GES Initialize maximum number of iterations 0 1

(GES) ﺍﺳﺘﺮﺍﺗژی ﺗکﺎﻣﻠی گﺮﻭﻩ ﺑﻨﺪی • • • Initialize : maximum number of iterations , β , λ , 0< α ≤ 1 , α 0 > 0 , αmin >0 , Ps ; Begin t ← 0 ; Gs← 0 ; α← α 0 ; creat a feasible solution Xt and evaluate it ; while stopping criteria are not true for i=1 to λ given the parent solution Xt , apply NSG algorithm to obtain the offspring ; end for apply the comparison criteria Xt and the λ generated offspring to select the best individual , that is Xt+1 (in case of ties select at random) ; If f(Xt+1 ) < f(Xt) Gs ← Gs + 1 ; End if If (t mod G) = 0 • α ← • • • Gs ← 0; End if t ← t+1 , αt ← α ; End while End 22 ﻣﻨﺎﺑﻊ پیﺸﻨﻬﺎﺩﺍﺕ ﻧﺘﺎیﺞ ﺣﻞ ﻣﺴﺎﻟﻪ 2 BPP ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی 1 BPP ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی پیﺸیﻨﻪ ﺗﺤﻘیﻖ ﻣﻘﺪﻣﻪ

N 1 C 1 W ﻧﺘیﺠﻪ ﺣﻞ ﻣﺴﺎﺋﻞ N=100 , C=100 , W 1∊[1, 100] W 2∊[20, 100] W 3∊[30, 100] Problem Instance N 1 C 1 W 1 -A N 1 C 1 W 1 -B N 1 C 1 W 1 -C N 1 C 1 W 1 -D N 1 C 1 W 1 -E N 1 C 1 W 1 -F N 1 C 1 W 1 -G N 1 C 1 W 1 -H N 1 C 1 W 1 -I N 1 C 1 W 1 -J N 1 C 1 W 2 -K N 1 C 1 W 2 -L N 1 C 1 W 2 -M N 1 C 1 W 2 -N N 1 C 1 W 2 -O N 1 C 1 W 2 -P N 1 C 1 W 2 -Q N 1 C 1 W 2 -R N 1 C 1 W 2 -S N 1 C 1 W 2 -T N 1 C 1 W 4 -A N 1 C 1 W 4 -C N 1 C 1 W 4 -E N 1 C 1 W 4 -G N 1 C 1 W 4 -I N 1 C 1 W 4 -K N 1 C 1 W 4 -M N 1 C 1 W 4 -O N 1 C 1 W 4 -Q N 1 C 1 W 4 -S BISON 25 31 20 28 26 27 25 31 25 26 35 31 30 33 29 33 36 34 37 38 35 36 38 37 35 41 41 34 34 36 GES+MTRP 25 31 20 28 26 27 25 31 25 26 35 31 30 33 29 33 36 34 37 38 35 36 38 37 35 41 41 34 34 36 Time(sec) 29. 48 58. 5 38. 4 41. 7 44. 3 71. 3 64. 7 66. 4 65. 6 69. 6 55. 21 47. 40 43. 42 69. 64 45. 7 46. 07 77. 43 59. 5 51. 74 49. 89 52. 5 50. 6 13. 8 13. 2 13. 5 13. 6 14. 5 13. 9 16. 08 36 ﻣﻨﺎﺑﻊ پیﺸﻨﻬﺎﺩﺍﺕ ﻧﺘﺎیﺞ ﺣﻞ ﻣﺴﺎﻟﻪ 2 BPP ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی 1 BPP ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی پیﺸیﻨﻪ ﺗﺤﻘیﻖ ﻣﻘﺪﻣﻪ

