# Facility Layout Problem with Alternative Facility Variants
## 1 Introduction
The hall is defined as a rectangular area with obstacles (i.e., where no workstation can be placed) and communications (i.e., the areas that can be used only by relevant parts of the workstations). Workstations have a rectangular working area to which one or more handling zones can be attached. Furthermore, input/output points are optionally defined as well. These are used to define dependencies among workstations, such as links for material or semi-product handling. Each workstation can appear in the floor plan in one of six possible orientations. To solve this FLP, single- and multi-objective evolutionary algorithms have been proposed in [32]. The main feature of the evolutionary algorithms is that they use an indirect representation. This means that the exact position and rotation of the workstations are not directly encoded into the solution representation. Instead, the floor plan is represented indirectly using a so-called priority list that encodes the order and how the workstations will be added to the floor plan. In this paper, we propose a new FLP variant with a new definition of loosely-defined facilities. Here, the facilities are not allowed to freely change their shapes within allowed boundaries. Instead, there are only several possible fixed-shape alternatives defined for each facility. The optimization task is to generate an optimal layout using exactly one variant per facility. Therefore, the optimization algorithm can not morph the shape of facilities arbitrarily. Instead, it has to choose among the feasible alternatives available for each facility. An important aspect of this FLP formulation is that the alternatives for a particular facility differ not only in shape and dimensions but also in other characteristics such as construction costs, operating costs, etc. Thus, a given selection of workstations' alternatives affects various quality and performance indicators of the corresponding layout. This work was motivated by our research activities carried out in cooperation with the SKODA AUTO a.s. company. Our joint project aimed to propose machine learning-based approaches to optimally place multiple assembly lines' workstations within a production hall, given particular objectives and constraints. This is an optimization problem that occurs every time the product portfolio assigned to the respective hall is to be changed. Then, the assembly lines must be re-configured accordingly and placed in the production hall most effectively while respecting the products' assembly workflow, production hall infrastructure, logistics, and other requirements and constraints. An essential part of this optimization process is the re-design of some of the existing workstations and the design of new ones. The idea behind the possible use of multiple workstation variants is inspired by real-life best practices used by the experts when designing feasible layouts of the workstations. Usually, many constraints and restrictions affect the workstation's shape, such as internal dependencies related to the particular technology implemented by the workstation, the workstation's interface with the outside world, etc. Thus, only a few well-defined realizations might be considered for a given workstation. To solve this FLP, we adopt the approach presented in [32] and further extend it so that multiple alternatives of each workstation can be defined and considered during the optimization process. To improve the exploration capabilities of the evolutionary algorithms, a new variation operator is defined for the extended representation. Additionally, a cooling schedule similar to the one used in simulated annealing [33; 34] is introduced. Its role is to control the search mode along the optimization process. It slowly turns the search mode from a global search to a local one in order to restrict variation operators' scope to the tail section of the priority list as the algorithm converges.