## 3 Formal Problem Definition
_completion time_ of the application jobs (25%) is also measured with respect to a user-given time frame of each application job and averaged. 3. _total makespan_ of all application jobs (15%)
4. the _rate of resource utilization_ (5%) is gathered for the first 75% of the total makespan only, as in the end phase of a schedule not all resources can be utilized. 5. _delay of inner grid jobs_ (20%) _inner grid jobs_ are all non-terminal grid jobs of an application job. If they start late, there is no or only little room to start the final grid job(s) earlier so that the complete application job is finished earlier, resulting in a better value of the main objective _completion time_. An earlier start of inner grid jobs is in fact a prerequisite for a faster processing of the application job, but it is not honored by the criteria discussed so far. Thus, the delays of inner grid jobs with respect to the earliest starting time of their application job are measured and averaged over all application jobs. For the costs, no corresponding action is required, as a change in costs caused by the substitution of a resource is registered immediately. This illustrates an important difference for an objective function used in an evolutionary search: It is not sufficient to assess quality differences well. The fitness function must also support the search process in finding the way to better solutions in order to achieve improvements. For the calculation of the weighted sum, the criteria must be somehow comparable. A further desirable property is that the formula for their calculation is independent of the scheduling task on hand. This is achieved by introducing relative measures where required. As _costs_ and _completion time_ are already calculated as the averaged rate of utilization of a user-given budget or time frame, they are comparable and their calculation method does not depend on the details of a given scheduling task. The same holds for the _rate of resource utilization_. In the first planning phase of GORBA described in the next section, lower and upper estimations for the processing times of all application jobs are calculated. They serve as a reference for the _total makespan_. Thus, the makespan can be expressed as rate of utilization of this time frame. As the remaining auxiliary criterion can also be calculated with respect to the given time frame of each application job before averaging, all criteria are calculated as a rate of budget or time frame utilization and are therefore comparable. The values are weighted using the above given weights, summed up, and the result may be reduced by the multiplication by the outcome of the penalty functions, if necessary. The weights are based on experience and aimed at reaching a fair compromise between users and resource providers. The tuning of the suggested adjustment is left to the system administrator. We use the weighted sum to aggregate the different criteria instead of Pareto optimization, because one solution, and not a set of Pareto-optimal ones, is required in an automated scheduling process. Pareto optimization would require a final selection step using something like weights as well for the different criteria to pick one result as the final solution.