Fig shows three results generated from the same

Fig. 11 shows three results generated from the same two-floor architectural program that contains 13 rooms. The variety of results implies that the automated layout optimization can assist architects during the conceptual design process by providing them numerous results within a short time. The three-level house takes about 5min on average to generate the results. The office building takes about 15min, while the two-level house only takes about 3min on average. The time spent by the multi-agent system is also less than 30s in all cases (Fig. 12).
Discussion and conclusion The model used by the evolutionary optimization is based on a 3-D grid system. This discrete model is easy to implement and does not require many calculations. For example, the volume of the room in the grid system can be determined by counting the number of cells. It can also generate layouts in different scales without numerous changes on time consumption by adjusting the bepridil of the grid. Furthermore, grid-aligned layouts are easier to build because all their components have the same size. However, the grid system limits the solution space. For instance, non-orthogonal layouts are difficult to generate within one grid system, and curve-shaped rooms cannot be achieved within this model. An alternative for this is adopting a multiple grid system (Hua, 2012) or a non-orthogonal grid system (Peng et al., 2014) or using the continuous model instead of the discrete one. However, the continuous model requires much more complex calculations and sometimes strong Boolean operations, which are difficult to implement. The approach provided by Merrell et al. (2010) and Rodrigues et al. (2013a, 2013b, 2013c) is an example of adopting the continuous model in a 2-D layout design. The results of these approaches are still orthogonal. The optimization adopts a simple evolutionary approach, where only one object is mutated and optimized. This approach is effective but may sometimes fall into local maxima. An alternative to this approach is the adoption of multi-optimization, such as the genetic algorithm. Assume the entire process is still the combination of a multi-agent system and an evolutionary optimization. Two possible approaches may apply the genetic algorithm into the latter process. The first one is that the integer indicator of the cells can be encoded as the gene, and the implementation of the crossover operation is not complicated. However, the crossover operation may easily produce discontinuous cases, which were mentioned in Section 3, and result in a large number of invalid results. The second is that the sequence of the push operation may be encoded as the gene. The crossover may then be the testing of different combinations of push operations. This approach is inspired by the approach proposed by Rosenman (1996) and Doulgerakis (2007). However, changing the sequence of the operations may cause the target faces to be unidentifiable because the positions and amount of the faces may change after each operation. Thus, a method to index faces must be developed.
Acknowledgements We are grateful to Dr. H. Hua for providing valuable references at the early stage of the research and Prof. P. Tang for her comments on the drafts of this paper. This research is funded by the National Natural Science Foundation of China (Grants 51478116 and 51538006).
Introduction The increasing lack of physical activity among all populations is considered a global public health problem (“WHO Physical Inactivity”, n.d.). Public health efforts to improve health typically promote moderate types of physical activity, such as walking and biking, because these are easier for inactive populations to begin and maintain and these are also easier to incorporate into daily routines (Frank et al., 2003). The built environment has been identified as an essential factor for integrating physical activity into one׳s daily life (Cerin et al., 2013; Frank et al., 2003; Frumkin et al., 2011; Sallis et al., 2011). International organizations such as the World Health Organization (WHO) have called for changes to be made in the built environment to improve human health through walking, including changes in urban design, transportation and recreational facilities (Adams et al., 2013). For such changes to be effective, it is critical to identify the design elements of the built environment that influence physical activity. In other words, what elements of the built environment encourage people to walk?