The above investigation indicates that

The above investigation indicates that discrete and continuous models are common for layout representation. Most approaches adopt a 2-D layout representation. Approaches that directly modify three-dimensional (3-D) spaces are rare. This trend may be explained by conventional and technical reasons. First, generated layouts represented by 2-D geometries can easily be converted into common architectural drawings. Second, 2-D computer graphics algorithms are stronger and faster than 3-D algorithms. Generating 2-D layouts is faster because the rooms in most buildings have the same height and can be directly extruded from the plan. However, such strategy may limit the solution space when designers intend to find novel combinations of building spaces. The strategy also encounters difficulties in dealing with situations such as multi-story buildings with different room heights or vertical rooms that cross several floors. Thus, we proposed an approach for spatial architectural layout design to directly modify architectural spaces. Our approach to the modeling of spatial layout improves the efficiency of topology finding. The major challenges of this work include (1) introducing a model for spatial layout representation, because few approaches directly modify architectural spaces, and (2) guaranteeing the efficiency of the program, because the number of possible arrangements in 3-D graphics is greater than that in 2-D ones. These challenges are tackled through the combination of a multi-agent system, which is inspired by Li (2012), and an evolutionary strategy. The former enhances the latter by providing it with topology-satisfied layouts. The latter, which is based on a grid system, improves the layouts to satisfy user-specified architectural criteria.

Agent-based topology finding

Spatial layout optimization
The spatial layout generated by the multi-agent system is optimized through an evolutionary approach to satisfy architectural criteria. The multi-agent system represents rooms as points and segments and does not contain information such as volumes and shapes. The generated layout cannot be further optimized without conversion. Under the consideration of the parp inhibitors of results and the difficulty of implementation, we adopt a grid system for the conversion. The comparison between the grid (discrete) model and the continuous model will be in Section 5. This optimization process continues running until amphibians manually stops or all criteria are satisfied.

Results
Several cases are provided for demonstration. The figures that show the layouts generated by the multi-agent system are captured from the screen. For illustration, the figures that show the optimized building layouts are rendered based on automatically generated 3-D models, without exterior walls or division into layers. The adopted architectural programs contain multiple floors and several cross-floor rooms and are manually encoded and written as an xml file. All cases are run on an Intel Core i7 clocked at 1.7GHz with 8GB memory. The program is written in JAVA 1.7 without multithread implementation.
The first case is a three-level house that includes 17 rooms and 1 staircase. Three of its rooms in different floors are connected with one other, and two of them are two-floor high. For the considerations of pipeline distribution and structure stability, all the halls and bathrooms in different floors are required to be aligned. One of the results is shown in Figs. 7 and 8 and implies that the proposed method performs well when dealing with cross-floor spaces. The room position generated by the multi-agent system is preserved in the optimized layout. The result satisfies the architectural criteria well, though few parts of the layout overhang.
Another case is a three-level office building that includes 1 staircase, 20 rooms, and 3 corridors. Half of the rooms are located on the first floor, and the other half are equally distributed on the second and third floors. This case aims to test corridors connected by a large number of rooms. Fig. 9 shows that the corridors are dragged by the rooms, extended, and shaped into capsules. A failure case exists on the first floor. Two rooms are collinear, and the outer one is blocked by the inner room. This error is fixed through the latter optimization process. However, it narrows the corridor and produces irregular architectural spaces (Fig. 10).