Table 57.89 57.89 1.203419 43.18 42.96 41.04 43.45 43.26

Table 4. Comparison of grouping efficacies of the existing algorithms and the proposed algorithmProblem No. HGGA GRASP SACF GLCA HGBPSO CARI Proposed  method Best solution Avg. CPU Time (sec.) Min. Max. 1 82.35 – – 82.35 82.35 – 82.35 82.35 82.35 0.04682 – 73.68 – – – 73.68 52.63 75.00 75.00 0.04693 69.57 62.50 69.57 69.57 69.57 62.50 69.57 69.57 69.57 0.04684 79.59 79.59 79.59 80.85 79.59 79.59 76.92 79.59 80.85 0.11745 76.92 76.92 76.92 76.92 76.92 76.92 76.92 76.92 76.92 0.06626 70.83 70.37 70.83 70.83 70.83 70.37 62.96 70.83 70.83 0.11477 60.87 53.13 60.87 60.87 60.87 53.84 57.14 60.87 60.87 0.11398 69.44 68.29 – 69.44 69.44 68.3 65.91 69.44 69.44 0.15309 85.25 85.25 85.25 85.25 85.25 85.25 85.25 85.25 85.25 0.267510 58.72 58.72 58.41 58.72 58.72 58.72 52.08 58.72 58.72 0.260911 75.00 70.59 75.00 75.00 75.00 70.59 64.00 75.00 75.00 0.182212 92.00 92.00 92.00 92.00 92.00 92.00 80.43 92.00 92.00 0.280113 72.06 69.86 71.21 73.53 72.06 69.86 68.75 73.13 73.53 0.804814 71.83 69.33 – 71.83 71.83 69.33 62.90 71.83 71.83 0.844215 52.75 51.96 – 53.41 53.41 50.98 51.09 53.26 53.41 1.061016 68.99 67.83 – – 68.99 67.83 68.70 68.99 68.99 1.379017 57.53 56.52 52.44 57.53 57.53 54.86 48.10 57.53 57.53 2.159418 57.73 54.46 – 57.73 57.73 54.46 56.00 57.89 57.89 1.203419 43.18 42.96 41.04 43.45 43.26 41.48 38.10 43.36 43.45 1.266420 50.81 49.65 50.81 50.81 50.81 49.65 49.15 52.07 52.07 0.928621 77.91 76.54 78.40 77.91 77.91 76.14 77.50 77.91 78.40 2.434222 57.98 58.15 56.04 57.98 57.98 56.98 56.47 58.60 58.60 2.452323 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 3.907724 85.11 85.11 85.11 85.11 85.11 85.11 85.11 85.11 85.11 3.928225 73.51 73.51 73.51 73.51 73.51 73.51 73.51 73.51 73.51 3.975126 53.29 51.97 52.44 53.29 53.29 51.90 50.65 53.29 53.29 4.004127 48.95 47.37 47.13 – 48.95 46.34 45.71 48.97 48.97 4.018128 47.26 44.87 44.64 – 47.26 44.10 41.73 48.91 48.91 4.012829 54.02 54.27 – 54.82 54.82 54.27 50.18 54.82 54.82 2.974430 46.91 46.06 – – – 44.35 44.98 47.35 47.35 6.033931 63.31 59.52 62.42 63.31 63.31 58.11 58.87 63.27 63.31 6.086232 59.77 60.00 – 59.77 59.77 58.47 57.67 60.12 60.12 7.737433 50.83 50.51 – – – 49.22 48.17 50.83 50.83 7.739234 46.35 45.93 – – – 44.18 44.76 46.87 46.87 22.057335 60.57 59.85 – 60.64 60.64 56.42 56.09 60.64 60.64 11.592036 84.03 84.03 – – – 84.03 82.03 84.03 84.03 55.7633Number of best solutions 20 8 11 23 21 8 30 36 Percentage of best solution 1 55.56 22.22 30.56 63.89 58.33 22.22 83.33 100.00 Percentage of best solution 2 57.14 22.86 50.00 82.14 67.74 22.86 83.33 100.00 Percentage of total gap 17.40 91.70 41.91 4.96 12.37 125.27 3.27 0.00 Table 5. Improved grouping efficacies produced by the proposed methodProblem No. Size HGGA GRASP 26 SACF GLCA HGBPSO CARI Proposed method(Max.) Best solution2 5×7 – 73.68 – – – 73.68 75.00 75.0018 18×24 57.73 54.46 – 57.73 57.73 54.46 57.89 57.8920 20×23 50.81 49.65 50.81 50.81 50.81 49.65 52.07 52.0722 20×35 57.98 58.15 56.04 57.98 57.98 56.98 58.60 58.6027 24×40 48.95 47.37 47.13 – 48.95 46.34 48.97 48.9728 24×40 47.26 44.87 44.64 – 47.26 44.10 48.91 48.9130 28 × 46 46.91 46.06 – – – 44.35 47.35 47.3532 30 × 50 59.77 60.00 – 59.77 59.77 58.47 60.12 60.1234 36 × 90 46.35 45.93 – – – 44.18 46.87 46.87

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