Page 63 - IJOCTA-15-2

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D. Balpınarlı, M. Onal / IJOCTA, Vol.15, No.2, pp.245-263 (2025)
Table 5. Comparison of results when T = 80

T N J Initial Solution LR time (Sec) TSA Results CPLEX Results LR Upper Bound CPLEX Upper Bound
819.12 12.78 1010.16 993.8 1048.38 2777.68
1642.23 13.01 2084.26 2035.3 2112.34 3316.08
5 735.78 11.89 1018.76 989.34 1078.65 1880.43
1034.25 14.32 1091.56 1141.42 1203.3 2035.70
1234.11 12.20 2031.84 1992.64 2104.67 3076.16
10
26498.15 13.07 33639.67 30153.63 35651.56 38967.31
27473.41 12.44 33069.59 30233.37 35682.73 40100.85
10 28876.53 13.47 33293.17 31920.03 36873.13 39354.74
21734.28 12.70 32572.25 26637.57 34951.16 38915.22
25478.36 13.19 31672.33 27057.26 34351.53 38228.97
1172.39 13.21 1744.89 1554.73 1849.42 3301.53
1323.57 13.62 1980.03 1777.82 2082.32 4257.50
5 1318.64 13.08 2118.02 1902.42 2333.39 4098.88
3956.34 14.09 5690.55 4921.44 6240.32 8125.20
3219.45 14.20 3846.01 3767.85 4619.89 7906.47
80 15
39523.89 12.91 50779.37 43574.82 51911.18 61730.09
39412.76 14.05 50864.98 44165.53 54123.73 64802.89
10 43498.12 14.73 50570.26 42715.58 54349.32 61091.39
28713.56 14.10 41338.57 37862.23 45519.83 59219.32
28129.65 14.34 42138.97 39779.69 44474.12 58930.81
-2927.87 14.39 -1927.39 -2128.24 -1691.61 2355.64
-12481.45 14.01 -8021.15 -8622.02 -6942.91 1786.21
5 -31419.38 14.77 -18080.72 -20758.34 -15125.14 812.12
-39128.72 14.88 -29685.11 -35360.29 -25792.65 838.29
-1998.32 14.86 -7968.17 -8289.68 -6556.89 1281.12
20
31419.67 15.15 45894.62 37203.52 55792.45 70930.48
35619.45 14.95 48550.68 41945.42 57417.46 76482.46
10 43792.65 14.21 58246.39 53871.44 68778.69 73528.32
31413.28 14.07 47582.00 34103.6 58582.56 67999.34
39591.87 14.50 56978.06 48918.77 69834.19 85060.56
Table 6. Comparison of algorithms’ average gap results

T N J Average TSA Gaps (%) Average CPLEX Gaps (%)
5 1.76 3.45
10
10 2.09 4.71
5 3.98 7.86
40 15
10 6.71 11.17
5 6.70 18.34
20
10 8.65 23.16
Average: 4.98 11.45
5 4.23 6.27
10
10 1.96 7.94
5 5.86 14.78
60 15
10 7.29 14.15
5 7.45 20.45
20
10 10.06 23.80
Average: 6.14 14.56
5 4.65 5.52
10
10 7.46 17.83
5 9.07 17.72
80 15
10 5.92 20.46
5 17.12 30.15
20
10 17.15 30.73
Average: 10.23 20.40
Total Average: 7.12 15.47

factor in the results of CPLEX. So for higher J relative contributions of T, N and J in predicting
values, our solution approach might outperform gap values. FIA is a heuristic measure used in
CPLEX even more. A significant three-way in- machine learning to evaluate the relative contri-
85
teraction effect also exists in the results of both bution of features to a predictive model (see ).
approaches. In FIA, the relative weights of the factors indi-
We also performed a Feature Importance cate the relative strength of association of each
Analysis (FIA) using a decision tree model to see factor with the value of the target variable. In
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