# Optimization of Carsharing Fleet Placement in Round-Trip Carsharing Service
## 6 Results
### Discussion  
**Efficiency and performance:** When optimality is of real concern, PolySCIP is best applied. However, its high execution time and memory requirements make it inapplicable in practice where the instance is anything greater than 1390 street nodes and 1063 buildings. PolySCIP was unable to find a solution at an acceptable time (unfinished even after 18 days), and these numbers do not represent anything close to the size of a typical large city. Greedy algorithms, on the other hand, have the lowest execution time of all, but their results are unacceptable for practical applications due to their low user coverage. The underperformance of basic heuristic algorithms is alleviated in the iterative version, however, it comes with an additional computation cost. Despite the low execution time for a small instance, it becomes an issue in a larger instance. In the MU1 instance, the simulations took 17 h to locate 100 carsharing stations (on Intel Xeon L5640 at 2.26 GHz and over 128 GB or memory).Increasing the number of stations or increasing the size of the analyzed area will increase the execution time (in a factorial term, \(n!\), where n is a number of locations) and can make it impractical. NSGA-II's main advantages are the approximated front, the ability to cope with the size of problem instance, and the ability to improve existing solutions even further if possible. NSGA-II is 30 times faster than iterative algorithms and is still able to produce alternative solutions without needing to rerun the algorithm and change weights (in a \begin{table}
\begin{tabular}{l l c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{**Algorithm**} & \multicolumn{2}{c}{**Coverage Oriented**} & \multicolumn{2}{c}{**Distance Oriented**} \\  & & **Covered Users** & **Walking Distance** & **Covered Users** & **Access Distance** \\ \hline \multirow{3}{*}{Simulation} & Simple Heuristic & 3421 & 399.4 & 1091 & 378.6 \\  & Iterative Heuristic & 14,892 & 399.8 & 1214 & 376.1 \\  & NSGA-II & 14,892 & 399.8 & 1256 & 375.2 \\ \hline \multirow{3}{*}{Real-world} & Simple Heuristic & 2291 & 399.8 & 1124 & 375.9 \\  & Iterative Heuristic & 13,224 & 399.8 & 986 & 374.2 \\ \cline{1-1}  & NSGA-II & 13,224 & 399.8 & 986 & 374.2 \\ \cline{1-1}  & Manual Allocation & 7864 & 399.8 & 7864 & 399.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparing the best results from each algorithm categories and manual allocation in MU1 instance. Figure 12: NSGA-II approximated Pareto front and solutions of heuristic algorithms in MU1 instance compared to the manual allocation (72 stations). bi-objective iterative algorithm). These properties make NSGA-II an attractive choice in finding applicable fleet placement solutions, additionally it yields a better quality solution in term of coverage than the manual allocation, which usually takes a much longer execution time. **Coverage vs. walking distance:** After observing the coverage quality of distance-oriented algorithms, we found that the after the minimization of walking distance, the distance is only marginally reduced. Further analysis was carried out on the MU1 instance, with an equal weight of 0.5 to both objectives for bi-objective-focused iterative algorithm. The solution should be at (\(-\)397, 3000) in the approximated Pareto front in Figure 10. However, it is located at (\(-\)399, 14,700) instead. There are also solutions where the walking distance and user coverage are low, this is because they place stations away from crowded areas and situate the stations near a few buildings, hence, claiming the low maximum walking distance and yield lower user coverage (see Figure 13). The decrease in walking distance (in those solutions) only translates to a two to three minutes difference on foot. The marginal difference in walking distance can be explained by the nature of the city. Users are clustered in a densely populated area.