# GA-Based Optimization Method for Mobile Crane Repositioning Route Planning
## 3 Mobile Crane Repositioning Route Optimization Method
### Near-Global Optimal Mobile Crane Reposition Route  
Meta-heuristics such as GA, SA, and TS are effective in solving the problem in this study. All three meta-heuristics have the ability to find better solution than the manual process. Several studies on the performance comparison of GA, SA, and TS have been conducted [23; 24; 25]. [PERSON] et al. [23] show that TS give better calibration results compared to the GA and SA. On the other hand, the study by [PERSON] et al. [25] found that GA has a better solution quality than SA, TS for solving QAP (Quadratic Assignment Problem) optimization problems, but, TS has a faster execution time than the others. This suggests that there may be differences in the performance of GA, SA, and TS depending on the type of problem. Therefore, this study adopts GA, which is the most diverse and widely used in the construction field, to solve the RCP problem. This module uses GA to find the near-global optimal reposition route for the mobile crane. The chromosome type, fitness function, and GA operation termination rules used to find the near-global optimal reposition route of the mobile crane are provided in detail below. First, the GA parameters (i.e., population size (\(PS\)), crossover rate (\(CR\)), mutation rate (\(MR\))) are set by the user. Then, RPOS sets the GA operation termination rules. For the termination rules, we used the four termination criteria provided by MATLAB: (1) Generation: the operation is terminated if the maximum number of generations is reached; (2) Stall-GenLimit: the operation is terminated if there is no improvement in the objective function during a specific number of generations (stall generation); (3) StallTimeLimit: the operation is terminated if there is no improvement in the objective function for a certain period; (4) TimeLimit: the operation is terminated if the maximum computation time is exceeded. Tolfun (= \(1\times 10^{-6}\)), which is set as a default value by the GA solver of MATLAB, is used to determine whether the objective function has improved. GA chromosomes are composed of a set of genes (\(gn\)). In RPOS, the GA chromosome is composed of a pair of the index (\(k\)) of the supply point (\(E^{i,k}\)), where the load can be lifted at a certain demand point (\(S^{i}\)), and the index (\(f\)) of the feasible point (\(F^{i,k,f}\)) for the \(S^{i}-E^{i,k}\) pair (Figure 3). The serial number of a gene (\(gn\)) pair is the same as the index (\(i\)) of the demand point. This number is determined by the load installation sequential order according to the construction plan. In other words, after installing the \(i\)-th load, the \(i+1\) load was installed. The gene serial number also follows this sequential order. The chromosome length, which is twice the number of loads to be installed (\(l\)), is determined by the number of installing loads. The search range of the optimal solution (\(S_{S}\)) is the number of combinations of the supply points (\(E^{i,k}\)) where loading is feasible at the demand point (\(S^{i}\)) and the feasible points (\(F^{i,k,f}\)) for the \(S^{i}-E^{i,k}\) pair (Equation (12)). \[S_{S}=\prod_{i}\left(\sum_{i,k}^{n(E^{i,k})}n\left(F^{i,k,f}\right)\right). \tag{12}\]  
RPOS sets the objective function of the GA as the total operating time of the crane to search for the optimal reposition route of the mobile crane. The total operating time is calculated by adding the load lifting time (\(ht\)), crane traveling time (\(tt\)), and crane installing/dismantling time (\(rt\)). As the optimal reposition route minimizes the total operating time, the fitness function\(f_{OT}\) is set as the inverse number of the total operating time (Equation (13)).