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

2 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 graphProcessor-interaction graph

3 Problem formulation Integer quadratic programming

4 Problem formulation Integer linear programming

5 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.

6 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.

7 Continuous PSO Algorithm  each particle particle i is randomly positioned in the solution space and is a candidate solution to the optimization problem  each particle particle i remembers the best position it visited so far, referred to as pbest i, and the best position by the entire swarm, referred to as gbest

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

9 Our HPSO for solving TAP Particle updating ： HPSO ： Embedding a hill-climbing approach. 1,…,|V 2 | the ith particle: …. 1,…,|V 2 |

10 Experimental Results Optimal parameterization (HPSO)

11 Experimental Results Optimal parameterization (GA) Coding scheme Fitness function Number of fitness evaluations

12 Experimental Result Exact solution using Lingo 8.0 Max. execution duration = 90 hours

13 Experimental Result Approximate solutions using GA and HPSO

14 Convergence analysis Gbest analysis

15 Convergence analysis Pbest analysis using entropy

16 Worst-case analysis Provide a guarantee of solution quality

17 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.