This breakscheduling system, which is included in Operating Hours Assistant 3.6, helps professional planners create high-quality shift plans, while satisfying labor rules and staffing requirements.

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Abstract. The problem of designing workforce shifts and break patterns is a relevant employee scheduling problem that arises in many contexts, especially in service industries. The issue is to find a minimum number of shifts, the number of workers assigned to them, and a suitable number of breaks so that the deviation from predetermined workforce requirements is minimized. We tackle this problem by means of a hybrid strategy in the spirit of Large Neighborhood Search, which exploits a set of Local Search operators that resort to a Constraint Programming model for assigning breaks. We test this strategy on a set of random and real life instances employed in the literature.

Shift design and break scheduling are important employee scheduling problems that arise in many contexts, especially at airports, call centers, and service industries. The aim is to find a minimum number of legal shifts, the number of workers assigned to them, and a suitable number of breaks so that the deviation from predetermined workforce requirements is minimized. Such problems have been extensively investigated in Operations Research and recently have been also tackled with Artificial Intelligence techniques. In this chapter we outline major characteristics of these problems and provide a literature survey over solution techniques to solve them. We then describe in detail two state-of-the-art approaches based on local search techniques. Finally, we discuss our experiences with the application of one of these techniques in a real life case study.

This chapter deals with the application of evolutionary approaches and other metaheuristic techniques for generating tree decompositions. Tree decomposition is a concept introduced by Robertson and Seymour [34] and it is used to characterize the difficulty of constraint satisfaction and NP-hard problems that can be represented as a graph. Although in general no polynomial algorithms have been found for such problems, particular instances can be solved in polynomial time if the treewidth of their corresponding graph is bounded by a constant. The process of solving problems based on tree decomposition comprises two phases. First, a decomposition with small width is generated. Basically in this phase the problem is divided into several sub-problems, each included in one of the nodes of the tree decomposition. The second phase includes solving a problem (based on the generated tree decomposition) with a particular algorithm such as dynamic programming. The main idea is that by decomposing a problem into sub-problems of limited size, the whole problem can be solved more efficiently. The time for solving the problem based on its tree decomposition usually depends on the width of the tree decomposition. Thus it is of high interest to generate tree decompositions having small widths.Finding the treewidth of a graph is an NP-hard problem [2]. In order to solve this problem different algorithms have been proposed in the literature. Exact methods such as branch and bound techniques can be used only for small graphs. Therefore, metaheuristic algorithms based on genetic algorithms [18] , simulated annealing [22], tabu search [14], iterated local search [29] , and antcolony optimization ([7], [9]) have been proposed in the literature to generate good upper bounds for larger graphs. Such techniques have been applied very successfully and they are able to find the best existing upper bounds for many benchmark problems in the literature.In this chapter we will first introduce the concept of tree decomposition, and then give a survey on metaheuristic techniques used to generate tree decompositions. Three approaches based on genetic algorithms, iterated local search and ant-colony optimization that were proposed in the literature will be described in detail. Finally, we will also mention briefly two recent approaches that exploit tree decompositions within metaheuristic search.