## 3 Results
### Phase I: Defining PC On-site Assembly Optimization Principles via BIM-GA Hybrid System
#### 3.2.2 Application of Genetic Algorithm
\begin{table}
\begin{tabular}{c|c} \hline \hline
**Project Name** & **P knowledge Industry Center** \\ \hline Period & 2022–2024 \\ Structure & Precast concrete \\ Purpose & Knowledge industry center \\ Site area & 7414 m\({}^{2}\) \\ Building area & 5170 m\({}^{2}\) \\ Floor area & 48,535 m\({}^{2}\) \\ No. of Floors & B1\(\sim\)10F \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Overview of the construction site. (Source: own elaboration). Figure 11: Integrated BIM representation of the construction site. (**a**) Floor Plan. (**b**) Elevation. (**c**) Zone information. (Source: own elaboration). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**No.** & **ID** & **x** & **y** & **z** & **Level** & **Zone** & **Installation** \\ \hline
0 & 442407 & \(-\)43,609 & \(-\)112,233 & 3800 & 2 & A & 1 \\
1 & 442452 & \(-\)32,609 & \(-\)112,233 & 3800 & 2 & A & 1 \\
2 & 442559 & \(-\)390 & \(-\)112,233 & 3800 & 2 & A & 1 \\... &... &... &... &... &... &... &... \\
206 & 471581 & 390 & \(-\)161,853 & 15,850 & 5 & B & 0 \\
207 & 471896 & 44,390 & \(-\)150,833 & 15,850 & 5 & B & 0 \\
208 & 471941 & 21,609 & \(-\)150,833 & 15,850 & 5 & B & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Information of PC column. (Source: own elaboration). highlighted beams and slabs shown in blue in Figure 12b. Examination of the simulation results from these scenarios was aimed at understanding how assembly sequences are generated to effectively address interference. Through interviews, it was discovered that in situations similar to this case study, a common alternative strategy on PC construction sites involves temporarily postponing sections prone to interference and proceeding with column tasks from the upper-left corner following the work cycle. Using this strategy, the system-generated assembly sequence results were examined. The assembly sequence generation was set for 23 June with a population size of 200 and 100 generations, a crossover probability of 0.2, and a mutation probability of 0.05. The A, B, and C values generated for each of the 200 sequences were normalized to each constraint to prevent varying degrees of constraint dominance across scales. Subsequently, the weights for each constraint were applied, resulting in the determination of the composite penalty score (P) for each assembly sequence. The fitness history count (N) in the table indicates the number of fitness histories calculated for this case study, and P represents the composite penalty score (Table 4). \begin{table}
\begin{tabular}{c c c} \hline \hline
**No. ** & **Assembly Sequence (Component ID)** & **Penalty Score** \\ \hline
1 & 467570, 467680, 468432, 467598, 470266, 467678, 468567, & 0.215 \\
2 & 470268, 470279, 468477, 469197, 470288, 470297, \(\ldots\) & 0.229 \\
2 & 467650,



The analysis identified an assembly sequence that significantly minimized penalties across the three constraints. This specific sequence, commencing with component ID 467570, demonstrates a total penalty value of 0.215, as shown in Figure 13a. A graphical representation of this, shown in Figure 13b, illustrates a converged fitness value of 4.69 for this sequence. The breakdown of penalty scores for this case includes 19 points attributed to task complexity, 34.58 points related to the adjacency of the work radius, and 0 points associated with the feasibility of component installation. The simulation of this assembly sequence using the Revit API is illustrated in Figure 14, in which the predominant factor shaping the assembly sequence is the feasibility of the components. On the expected date of 24 June, where the interference was foreseen, no components were installed at the designated location. Images 1 and 2 in Figure 14 show a sequence of consecutive beam installations near the initial component. Image 4 in Figure 14 illustrates the process of generating the assembly sequence as of June 24 th. In this situation, components strategically avoid installation in the highlighted red areas to prevent interference, prioritizing column installations on the upper levels.