The author wishes to provide the below corrigendum to the published version of their piece:

\begin{align*}landingtim{e_i} = mp{t_i} + durmptfaf + \left( {{{dist} \over {vfa{f_o}}}*ct} \right),\,fmod{e_i} = 1,\,\forall i \in I,\forall o \in O\,\end{align*}

\begin{align*}landingtim{e_{i2}} - landingtim{e_{i1}} \geqslant csar{r_{o1,o2}} - M{\rm{*}}\left( {1 - y{2_{i1,i2}}} \right),\end{align*}

\begin{align*}i1 \ne i2,{\rm{\;}}o1 = ca{t_{i1,{\rm{\;}}}}o2 = ca{t_{i2,{\rm{\;}}}}\,fmod{e_{i1}} = 1,{\rm{\;}}fmod{e_{i2}} = 1,\,\forall \left( {i1,i2} \right) \in I,{\rm{\;}}\forall \left( {o1,o2} \right) \in O\end{align*}

\begin{align*}landingtim{e_{i1}} - landingtim{e_{i2}} \geqslant csar{r_{o1,o2}} - M*y{2_{i1,i2}}{\rm{\;}},{\rm{\;}}\end{align*}

\begin{align*}i1 \ne i2,{\rm{\;}}o1 = ca{t_{i2}},{\rm{\;}}o2 = ca{t_{i1}},{\rm{\;}}fmod{e_{i1}} = 1,{\rm{\;}}fmod{e_{i2}} = 1,\,\forall \left( {i1,i2} \right) \in I,{\rm{\;}}\forall \left( {o1,o2} \right) \in O\end{align*}

When looking at delay times on an average basis, it is evident that HTP flights under the category distribution of 100M exhibited the lowest delay times in the EC model. For the other distributions, it can be observed that CS model has proven to be more effective in reducing delay times for HTP flights compared to other models. However, due to the trade-off approach, it has affected the delay times for LTP aircraft, but it has not significantly deviated from the results obtained from the other models.

The percentages provided in Figure 3 encompass the comparison of the results between the SOO model and the respective MOO models based on the averages for the given category distributions. Positive values indicate that the SOO model produced better results while negative values indicate that the corresponding MOO model achieved superior results.

Table 2.

Average delays of HTP and LTP flights (sec.)

Figure 3.

Comparison of models in terms of HTP and LTP delays

In Figure 4, average delay times for each distribution are provided for the MOO and the SOO models. As evident from this figure, the model has scarcely utilized holding delays in any solution model or category distribution.

Figure 4.

Type of delays

Multi-objective optimization inherently provides decision-makers with various solutions, catering to the complexities of conflicting objectives. The number of pareto-optimal points obtained from each MOO model is presented in Figure 5.

Figure 5.

Total number of pareto optimal points

Figure 6 depicts the pareto-optimal fronts generated by the MOO models for the results of a randomly selected test problem in this study. In this figure, the discrepancy in the number of pareto-optimal points among the MOO models may indicate the effectiveness of each model in exploring the solution space. Specifically, the EC model seems to be the most effective in finding various trade-off solutions compared to the other models for the related category distribution and test problem.

Figure 6.

Pareto optimal fronts of each MOO model (a: 70H-30M; test no: 1, b: 100M; test no: 1)

Emission values calculated based on the MOO and the SOO models are represented in Figure 7. In the figure, average emission values for HC, CO, and NOx are provided for each MOO and the SOO model. In a 50H-50M distribution, the SOO model may be considered better choice for CO among the MOO models, whereas for NOx in the same distribution, the EC model yields a lower emission value. In the 100M distribution, the SOO and EC delivered better results than the others for the CO and the NOx pollutant, respectively.

Figure 7.

Emission values for HC, CO and NOx

For statistical analysis, Post hoc tests were performed based on ANOVA test results and given in Table 5.

Table 5.

Post hoc tests