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The personnel scheduling problem is a well-known NP-hard combinatorial problem. Due to the complexity of this problem and the size of the realworld instances, it is not possible to use exact methods, and thus heuristics, meta-heuristics, or hyper-heuristics must be employed. The majority of heuristic approaches are based on iterative search, where the quality of intermediate solutions must be calculated. Unfortunately, this is computationally highly expensive because these problems have many constraints and some are very complex. In this study, we propose a machine learning technique as a tool to accelerate the evaluation phase in heuristic approaches. The solution is based on a simple classifier, which is able to determine whether the changed solution (more precisely, the changed part of the solution) is better than the original or not. This decision is made much faster than a standard cost-oriented evaluation process. However, the classification process cannot guarantee 100% correctness. Therefore, our approach, which is illustrated using a tabu search algorithm in this study, includes a filtering mechanism, where the classifier rejects the majority of the potentially bad solutions and the remaining solutions are then evaluated in a standard manner. We also show how the boosting algorithms can improve the quality of the final solution compared with a simple classifier. We verified our proposed approach and premises, based on standard and real-world benchmark instances, to demonstrate the significant speedup obtained with comparable solution quality.Keywords neural network · nurse rostering problem · adaptive boosting · pattern learning.R. Václavík ( ) · P.Šůcha · Z. Hanzálek

An acceptable response time of a server is an important aspect in many client-server applications; this is evident in situations in which the server is overloaded by many computationally intensive requests. In this work, we consider that the requests, or in this case tasks, generated by the clients are instances of optimization problems solved by anytime algorithms, i.e. the quality of the solution increases with the processing time of a task. These tasks are submitted to the server which schedules them to the available computational resources where the tasks are processed. To tackle the overload problem, we propose a scheduling algorithm which combines traditional scheduling approaches with a quality control heuristic which adjusts the requested quality of the solutions and thus changes the processing time of the tasks. Two efficient quality control heuristics are introduced: the first heuristic sets a global quality for all tasks, whereas the second heuristic sets the quality for each task independently. Moreover, in practice, the relationship between the processing time and the quality is not known a priori. Because it is crucial for scheduling algorithms to know at least the estimation of these relationships, we propose a general procedure for estimating these relationships using information obtained from the already executed tasks. Finally, the performance of the proposed scheduling algorithm is demonstrated on a real-world problem from the domain of personnel rostering with very good results.

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