N 2 C 1 W ﻧﺘیﺠﻪ ﺣﻞ ﻣﺴﺎﺋﻞ N=150 , C=100 W 1∊[1, 100] W 2∊[20, 100] W 3∊[30, 100] Instance N 2 C 1 W 1 -A N 2 C 1 W 1 -C N 2 C 1 W 1 -E N 2 C 1 W 1 -G N 2 C 1 W 1 -I N 2 C 1 W 1 -K N 2 C 1 W 1 -M N 2 C 1 W 1 -O N 2 C 1 W 1 -Q N 2 C 1 W 1 -S N 2 C 1 W 2 -B N 2 C 1 W 2 -D N 2 C 1 W 2 -F N 2 C 1 W 2 -H N 2 C 1 W 2 -J N 2 C 1 W 2 -L N 2 C 1 W 2 -N N 2 C 1 W 2 -P N 2 C 1 W 2 -R N 2 C 1 W 2 -T N 2 C 1 W 4 -A N 2 C 1 W 4 -C N 2 C 1 W 4 -E N 2 C 1 W 4 -G N 2 C 1 W 4 -I N 2 C 1 W 4 -K N 2 C 1 W 4 -M N 2 C 1 W 4 -O N 2 C 1 W 4 -Q N 2 C 1 W 4 -S BISON 48 46 58 60 62 55 46 48 46 45 61 74 65 70 67 62 64 68 67 66 73 77 73 71 73 70 72 80 75 80 GES with MTRP 48 46 58 60 62 55 46 48 46 45 61 74 65 70 67 62 64 68 67 66 73 77 73 71 73 70 72 80 75 80 Time(sec) 17. 3 18. 4 19. 5 18. 7 17. 6 20. 0 17. 8 18. 1 19. 2 19. 0 18. 9 19. 3 19. 2 19. 4 18. 7 18. 2 18. 4 19. 0 18. 8 18. 9 19. 1 20. 0 19. 7 19. 8 20. 1 20. 3 20. 2 20. 0 19. 9 37 ﻣﻨﺎﺑﻊ پیﺸﻨﻬﺎﺩﺍﺕ ﻧﺘﺎیﺞ ﺣﻞ ﻣﺴﺎﻟﻪ 2 BPP ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی 1 BPP ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی پیﺸیﻨﻪ ﺗﺤﻘیﻖ ﻣﻘﺪﻣﻪ

N 3 C 1 W ﻧﺘیﺠﻪ ﺣﻞ ﻣﺴﺎﺋﻞ N=200 , C=100 instance N 3 C 1 W 1 -A N 3 C 1 W 1 -C N 3 C 1 W 1 -E N 3 C 1 W 1 -G N 3 C 1 W 1 -I N 3 C 1 W 1 -K N 3 C 1 W 1 -M N 3 C 1 W 1 -O N 3 C 1 W 1 -Q N 3 C 1 W 1 -S N 3 C 1 W 2 -A N 3 C 1 W 2 -C N 3 C 1 W 2 -E N 3 C 1 W 2 -G N 3 C 1 W 2 -I N 3 C 1 W 2 -K N 3 C 1 W 2 -M N 3 C 1 W 2 -O N 3 C 1 W 2 -Q N 3 C 1 W 2 -S N 3 C 1 W 4 -A N 3 C 1 W 4 -C N 3 C 1 W 4 -E N 3 C 1 W 4 -G N 3 C 1 W 4 -I N 3 C 1 W 4 -K N 3 C 1 W 4 -M N 3 C 1 W 4 -O N 3 C 1 W 4 -Q N 3 C 1 W 4 -S W 1∊[1, 100] BISON 105 99 98 111 100 102 106 98 98 100 125 132 126 120 136 127 135 130 149 146 142 148 140 147 149 143 146 145 W 2∊[20, 100] GES with MTRP 105 99 98 111 100 102 106 98 98 100 125 132 126 120 136 127 135 130 149 146 142 148 140 147 149 143 146 145 W 3∊[30, 100] Time(sec) 35. 4 35. 6 35. 7 36. 1 36. 2 35. 9 36. 4 36. 7 36. 8 37. 0 37. 1 37. 2 37. 1 37. 4 37. 5 37. 4 37. 6 37. 8 37. 7 37. 9 37. 8 37. 7 37. 6 37. 7 37. 8 37. 7 37. 5 37. 6 38 ﻣﻨﺎﺑﻊ پیﺸﻨﻬﺎﺩﺍﺕ ﻧﺘﺎیﺞ ﺣﻞ ﻣﺴﺎﻟﻪ 2 BPP ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی 1 BPP ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی پیﺸیﻨﻪ ﺗﺤﻘیﻖ ﻣﻘﺪﻣﻪ

Hard ﻧﺘیﺠﻪ ﺣﻞ ﻣﺴﺎﺋﻞ INSTANCE M* GGA GES with MTRP Time(sec) Hard 1 57 57 57 133. 6 Hard 2 56 57 56 136. 7 Hard 3 55 56 56 135. 9 Hard 4 56 58 57 138. 1 Hard 5 57 57 57 135. 2 Hard 6 57 57 57 134. 4 Hard 7 55 55 55 133. 7 Hard 8 57 57 57 132. 1 Hard 9 57 57 56 131. 7 Hard 0 56 56 56 139. 9 39 ﻣﻨﺎﺑﻊ پیﺸﻨﻬﺎﺩﺍﺕ ﻧﺘﺎیﺞ ﺣﻞ ﻣﺴﺎﻟﻪ 2 BPP ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی 1 BPP ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی پیﺸیﻨﻪ ﺗﺤﻘیﻖ ﻣﻘﺪﻣﻪ

