Dynamic Weight Setting for Personnel Scheduling with Many Objectives

Abstract

When large sets of constraints and objectives are combined in a practical optimization problem, managing all these potentially conflicting goals can become very difficult and might require to solve an instance multiple times. First, an instance might be infeasible with the current constraints, in which case our system introduces a novel violation score to help identify the constraints that need to be relaxed for the next run. Second, multiple objectives are often combined using a linear combination with hand-crafted weights, which are very difficult to set such that the result matches the expectations regarding the balance between individual objectives. Instead, the user can tell our system particular thresholds for the expected changes in objectives, e.g., to reduce objective 1 by 10 % while not increasing objective 2 by more than 5 %. Dynamic weight setting automatically adapts the weights to reach these thresholds or uses the violation scores to explain reasons for not reaching thresholds. It can not only be used for soft constraints, but also to determine weights when hard constraints are internally represented as soft constraints in meta-heuristics. While the methodology is general, we have implemented it in the context of a personnel scheduling framework of our industry partner and present a detailed evaluation on the domain of Bus Driver Scheduling, where its benefits can be seen in multiple scenarios.