## Nomenclature  
\(G\)Undirected weighted graph  
\(G_{\overline{T}}\)Sub-graph in \(G\), representing a spanning tree which takes OS as the root node  
\(K\)Maximum number of feeder lines  
\(M\)Number of wind turbines (WT) \begin{tabular}{l l} \(N\) & Number of cable types \\ \(T\) & The lifetime of the wind farm (Year) \\ \(K\) & Index of feeder \\ \(P\) & Index of cable type \\ \(r\) & Index of wind farm operation period \\ \(\mathbf{S_{\mathrm{rated}}}\) & Rated apparent power of WT (MVA) \\ \(P_{rated}\) & Rated active power of WT (MW) \\ \(\mathbf{I_{\mathrm{rated}}}\) & Rated current of WT (A) \\ \(U_{rated}\) & Rated voltage of WT (kV) \\ \(C_{Total}\) & The total cost for the wind farm (Euro) \\ \(Z_{Trench}\) & The trenching cost of cables (Euro) \\ \(Z_{Cable}\) & The purchase cost of cables (Euro) \\ \(Z_{EnergyLoss}\) & The power losses cost (Euro) \\ \(C_{p}\) & The unit cost of cable \(p\) (Euro/km) \\ \(R_{p}\) & The unit resistance of cable \(p\) (\(\mathbf{\Omega}\)) \\ \(I_{max,p}\) & Current-carrying capacity of cable \(p\) (kA) \\ \(C_{Trench}\) & Unit trenching cost of cable (Euro/km) \\ \(C_{Energyloss}\) & The unit cost of energy loss of cable (Euro/MWh) \\ \(\tau_{\mathrm{A}}\) & Duration time of peak energy loss (h) \\ \(cos\mathbf{\mu}\) & Power factor \\ \(D\) & Interest rate \\ \(E_{m}\)\(=(ex_{m},ey_{m})\) & The coordinate of WT \(m\) \\ \(L_{m}\) & The distance between OS and WT \(m\) (m) \\ \(L^{\prime}_{m,m^{\prime}}\) & The distance between WT \(m\) and WT \(m^{\prime}\) (m) \\ \(I_{G_{T},k,m,p}\) & The current between OS and WT \(m\) in feeder \(k\) of \(G_{T}\) when the \(p\) type's of the cable is used (A) \\ \(I^{\prime}_{G_{T},k,m,m^{\prime},p}\) & The current between WT \(m\) and \(m^{\prime}\) in feeder \(k\) of \(G_{T}\) when the \(p\) type's of the cable is used (A) \\ \(O_{G_{T},k,m,p}\) & Number of WTs carried by type \(p\) cable between OS and WT \(m\) in feeder line \(k\) of \(\mathbf{G_{T}}\) \\ \(O^{\prime}_{G_{T},k,m,m^{\prime},p}\) & Number of WTs carried by type \(p\) cable between WT m and m' in feeder line \(k\) of \(\mathbf{G_{T}}\) \\ \(S_{G_{T},k,m,p}\) & If feeder \(k\) of \(G_{T}\) uses type \(p\) cable to connect OS with WT \(m\), \(\mathbf{g_{G_{T},k,m,p}}=1\), \\ \(S^{\prime}_{G_{T},k,m,m^{\prime},p}\) & If feeder \(k\) of \(G_{T}\) uses type \(p\) cable to connect WT m with WT \(m^{\prime}\), \(\mathbf{g_{G_{T},k,m,p}}=1\), \\ \(S^{\prime}_{G_{T},k,m,m^{\prime},p}\) & otherwise \(\mathbf{g_{G_{T},k,m,p}}=0\). \\ \(S^{\prime}_{G_{T},k,m,p}\) & If WT \(m\) is the last WT which feeder \(k\) of \(G_{T}\) uses type \(p\) cable to connect with, \\ \(S^{\prime}_{G_{T},k,m,p}\) & \(S^{\prime}_{G_{T},k,m,p}=1\), otherwise \(\mathbf{g^{\prime}_{G_{T},k,m,p}}=0\). \\ \(Q\) & Population size \\ \(\mathbf{x_{i}}\)\(\mathbf{{}_{t}}\)\(\mathbf{{}_{t}}\)\(\mathbf{{}_{t+1}}\) & The position of bat \(i\) at \(the\) th and \(t+1\)th generation respectively \\ \(\mathbf{x_{*,t}}\) & The optimal position of \(t\)th generation \\ \(\mathbf{v_{i,t}}\)\(\mathbf{{}_{t+1}}\) & The velocity of bat \(i\) at \(the\) th and \(t+1\)th generation respectively \\ \(f_{i,t}\) & The pulse of bat \(i\) at \(the\) th and \(t+1\)th generation respectively \\ \(f_{rand}\) & Randomly generated frequency \\ \(\mathbf{A_{i,t}}\), \(\mathbf{{}_{i,t+1}}\) & The pulse loudness of bat \(i\) at \(the\) th and \(t+1\)th generation respectively \\ \(\mathbf{R_{i,0}}\), \(\mathbf{R_{i,t+1}}\) & The initial and \(t+1\)th generation's emission frequentness of bat \(i\) \\ \(\mathbf{\alpha}\)\(\mathbf{{}_{i}}\)\(\mathbf{{}_{\gamma}}\) & The impact factor of pulse loudness and emission \\ \(\mathbf{x_{LevelOne,i,t}}\), \(\mathbf{x_{LevelTwo,i,t}}\) & The position of \(t\)th generation's bat at first and second layer \\ \(W\), \(H\) & The dimension of bats at first and second layer \\ \(a\), \(b\) & The factor that used to judge the crossing cables \\ \(Fit\) & Fitness \\ \(P\)\(\mathbf{N}\) & Penalty factor \\ \(\mathbf{CI}\) & The overall number of crossing cables \\ \end{tabular}