I currently have a scheduling algorithm which computes an approximate solution, say S, for the nominal scenario of a given problem instance, say N. Given that N changes in a way and becomes infeasible, I want to reuse S and complement it in a way so that:
- The method is able to compute a solution (by relaxing some of the constraints)
- The new solution violates a minimum amount of constraints.
The new problem essentially becomes the following: We have a set of tasks, each task with release time, deadline, duration, and a set of time slots. We can assign tasks to run in parallel and they are pre-emptible. Objective is to assign the tasks in a way that minimizes the total number of cores used.
Is someone aware of such scheduling problem in the literature or any suggestions how to address it?