The optimal combination of parameters get from lots of test issues is: ρ = 0.4, Q = 5, α = 1 and β = 1. Meanwhile, the number of the ants equals the amounts of the cities, and perform 25 trials (1500 iterations in each trial) on each problem. The experimental results are shown in Table 1, Table 2 and Table 3, where traditional algorithm stands for the MMAS algorithm, average is the average time required to find the best solution in a trial, allowed is the longest time allowed to be executed in each trial, and number means the number of trials to obtain the best solution. The numbers included in the name of the problems denote the numbers of cities for its corresponding problem. For the sake of convenient illustration, Traditional Algorithm  was noted as TA.