5. Conclusions

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 certain exploitation capability to avoid getting trapped in local optimums.

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. Dev = 10.99% can be obtained.

By using the SGP to control the search behavior, either exploitation or exploration would make the algorithm simplified and also reduce the execution time.

Meanwhile, high diversity in the early stage and low diversity in the later stage are preferred for searching in the solution space provided as indicated in Figure 9. Therefore, the proposed SGPSO with lower SGP is suggested for solving workflow class scheduling problem in the grid.

Unlike in [15], using heuristics to find initial solutions is not adopted in this work. Therefore, there is no need to consider which heuristic should be designed to increase performance, and hence the algorithm is thus easier to implement. In [15], the best result comes with the constriction factor χ = 0.5 which was obtained after thorough testing. However, the best result can be yielded with the commonly suggested value χ = 0.72984. Hence, the laborious work of finding the best constriction factor value is eliminated.

The experimental results show that the proposed method can effectively solve grid task scheduling problems and boost grid performance. In reality, there are many problems similar to grid task scheduling problems, such as the multimode resource-constrained project scheduling problems (MRCPSPs). In the future, the method proposed in this study will be applied to find solutions to MRCPSP-type problems.
