## 5 Case Studies for Construction Site Layout Planning and Managerial Implication
### Case Study 1  
In this case, the primary objective is to design the temporary construction facilities layout aimed at minimizing the total travelling distance of site workers between different facilities. The site layout has \(11\) facilities and \(11\) locations, as can be seen in Figure 3. Side gate and main gate are fixed location while others are not. The list of facilities used in this case study is shown below:  
Figure 2: Parameter settings result of _pop_size_ and _maxFE_ for SOS and HSOS-LS. 1. Site office (F1)
2. Falsework workshop (F2)
3. Labour residence (F3)
4. Storeroom 1 (F4)
5. Storeroom 2 (F5)
6. Carpentry workshop (F6)
7. Reinforcement steel workshop (F7)
8. Side gate (F8, fixed to L1)
9. Electrical, water and other utilities control room (F9)
10. Concrete batch workshop (F10)
11. The main gate (F11, fixed to L10)  
The objective is to design a temporary facilities layout to get the minimum travel distance, which is calculated by multiplying the frequency and distance between each facility. The daily frequency of trips and the distance between locations are shown in Tables 1 and 2. The objective function is defined using Equations (1)-(4). \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Facility**} & \multicolumn{8}{c}{**Facility**} \\ \cline{2-13}  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** \\ \hline
1 & 0 & 5 & 2 & 2 & 1 & 1 & 4 & 1 & 2 & 9 & 1 \\
2 & 5 & 0 & 2 & 5 & 1 & 2 & 7 & 8 & 2 & 3 & 8 \\
3 & 2 & 2 & 0 & 7 & 4 & 4 & 9 & 4 & 5 & 6 & 5 \\
4 & 2 & 5 & 7 & 0 & 8 & 7 & 8 & 1 & 8 & 5 & 1 \\
6 & 1 & 2 & 4 & 7 & 3 & 0 & 5 & 8 & 4 & 7 & 5 \\
7 & 4 & 7 & 9 & 8 & 4 & 5 & 0 & 7 & 6 & 3 & 2 \\
8 & 1 & 8 & 4 & 1 & 1 & 8 & 7 & 0 & 9 & 4 & 8 \\
9 & 2 & 2 & 5 & 8 & 3 & 4 & 6 & 9 & 0 & 5 & 3 \\
10 & 9 & 3 & 6 & 5 & 3 & 7 & 3 & 4 & 5 & 0 & 5 \\
11 & 1 & 8 & 5 & 1 & 6 & 5 & 2 & 8 & 3 & 5 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Frequencies of trips between facilities. Figure 3: Solution representation. SOS, PSO, differential evolution (DE), and the proposed HSOS-LO were applied in the case study and were compared to each other. All previously mentioned metaheuristic algorithms were adapted to search towards the optimal solutions of construction site layout problem. Each algorithm was run for 100 simulations, and the mean of the best value was recorded. Numerical comparison results of each algorithm are discussed in this section. Each algorithm has 50 populations (pop_size). A maximum number of evaluations (maxFE) is 3000 for all algorithms (equal to 60 iterations for both PSO and DE; 30 iterations for SOS; and 20 iterations for HSOS-LO). The results of the comparisons are presented in Table 3. Table 3 shows the information regarding the best, average, worst, and standard deviations of objective value. Furthermore, the percentage difference between best to average, best to worst, and average computational time is reported. The obtained results have indicated that HSOS-LO manages to outperform the competing algorithms in fitness value and consistency. It can get the most optimum solution (minimum travel distance = 12,546) with the best average, worst, and standard deviation iteration (12,553.86, 12672, and 19.37, respectively). Also, the average computational time of each instance by HSOS-LO is 0.084 s.  
This study also compares HSOS-LO with the outcome of previous research studies. The comparison results are shown in Table 4. Based on the simulation results, HSOS-LO is able to outperform other algorithms such as GA, TS, CBO, and ECBO. HSOS-LO manages to have the most consistent result with the least number of iterations and function evaluations. It can be seen that the number of search spaces of possible solution combinations is 9! (because two facilities are fixed). Hence, the possible layout arrangement is 362,880 possibilities. HSOS-LO only needs 3000 attempts on average to get the solution with the objective value equal to the best-known solution consistently, which is about 0.8267% of the total attempts.