Table 1 The link traversing cost functions \(\pmb{t_{a}(\hat{f})}\)

\(t_{1}(\hat{f})=5\cdot10^{-5}\hat{f}_{1}^{4}+5\hat{f}_{1}+2\hat {f}_{2}+500\)

\(t_{15}(\hat{f})=3\cdot10^{-5}\hat{f}_{15}^{4}+9\hat {f}_{15}+2\hat{f}_{14}+200\)

\(t_{2}(\hat{f})=3\cdot10^{-5}\hat{f}_{2}^{4}+4\hat{f}_{2}+4\hat {f}_{1}+200\)

\(t_{16}(\hat{f})=8\hat{f}_{16}^{4}+5\hat{f}_{12}+300\)

\(t_{3}(\hat{f})=5\cdot10^{-5}\hat{f}_{3}^{4}+3\hat{f}_{3}+\hat {f}_{4}+350\)

\(t_{17}(\hat{f})=3\cdot10^{-5}\hat{f}_{17}^{4}+7\hat {f}_{17}+2\hat{f}_{15}+450\)

\(t_{4}(\hat{f})=3\cdot10^{-5}\hat{f}_{4}^{4}+6\hat{f}_{4}+3\hat {f}_{5}+400\)

\(t_{18}(\hat{f})=5\hat{f}_{18}+\hat{f}_{16}+300\)

\(t_{5}(\hat{f})=6\cdot10^{-5}\hat{f}_{5}^{4}+6\hat{f}_{5}+4\hat {f}_{6}+600\)

\(t_{19}(\hat{f})=8\hat{f}_{19}+3\hat{f}_{17}+600\)

\(t_{6}(\hat{f})=7\hat{f}_{6}+3\hat{f}_{7}+500\)

\(t_{20}(\hat{f})=3\cdot 10^{-5}\hat{f}_{20}^{4}+6\hat{f}_{20}+\hat{f}_{21}+300\)

\(t_{7}(\hat{f})=8\cdot10^{-5}\hat{f}_{7}^{4}+8\hat{f}_{7}+2\hat {f}_{8}+400\)

\(t_{21}(\hat{f})=4\cdot10^{-5}\hat{f}_{21}^{4}+4\hat {f}_{21}+\hat{f}_{22}+400\)

\(t_{8}(\hat{f})=4\cdot10^{-5}\hat{f}_{8}^{4}+5\hat{f}_{8}+2\hat {f}_{9}+650\)

\(t_{22}(\hat{f})=2\cdot10^{-5}\hat{f}_{22}^{4}+6\hat {f}_{22}+\hat{f}_{23}+500\)

\(t_{9}(\hat{f})=10^{-5}\hat{f}_{9}^{4}+6\hat{f}_{9}+2\hat {f}_{10}+700\)

\(t_{23}(\hat{f})=3\cdot10^{-5}\hat{f}_{23}^{4}+9\hat {f}_{23}+2\hat{f}_{24}+350\)

\(t_{10}(\hat{f})=4\hat{f}_{10}+\hat{f}_{12}+800\)

\(t_{24}(\hat {f})=2\cdot10^{-5}\hat{f}_{24}^{4}+8\hat{f}_{24}+\hat{f}_{25}+400\)

\(t_{11}(\hat{f})=7\cdot10^{-5}\hat{f}_{11}^{4}+7\hat{f}_{11}+4\hat {f}_{12}+650\)

\(t_{25}(\hat{f})=3\cdot10^{-5}\hat{f}_{25}^{4}+9\hat {f}_{25}+3\hat{f}_{26}+450\)

\(t_{12}(\hat{f})=8\hat{f}_{12}+2\hat{f}_{13}+700\)

\(t_{26}(\hat {f})=6\cdot10^{-5}\hat{f}_{26}^{4}+7\hat{f}_{26}+8\hat{f}_{27}+300\)

\(t_{13}(\hat{f})=10^{-5}\hat{f}_{13}^{4}+7\hat{f}_{13}+3\hat {f}_{18}+600\)

\(t_{27}(\hat{f})=3\cdot10^{-5}\hat{f}_{27}^{4}+8\hat {f}_{27}+3\hat{f}_{28}+500\)

\(t_{14}(\hat{f})=8\hat{f}_{14}+3\hat{f}_{15}+500\)

\(t_{28}(\hat {f})=3\cdot10^{-5}\hat{f}_{28}^{4}+7\hat{f}_{28}+650\)