A Fast metaheuristic for scheduling tasks with multiple modes

We consider the following multi-mode task scheduling problem. Given are a set of independent tasks, and a set of single unit dedicated renewable resources. At any time each resource can be used by a single task at most. Each task has to be executed without preemption in one out of its possible execution modes, where each mode identifies a subset of resources simultaneously required by the task for its execution. The aim of the problem is to find a mode assignment for each task, and a schedule of the tasks to be executed in the assigned modes, such that the total amount of resources requested by tasks in any time period does not exceed the resource availability, and the schedule length, i.e., the makespan, is minimized. From the complexity viewpoint this problem is NP-hard. Heuristic algorithms for scheduling tasks with multiple modes for the minimum schedule length criterion involve in general two distinct phases, task mode assignment and task scheduling. In this paper, we propose a novel two-phase approach metaheuristic based on strategic oscillation and on a randomized choice of the neighborhood of the local search to avoid being trapped in local optima. The proposed approach, that can be interpreted as a simplification of a previous work by the authors, is compared to two state-of-the-art algorithms.