Research Article

A Multiple-Starting-Path Approach to the Resource-Constrained th Elementary Shortest Path Problem

Table 2

Computational result for = 2, 5.

Lawler MSP Gap (%) Lawler MSP Gap (%)
TimeStatesTimeStatesTimeStatesTimeStatesTimeStatesTimeStates

c1010.22 2620150.05 5162079.3 80.3 0.30 3281150.05 5188884.2 84.2
c1021.53 16745570.27 29215382.1 82.6 1.97 22380640.26 28819586.6 87.1
c1035.42 52086811.29 103425576.3 80.1 13.71 136550841.28 102766990.7 92.5
c10414.31 113526553.58 226439275.0 80.1 24.12 201390513.73 230482284.5 88.6
c1050.31 3675440.06 7126579.7 80.6 0.39 4715890.07 7151483.5 84.8
c1060.41 5021590.09 10046778.0 80.0 0.50 6113950.09 10075281.7 83.5
c1070.40 4804880.09 9704778.3 79.8 0.52 6373150.09 9717583.4 84.8
c1080.72 8772500.17 18097176.8 79.4 1.47 18648240.16 18599088.9 90.0
c1091.26 15194720.27 30939478.3 79.6 2.53 31778070.28 32046189.0 89.9
r1010.06 669440.02 2006368.3 70.0 0.16 1741870.02 2038786.6 88.3
r10211.40 36264322.09 93801681.7 74.1 13.84 50655262.10 93859284.8 81.5
r1038.80 54124232.20 119576675.0 77.9 15.66 110337992.53 130163683.8 88.2
r10435.32 1163974517.01 458656651.8 60.6 40.27 221295468.01 308973680.1 86.0
r1050.25 2685130.06 5540476.0 79.4 0.54 5877170.06 5579988.3 90.5
r10614.28 43132283.49 141912675.5 67.1 20.98 71966994.43 156698678.9 78.2
r10718.37 76457764.04 186347578.0 75.6 28.68 141668964.00 185491986.0 86.9
r10822.13 106149574.61 225459179.2 78.8 28.20 1627683710.26 346573563.6 78.7
r1090.81 8394220.18 16084977.8 80.8 1.63 18162960.18 16454688.8 90.9
r1105.04 31851930.91 67406481.9 78.8 9.06 79911780.92 68042089.9 91.5
r11136.20 66644113.88 176265689.3 73.6 38.01 110112123.91 176401789.7 84.0
r11211.51 66184337.31 271461836.5 59.0 22.79 143072865.22 227857077.1 84.1
rc1010.16 1714700.04 4071973.9 76.3 0.34 3641950.04 4080387.5 88.8
rc1020.73 8217740.17 16497977.2 79.9 1.77 20262380.17 17062790.5 91.6
rc1032.53 25026120.49 45449680.8 81.8 4.24 47208300.49 45497288.6 90.4
rc10432.02 93200681.86 130347794.2 86.0 33.66 111643781.57 119712095.3 89.3
rc1050.43 4731900.11 11054074.1 76.6 0.99 11414810.11 11056589.1 90.3
rc1060.54 5862910.14 13114074.0 77.6 0.96 11119320.14 13149785.5 88.2
rc1071.62 16340320.45 40216672.2 75.4 3.16 33634440.46 40627185.6 87.9
rc1083.15 31127490.82 71740173.8 77.0 6.92 73091950.84 71823287.9 90.2