)

Coding scheme Fitness function Number of fitness evaluations

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Experimental Result Exact solution using Lingo 8.0

Max. execution duration = 90 hours

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Experimental Result Approximate solutions using GA and HPSO

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Convergence analysis Gbest analysis

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Convergence analysis Pbest analysis using entropy

Kispbestsprob ijj ,...,2,1Pr

n

sjjj sprobsprobentropy

12log

r

sj rentropyentropy

1

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Worst-case analysis Provide a guarantee of solution quality

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Conclusion

The results showed that the proposed method is more effective and efficient then GA.

Also, our method converges at a faster rate and is suited to large-scaled task assignment problems.