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This paper is motivated by, but not limited to, the task of scheduling jobs organized in workflows to a computational grid. Due to the dynamic nature of grid computing, more or less permanent replanning is required so that only very limited time is available to come up with a revised plan. To meet the requirements of both users and resource owners, a multi-objective optimization comprising execution time and costs is needed. This paper summarizes our work over the last six years in this field, and reports new results obtained by the combination of heuristics and evolutionary search in an adaptive Memetic Algorithm. We will show how different heuristics contribute to solving varying replanning scenarios and investigate the question of the maximum manageable work load for a grid of growing size starting with a load of 200 jobs and 20 resources up to 7000 jobs and 700 resources. Furthermore, the effect of four different local searchers incorporated into the evolutionary search is studied. We will also report briefly on approaches that failed within the short time frame given for planning.

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