## 6 Numerical Experiments
### Comprehensive Evaluation of the Algorithms
#### 6.4.1 Objective Function and Computational Time Values  
Both objective function and computational time values are important indicators, which must be considered in evaluation of the algorithmic performance. The objective function values define the quality of solutions, which is a primary interest of the decision makers (in this study, the primary decision maker is the MCT operator). However, the algorithms, which require a prohibitively large amount of computational time to obtain good-quality solutions, are not favorable from the practical standpoint (e.g., the exact optimization algorithms generally require a prohibitively large amount of computational time to solve the problems of a high complexity). The objective function and computational time values were retrieved for all the developed solution algorithms and large size problem instances, and results are reported in Table 5. Specifically, Table 5 provides the following information for each large size problem instance: (1) instance number; (2) number of vessels; (3) number of berths; (4) average objective function value for each solution algorithm; and (5) average computational time (denoted as CPU) for each solution algorithm. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{ \begin{tabular}{c} **Number** \\ **of Vessels** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Number** \\ **of Berths** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **EA** \\ **Objective, h** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **CPU, s** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Objective, h** \\ \end{tabular}  } & \multirow{2}  
It was found that the SAEA algorithm outperformed the AEA, DPCEA, and EA algorithms in terms of the objective function value at termination on average by 4.01%, 6.83%, and 11.84%, respectively, over the generated large size problem instances. Superiority of the SAEA algorithm over the other algorithms can be explained by the fact that the crossover and mutation probabilities are encoded in the SAEA chromosomes and evolve throughout the algorithmic run, which further allows more efficient exploration and exploitation of the search space. The adaptive parameter control strategy, deployed within the AEA algorithm, was found to be more efficient as compared to the deterministic parameter control strategy, deployed within the DPCEA algorithm. The latter finding can be justified by the fact that AEA had been adjusting the crossover and mutation probabilities based on feedback from the search, while DPCEA had been altering the crossover and mutation probabilities based on the piecewise function without considering any feedback from the search. The worst performance was demonstrated by the EA algorithm, which relied on the parameter tuning and did not change the crossover and mutation probabilities throughout the algorithmic run. Therefore, constant crossover and mutation probability values significantly limit explorative and exploitative capabilities of the EA algorithm. The computational time comprised on average 51.26 s, 45.26 s, 41.36 s, and 27.79 s over the generated large size problem instances for the SAEA, AEA, DPCEA, and EA algorithms, respectively. An increasing time complexity of the SAEA algorithm can be explained by the fact that SAEA has longer chromosomes, i.e., additional genes are encoded to represent crossover and mutation probabilities for each chromosome in the population. Furthermore, those additional genes also undergo the SAEA operations (see Section 4.6 of the manuscript for more details), which incurs an increasing computational time. However, the maximum SAEA computational time did not exceed 64.96 s, which can be considered to be acceptable from the practical standpoint. Specifically, the MCT operator will be able to develop berth schedules using the SAEA algorithm within a relatively short span of time.