Acknowledgements

Figure 10 shows that the minimal fitness (44.5) can be obtained when SGP = 0.1 and SGP = 0.8. However, the minimum average fitness (45.88) is obtained when SGP = 0.1. The results coincide with the above experiment consequences. The comparison between this work and [15] is

According to Table 6, with a small SGP value, the task scheduling outcomes of J15 will become better as the number of iterations increases (100 iterations ! 300 iterations). This is because small SGP values tend to lead to the use of individual experience. In other words, the particles perform exploration search in solution space. In consequence, to obtain the optimums in the

Chen [15] Chen [15] This work

χ = 0.75 χ = 0.5 χ = 0.72984, SGP = 0.1

Workflow application is the most common application in the grid. However, the workflow scheduling heavily affects the performance of workflow execution application. Two PSOs were used to solve task-resource matching and task execution priority subproblems of the workflow scheduling. A new and simplified velocity update rule extended from the ACO state transition rule is designed in constriction PSO for solving the task execution priority subproblem. Restated, the search control is based on a suggested SGP inspired by the ACO's transition rule. This constriction PSO-based algorithm is named stochastic greedy PSO (SGPSO), which provides both exploration and exploitation abilities during search. The main purpose is to strengthen the exploration capacity of the PSO in the solution search process while providing

Avg. 60.15 54.26 47.71

Avg. 55.45 50.36 45.88

According to experimental results as indicated in Table 3, high SGP provides global experience guidance and causes premature convergence, hence easy to trap on local optimal such as only exploitation applied in SGP = 1.0 and Avg.Dev = 12.05% yielded. When SGP = 0, the algorithm would conduct self-search such that only exploration is enabled that causes slow convergence and Avg.Dev = 12.43% obtained. Better solutions can be found while providing enough exploration and certain exploitation capabilities such as SGP = 0.1; the lowest Avg.

certain exploitation capability to avoid getting trapped in local optimums.

vast solution space will consume much time, and the convergence is delayed.

100 iter. Min. 45.50 44.50 46.75

300 iter. Min. 44.50 44.50 44.50

listed in Table 6.

56 Particle Swarm Optimization with Applications

5. Conclusions

Table 6. Performance comparison on J15 in [15].

Dev = 10.99% can be obtained.

This work was partly funded and supported by the Ministry of Science and Technology, Taiwan, under contract MOST 104-2221-E-167-011.
