# An Integrated Optimization Method of High-Speed Railway Rescheduling Problem at the Network Level
## 3 Multi-Objective Integrated Optimization Model
### Symbols and Parameters
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Definition** \\ \hline \(WM_{5}^{c,t}\) & The mileage of standby train-set \(b\) after it completes the circulation \(c\) which contains train \(t\). \\ \(ADD_{b}^{c,t}\) & The distance between standby train-set \(b\) and its allocated depot after the standby train-set \(b\) completes circulation \(c\) which contains train \(t\). \\ \(OC_{b}\) & The operating cost per mileage of standby train-set \(b\). \\ \(SC_{b}\) & The seating capacity of standby train-set \(b\). \\ \(SC_{i}\) & The seating capacity of standby train-set \(b\). \\ \(DPS^{c,t}\) & The seating capacity of train-set \(i\). \\ \(TMS^{c,t}\) & The termalization of train \(t\) in circulation \(c\). \\ \(PAT_{1}^{c,t}\) & The planned arrival time of train \(t\) at station \(j\) in circulation \(c\) \\ \(PDT_{1}^{c,t}\) & The planned departure time of train \(t\) at station \(j\) in circulation \(c\) \\ \(WPS_{1}^{c,t}\) & Whether train \(t\) is planned to stop at station \(j\) in circulation \(c\). \\ \(EST_{j}\) & Extra stop time of trains at station \(j\). \\ \(EDT_{j}\) & Extra departure time of trains at station \(j\). \\ \(TSI_{j}\) & Train stopping time at station \(j\). \\ \(STSC_{c,t}^{c,t^{\prime}}\) & The station where short train \(t\) in circulation \(c\) and short train \(t^{\prime}\) in circulation \(c^{\prime}\) are coupled. \\ \(STDS_{c,t}^{c,t^{\prime}}\) & The station where short train \(t\) in circulation \(c\) and short train \(t^{\prime}\) in circulation \(c^{\prime}\) are decoupled. \\ \(SS_{s}\) & The start station of section \(s\). \\ \(ES_{s}\) & The end station of section \(s\). \\ \(CS_{c,t}^{c,t^{\prime}}\) & The common sections of train \(t\) in circulation \(c\) and train \(t^{\prime}\) in circulation \(c^{\prime}\). Assuming the common sections are \\ \(m\), \(m+1\), \(\ldots\), \(n-1\), \(n\), then \(CS_{c,t}^{c,t^{\prime}}=\{m,m+1,\ldots,n-1,n\}\). \\ \(SS_{m}\) & The start station of the section where the interruption occurs. \\ \(ES_{m}\) & The end station of the section where the interruption occurs. \\ \(ST_{int}\) & The start time of the interruption. \\ \(ET_{int}\) & The end time of the interruption. \\ \(PAT_{1}^{c,t,x}\) & The passenger number of demand \(x\) for train \(t\) in circulation \(c\). \\ \(PDT_{1}^{c,t,x}\) & The departure time for passenger demand \(x\) of train \(t\) in circulation \(c\) at station \(j\). \\ \(DPS^{c,t,x}\) & The departure station for passenger demand \(x\) of train \(t\) in circulation \(c\). \\ \(APS^{c,t,x}\) & The arrival station for passenger demand \(x\) of train \(t\) in circulation \(c\). \\ \(PBS_{j,j+1}^{c,t,x}\) & Whether the passenger demand \(x\) of train \(t\) in circulation \(c\) passes through section \(j,j+1\), \(PBS_{j,j+1}^{c,t,x}=1\) represents that \\ \(PBS_{j,j+1}^{c,t,x}\) & passenger demand \(x\) passes through section \(j,j+1\); otherwise, \(PBS_{j,j+1}^{c,t,x}=0\). \\ \(RT_{1j+1}\) & The running time of the train in section \(j,j+1\). \\ \(ADT\) & The acceptable maximum associated delay time. \\ \(A\) & The acceptable maximum coefficient of overcrowding. \\ \(TDH\) & The minimize train delivery headway of two trains. \\ \(COT\) & The operation time of train coupling. \\ \(DOT\) & The operation time of train decoupling. \\ \(SVT_{j}\) & The serving time of train-set at station \(j\). \\ \(PT_{CAN}^{c,t}\) & The penalty time of cancelling train \(t\) in circulation \(c\). \\ \(M\) & A sufficiently large numerical value \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Symbols.