IEEE Computational Intelligence Magazine - November 2023 - 53

TABLE IV The average performance over 30 independent runs of the compared algorithms on the mdBeijing dataset. For each
instance, the minimal mean total cost is marked in bold. Under Wilcoxon rank sum test with significance level of 0.05, an algorithm is
marked with "  " ( " + " ) if it is significantly worse (better) than RoCaSH2.
NAME
jVjjEjjTj Q
HGA
AVERAGE
STD
MDMA
UHGS
RoCaSH
AVERAGE STD AVERAGE STD AVERAGE
RoCaSH2
STD AVERAGE
STD
mdBeijing-1 2820 3584 358 25000 719234.97- 11886.66 686975.27- 2276.83 700976.03- 16440.32 670299.77- 2498.79 668445.23 2591.43
mdBeijing-2 2820 3584 717 25000 1150250.27- 24800.00 991639.77- 5983.89 1067059.50- 34534.73 969526.90- 3987.90 967421.00 2069.03
mdBeijing-3 2820 3584 1075 25000 1617555.90- 52678.27 1291706.77- 7998.94 1428907.13- 51311.48 1262995.90- 5536.61 1255489.40 5982.75
mdBeijing-4 2820 3584 1434 25000 2094669.57- 57565.46 1532919.13- 8790.30 1762055.47- 42994.03 1501499.47- 6308.62 1483625.37 6238.16
mdBeijing-5 2820 3584 1792 25000 2509434.83- 84950.27 1765292.37- 12919.29 2091122.90- 41928.83 1730308.47- 8791.86 1713324.33 8715.03
mdBeijing-6 2820 3584 2151 25000 3015946.30- 77773.91 2037539.30- 12574.15 2463738.90- 69502.68 2006983.97- 10079.70 1971272.43 6149.36
mdBeijing-7 2820 3584 2509 25000 3478082.53- 84965.25 2241324.77- 16682.94 2769506.53- 46033.13 2198449.20- 12032.60 2161050.13 8318.29
mdBeijing-8 2820 3584 2868 25000 3870752.67- 114643.10 2411349.87- 15910.58 3050471.73- 52036.64 2376049.93- 12630.50 2332161.03 11504.30
mdBeijing-9 2820 3584 3226 25000 4359410.80- 137537.60 2660257.63- 16518.70 3360111.40- 77995.75 2614046.63- 11341.60 2562072.23 12059.96
mdBeijing-10 2820 3584 3584 25000 4769283.93- 144797.70 2856373.80- 16984.42 3622938.57- 83524.41 2800199.50- 12662.80 2745051.63 13751.34
Mean
2758462.18
B-C-W
10-0-0
1847537.87
10-0-0
2231688.82
10-0-0
1813035.97
10-0-0
1785991.28
FIGURE 4. Convergence curves on the mdEGL-G1-A, mdEGL-G1-E, mdEGL-G2-A,and mdEGL-G2-E instances.
FIGURE 5. Convergence curves on the mdHefei-1, mdHefei-4, mdHefei-7,and mdHefei-10 instances.
is difficult to put their curves togetherwith others. Therefore, the
curves ofHGAandUHGS are omitted in the figure.
From Figure 5, it can be seen that both RoCaSH and
RoCaSH2 significantly outperformed MDMA. This demonstrates
the effectiveness of the divide-and-conquer strategy,
which is used by both RoCaSH and RoCaSH2. On mdHefei-1,
RoCaSH achieved a much better initial solution than
RoCaSH2. However, RoCaSH2 quickly caught up and
achieved almost the same final performance as that ofRoCaSH.
On mdHefei-4, mdHefei-7,and mdHefei-10, all the algorithms
NOVEMBER 2023 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 53

IEEE Computational Intelligence Magazine - November 2023

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