**7. Conclusion**

In this book chapter we presented the modified Genetic Algorithm and its combination with the w-Tabu algorithm to form a new algorithm called w-TG to solve the problem of optimizing runtime of the Grid-based workflows within the SLA context. In our work, the distinguishing characteristic is that each sub-job of a workflow can be either a sequential or parallel program. In addition, each grid service can handle many sub-jobs at a time and its resources are reserved. The w-Tabu algorithm creates a set of referent solutions, which distribute widely over the search space, and then searches around those points to find the local minimal solution. We proposed a special genetic algorithm to map workflow to the Grid resources called w-GA. In the w-GA algorithm, we applied many dedicated techniques for workflow within the crossover and mutation operations in order to improve the searching quality. The experiment showed that both the w-GA and the w-Tabu found solutions with great differing quality in some cases. When the size of the workflow is very big and the runtime of the w-GA and the w-Tabu to find out solution also reaches the limit, the quality of the w-GA is not as good as the w-Tabu algorithm. The combined algorithm can fix the disadvantage of the individual algorithms. Our performance evaluation showed that the combined algorithm created solution of equal or better quality than the previous algorithm

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**On the Effect of Applying the Task Clustering**

Actual task execution models over the networked processors, e.g., cluster, grid and utility computing have been studied and developed for maximizing the system throughput by utilizing computational resources. One of major trends in task execution types is to divide the required data into several pieces and then distribute them to workers like "master-worker model". In contrast to such a data intensive job, how to divide a computational intensive job into several execution units for parallel execution is under discussion from theoretical points of view. If we take task parallelization into account in a grid environment such as a computational grid environment, an effective task scheduling strategy should be established. In the light of combining task scheduling concepts and grid computing methodologies, heterogeneity with respect to processing power, communication bandwidth and so on should be incorporated into a task scheduling strategy. If we assume the situation where multiple jobs are being submitted in the unknown number of computational resources over the Internet, objective functions can be considered as follows: (i) Minimization of the schedule length (the time duration from per each job, (ii) Minimization of the completion time of the last job, (iii) Maxmization of the degree of contribution to the total speed up ratio for each computational resources. As one solution for those three objective functions, in the literature(Kanemitsu, 2010) we proposed a method for minimizing the schedule length per one job with a small number of computational resources (processors) for a set of identical processors. The objective of the method is "utilization of computational resources". The method is based on "task clustering" (A. Gerasoulis, 1992), in which tasks are merged into one "cluster" as an execution unit for one processor. As a result, several clusters are generated and then each of which becomes one assignment unit. The method proposes to impose the lower bound for every cluster size to limit the number of processors. Then the literature theoretically showed the

However, which processor should be assigned to a cluster is not discussed because the proposal assumes identical processors. If we use one of conventional cluster assignment

near-optimal lower bound to minimize the schedule length.

**1. Introduction**

**for Identical Processor Utilization to**

Hidehiro Kanemitsu1, Gilhyon Lee1, Hidenori Nakazato2,

<sup>1</sup>*Graduate School of Global Information and Telecommunication Studies,*

**Heterogeneous Systems**

Takashige Hoshiai<sup>2</sup> and Yoshiyori Urano<sup>2</sup>

<sup>2</sup>*Global Information and Telecommunication Institute,*