ﻧﺘیﺠﻪ ﺣﻞ ﻧﻤﻮﻧﻪ ﻣﺴﺎﺋﻞ ﺩﻭ ﺑﻌﺪی - کﻼﺱ 1 H=10 , W=10 N=100 N=60 N=80 INSTANCE time GES Ub Lb 211 29 28 28 150 26 25 24 102 23 23 22 1 235 31 31 31 156 26 26 26 110 19 19 18 2 227 30 29 29 167 28 27 27 113 21 21 21 3 231 30 30 30 169 27 27 27 114 22 22 22 4 236 33 32 32 171 27 26 26 116 19 19 19 5 235 38 37 37 168 28 28 28 115 17 17 17 6 236 28 28 28 172 31 31 31 117 16 16 15 7 236 33 33 33 170 30 29 29 117 21 21 21 8 239 33 31 31 173 30 30 30 114 18 18 18 9 241 38 38 38 173 27 26 26 112 24 24 24 10 40 ﻣﻘﺪﻣﻪ پیﺸیﻨﻪ ﺗﺤﻘیﻖ ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی 1 BPP ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی 2 BPP ﻧﺘﺎیﺞ ﺣﻞ ﻣﺴﺎﻟﻪ پیﺸﻨﻬﺎﺩﺍﺕ ﻣﻨﺎﺑﻊ

ﻧﺘﺎیﺞ ﺣﻞ ﻧﻤﻮﻧﻪ ﻣﺴﺎﺋﻞ ﺩﻭ ﺑﻌﺪی - کﻼﺱ 6 H=300 , W=300 N=100 N=60 N=80 INSTANC E time GES Ub Lb 126 3 3 3 104 3 3 3 89 3 2 2 1 125 4 4 3 104 3 3 3 88 2 2 128 3 3 3 105 3 3 3 87 2 2 2 3 127 3 3 3 103 3 89 2 2 2 4 128 4 3 3 104 3 3 3 88 2 2 2 5 125 4 4 4 105 3 3 3 88 2 2 2 6 130 3 3 3 106 3 3 3 86 2 2 2 7 125 4 4 3 105 4 3 3 89 3 2 2 8 126 4 3 3 107 3 3 3 90 2 2 2 9 124 4 102 3 3 3 87 3 3 3 10 41 ﻣﻘﺪﻣﻪ پیﺸیﻨﻪ ﺗﺤﻘیﻖ ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی 1 BPP ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی 2 BPP ﻧﺘﺎیﺞ ﺣﻞ ﻣﺴﺎﻟﻪ پیﺸﻨﻬﺎﺩﺍﺕ ﻣﻨﺎﺑﻊ

ﻧﺘﺎیﺞ ﺍﺟﺮﺍی ﻧﻤﻮﻧﻪ ﻣﺴﺎﺋﻞ ﺩﻭ ﺑﻌﺪی - کﻼﺱ 10 H=100 , W=100 N=60 N=80 INSTANCE time GES Ub Lb 184 16 15 14 145 14 13 12 161 12 12 11 1 191 17 16 15 150 11 11 10 140 12 12 12 2 197 16 16 15 153 11 11 11 158 11 11 11 3 205 18 18 17 158 14 14 13 160 8 8 7 4 210 19 18 17 161 15 14 14 152 8 8 8 5 195 13 13 13 158 13 13 13 146 13 13 13 6 192 15 14 13 151 14 14 14 157 11 10 10 7 197 18 18 18 138 11 10 10 156 10 10 10 8 198 16 16 16 147 13 13 12 151 9 9 8 9 196 15 151 16 15 14 148 8 10 42 ﻣﻘﺪﻣﻪ پیﺸیﻨﻪ ﺗﺤﻘیﻖ ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی 1 BPP ﺭﻭﺵ ﺣﻞ پیﺸﻨﻬﺎﺩی 2 BPP ﻧﺘﺎیﺞ ﺣﻞ ﻣﺴﺎﻟﻪ پیﺸﻨﻬﺎﺩﺍﺕ ﻣﻨﺎﺑﻊ

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