Execution time Next, we discuss the difference in the computation time of the GA when using the different population diversity measures. Table 3 lists the average computation time in seconds for the GA using the different population diversity measures. Results are presented for six selected instances listed in the table to avoid displaying a huge amount of data, where two instances ($10,000) were randomly selected from each of the three benchmark sets. In addition, the bottom line (Ave. ratio) of the table shows the ratio of the execution time to that of the GA using $Hini$ averaged over the six instances. The table shows that the execution time tends to increase as the value of $m$ increases in the population diversity measures $Hm$ and $Hmadj$. This is mainly because of the increase in the computational effort of calculating $ΔH(y)$ in the evaluation function (14). Note that the execution times of $Hm$ are smaller than those of $Hmadj$ (for the same value of $m$) even though the calculation of $Hmadj$ is simpler than that of $Hm$. The reason for this is that the number of generations of the GA required to complete the search was smaller when $Hm$ was used than when $Hmadj$ was used. As for the population diversity measure $H6vari$ with various values of $ratio$, the results are similar to that of $H6adj$.

Table 3:
Average execution time (in seconds) of the GA using different population diversity measures.
$H6vari(ratio)$
$Hind$$Greedy$$D$(0.02)(0.05)(0.1)(0.2)(0.4)
usa13509 2429 1097 2442 3458 3704 3620 3475 3068
d15112 3482 1932 3640 5743 5543 5127 4841 4284
it16862 2958 1547 3009 5201 4803 4600 4341 4104
pjh17845 1636 947 1677 2803 2685 2600 2497 2351
fma21553 2053 1094 2084 3518 3354 3285 3154 2982
sw24978 5930 3351 6142 10388 9769 9386 8744 8199
Ave. ratio — 0.53 1.02 1.69 1.61 1.55 1.47 1.36
$Hm$ $Hmadj$
$m=2$ $m=3$ $m=4$ $m=5$ $m=6$ $m=8$ $m=2$ $m=3$ $m=4$ $m=5$ $m=6$ $m=8$
usa13509 2402 2352 2451 2614 2726 3069 2619 2717 2951 3218 3564 4471
d15112 3562 3550 3634 3982 4161 4901 3718 3762 4106 4567 4967 6632
it16862 3077 3087 3208 3406 3720 4294 3162 3290 3649 4139 4614 5936
pjh17845 1675 1729 1866 1969 2108 2488 1759 1861 2014 2257 2443 3033
fma21553 2109 2133 2248 2385 2582 3037 2214 2294 2528 2789 3072 3821
sw24978 6259 6065 6433 6849 7340 8382 6295 6729 7504 8169 9168 11600
Ave. ratio 1.03 1.03 1.08 1.15 1.23 1.42 1.07 1.12 1.23 1.36 1.50 1.90
$H6vari(ratio)$
$Hind$$Greedy$$D$(0.02)(0.05)(0.1)(0.2)(0.4)
usa13509 2429 1097 2442 3458 3704 3620 3475 3068
d15112 3482 1932 3640 5743 5543 5127 4841 4284
it16862 2958 1547 3009 5201 4803 4600 4341 4104
pjh17845 1636 947 1677 2803 2685 2600 2497 2351
fma21553 2053 1094 2084 3518 3354 3285 3154 2982
sw24978 5930 3351 6142 10388 9769 9386 8744 8199
Ave. ratio — 0.53 1.02 1.69 1.61 1.55 1.47 1.36
$Hm$ $Hmadj$
$m=2$ $m=3$ $m=4$ $m=5$ $m=6$ $m=8$ $m=2$ $m=3$ $m=4$ $m=5$ $m=6$ $m=8$
usa13509 2402 2352 2451 2614 2726 3069 2619 2717 2951 3218 3564 4471
d15112 3562 3550 3634 3982 4161 4901 3718 3762 4106 4567 4967 6632
it16862 3077 3087 3208 3406 3720 4294 3162 3290 3649 4139 4614 5936
pjh17845 1675 1729 1866 1969 2108 2488 1759 1861 2014 2257 2443 3033
fma21553 2109 2133 2248 2385 2582 3037 2214 2294 2528 2789 3072 3821
sw24978 6259 6065 6433 6849 7340 8382 6295 6729 7504 8169 9168 11600
Ave. ratio 1.03 1.03 1.08 1.15 1.23 1.42 1.07 1.12 1.23 1.36 1.50 1.90

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