# Concealed Conduit Routing in Building Slabs
## 1 Introduction
### Related Work
Their approach combines fuzzy logic, a dependency structure matrix, and hierarchical clustering techniques. Their goal is to minimize installation costs by identifying the optimum number of modules and the best division points of the MEB systems. The goals of these studies are similar to ours. The resultant pipes are part of MEB systems. However, the workspace of our method is different from theirs. Our routing environment is confined within the slabs of buildings. Electrical system design is vital for buildings and communities. [PERSON] et al. presented studies on the supportive roles of BIM tools in the design, analysis, planning, and construction of electrical trade systems [16]. They found that the combination of BIM and GIS is useful for smart electrical grid construction. Managing the construction of MEB systems is as important as the design work. In the paper of [17], [PERSON] et al. expanded the functionalities of BIM systems and incorporated construction management techniques for building MEB systems. Their 3D MEB design system offers a visualization function such that the target MEB system can be visually explored before the installation. Their system reduces manual work and resolves conflicts by developing better workflows and management strategies. As a result, the productivity, accuracy, and efficiency of the construction works are increased while the building expense is reduced. These investigations verify that the BIM systems of buildings have become the de facto digital representation methods in modern construction industries, and the geometrical information of the resultant pipes of the MEB systems should be integrated into BIM systems. Piping is no longer a standalone process. The representation of the workspace influences the efficiency of the routing process. In most published studies, the workspaces and the pipes were represented by a single layer of structures. In the work of [18], [PERSON] et al. proposed a hierarchical layout of the subsea production control system in the 3D undersea working environment. In their approach, they used a multi-layer star-tree structure to create the layout of the control network. To find the optimal layout, they combined the construction costs of the control center, distribution units, control modules, and umbilical and fly lines to form an objective function. Then, they applied constraints upon the design such that the connection, terrain, position, and pipe route requirements could be met. Finally, they utilized A* and swarm-intelligence algorithms to solve the system and generate the resultant production control system. Their problem domain representation method is hierarchical. However, the representation is an abstract structure, a multi-layer star tree in the 3D undersea space. On the other hand, our workspace encoding scheme uses both an abstract graph and a set of solid 3D images (the slabs). Hence, ours is more suitable for the routing process inside the walls, floors, and ceilings of buildings. The piping algorithms invented by these related research studies focused on routing exposed conduits in open spaces or on object surfaces. Their workspace representation schemes are not suitable for encoding the slabs of a building. Their path-finding methods cannot explore the internals of the slabs. Employing their piping algorithms to arrange concealed conduits would result in unqualified pipes or violations of safety regulations and geometric constraints. Thus, in this research, we propose a new piping algorithm dedicated to laying out concealed conduits in modern buildings. The rest of this article is organized as follows: Our workspace-encoding strategy and path-finding scheme are described in Section 2. Test results are presented and explained in Section 3. The discussion, potential applications, and future work are contained in Section 4. This article ends with the conclusion part in Section 5.