Computational Grid emerged to satisfy the rising demand for bandwidth, storage, and computational resources. Job Scheduling on computational grids is identified as NP-hard problem due to the heterogeneity of grid resources. Numerous researches have applied metaheuristics to find polynomial times for the job scheduling problem. These metaheuristics generated good but not optimal schedules. The current metaheuristics suffer from several limitations that cause long makespan time and flowtime. The aim of this research is to design and implement grid job scheduling approaches to map clients’ jobs to the available resources in order to finish the submitted jobs within the optimal makespan time and flowtime. This research presents novel static, hybrid static and dynamic metaheuristics approaches based on Firefly Algorithm for grid job scheduling. Based on the review of the available literature, Firefly Algorithm has yet to be applied in the job scheduling on computational grid. Experiments using simulations and real workload traces were conducted to study the performance of the proposed scheduling approaches. Empirical results revealed that the proposed scheduling approaches outperform other scheduling approaches in the case of typical and heavy workloads in terms of both makespan time and flowtime. The average improvement ratios achieved by the static, hybrid static and dynamic scheduling approaches over Genetic Algorithm in the case of makespan time were 23%, 32% and 28% respectively for typical workloads, and 51%, 59% and 42% for heavy workloads. In the case of flowtime, the average improvement ratios were 62%, 81 % and 21% respectively for typical workloads, and 40%, 58% and 57% for heavy workloads.
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