Research Article

A High-Performance Genetic Algorithm: Using Traveling Salesman Problem as a Case

Table 4

Simulation results of UMDA, EHBSA, ACS, and DPSO.

Data set PREUMDA PREEHBSAPREACSPREDPSO

a280 ( )6.73 (3.14%) −66.001.59 (1.85%)−69.82−3.31 (1.24%)−22.14−5.13 (2.56%)−75.00
2,722.102,687.782,625.382,701.27
u574 ( )−4.52 (0.71%) −58.610.52 (0.80%)−67.460.64 (0.86%)−69.01−7.85 (4.25%)−84.39
39,013.0039,392.9038,299.7039,031.40
u724 ( )−4.14 (0.67%) −59.470.39 (0.78%)−67.95−0.85 (0.77%)−78.31−4.20 (4.19%)−84.66
44,419.9044,347.5042,805.4044,854.00
u1060 ( )−4.76 (0.70%) −73.35−0.09 (0.76%)−74.111.46 (0.66%)−80.67−1.35 (3.24%)−87.93
239,226.00238,155.00234,396.00242,863.00
u1432 ( )−2.93 (0.65%) −70.610.51 (0.67%)−73.320.29 (0.66%)−73.85−0.11 (0.65%)−76.42
163,520.00163,504.00161,204.00183,637.00
pr2392 ( )−3.51 (0.46%) −81.97−0.90 (0.52%)−75.592.51 (0.79%)−89.26−0.68 (0.42%)−91.16
406,302.00404,867.00401,594.00452,346.00
pcb3038 ( )−3.36 (0.33%) −69.17−0.86 (0.32%)−76.674.58 (0.57%)−91.07−0.13 (0.55%)−86.84
148,258.00148,374.00149,715.00165,307.00
fnl4461 ( )−3.60 (0.22%) −73.20−1.46 (0.29%)−79.022.09 (0.63%)−92.30−0.16 (0.38%)−86.35
195,063.00195,747.00200,487.00219,180.00
usa13509 ( )−4.14 (0.27%) −70.52−2.39 (0.26%)−73.011.16 (0.34%)−93.45−0.49 (0.31%)−88.24
21,479,200.0021,531,300.0022,584,600.0024,222,100.00

Average −2.69−69.210.3−73.000.95−76.67−2.23−84.55

: time in seconds; : best solution in 30 runs; : coefficient of variation as defined in Table 2.