From: A hybrid metaheuristic for solving asymmetric distance-constrained vehicle routing problem
# vertices | # vehicles | p | OPT (M5SBB) | VNS | HVT | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Best.Sol | \(\hbox {Gap}_1\) | Time | Best.Sol | Aver.Sol | \(\hbox {Gap}_1\) | Gap Best-to-Best | Time | ||||
40 | 2 | 1 | inf | inf | inf | inf | 157 | 157 | inf | inf | 0.45 |
40 | 2 | 2 | inf | inf | inf | inf | 214 | 214 | inf | inf | 0.44 |
40 | 2 | 3 | (180) | 188 | 4.44 | 100 | 176 | 176 | 2.22 | − 6.38 | 0.47 |
40 | 2 | 4 | 187 | 202 | 8.02 | 100 | 187 | 187 | 0.00 | − 7.43 | 0.47 |
40 | 4 | 1 | (171) | 177 | 3.51 | 100 | 169 | 169 | 1.17 | − 4.52 | 0.43 |
40 | 4 | 2 | 224 | 228 | 1.79 | 100 | 224 | 224 | 0.00 | − 1.75 | 0.45 |
40 | 4 | 4 | inf | inf | inf | inf | 223 | 223 | inf | inf | 0.46 |
60 | 3 | 2 | 222 | 241 | 8.56 | 100.05 | 230 | 230 | 3.60 | − 4.56 | 1.54 |
60 | 3 | 3 | 192 | 213 | 10.94 | 100 | 198 | 198 | 3.13 | − 7.04 | 1.46 |
60 | 3 | 4 | 205 | 218 | 6.34 | 100.03 | 205 | 205 | 0.00 | − 5.96 | 1.46 |
60 | 6 | 1 | 203 | 217 | 6.9 | 100.02 | 215 | 215 | 5.91 | − 0.92 | 1.53 |
60 | 6 | 2 | (254) | 265 | 4.33 | 100.06 | 252 | 252 | 0.79 | − 4.91 | 1.57 |
60 | 6 | 3 | (228) | 234 | 2.63 | 100.05 | 221 | 221 | 3.07 | − 5.56 | 1.6 |
60 | 6 | 4 | 238 | 254 | 6.72 | 100.02 | 238 | 238 | 0.00 | − 6.30 | 1.45 |
80 | 4 | 1 | 198 | 228 | 15.15 | 100.05 | 219 | 219 | 10.61 | − 3.95 | 4.56 |
80 | 4 | 2 | 237 | 260 | 9.7 | 100.02 | 249 | 249 | 5.06 | − 4.23 | 4.59 |
80 | 4 | 3 | 211 | 233 | 10.43 | 100.03 | 211 | 211 | 0.00 | − 9.44 | 4.45 |
80 | 4 | 4 | 215 | 250 | 16.28 | 100.03 | 215 | 215 | 0.00 | − 14.00 | 4.29 |
80 | 8 | 1 | 231 | 252 | 9.09 | 100.03 | 239 | 239 | 3.46 | − 5.16 | 4.35 |
80 | 8 | 2 | (281) | 302 | 7.47 | 100.05 | 276 | 276 | 1.78 | − 8.61 | 4.66 |
80 | 8 | 3 | 242 | 255 | 5.37 | 100.2 | 261 | 261 | 7.85 | 2.35 | 4.32 |
80 | 8 | 4 | 238 | 251 | 5.46 | 100.19 | 238 | 238 | 0.00 | − 5.18 | 4.62 |
100 | 5 | 2 | 256 | 287 | 12.11 | 100.17 | 279 | 279 | 8.98 | − 2.79 | 17.6 |
100 | 10 | 1 | 232 | 259 | 11.64 | 100.08 | 238 | 238 | 2.59 | − 8.11 | 16.36 |
100 | 10 | 2 | 309 | 331 | 7.12 | 100.08 | 315 | 315 | 1.94 | − 4.83 | 16.53 |
100 | 10 | 3 | 270 | 292 | 8.15 | 100.23 | 271 | 271 | 0.37 | − 7.19 | 16.29 |
100 | 10 | 4 | 255 | 276 | 8.24 | 100.22 | 279 | 279 | 9.41 | 1.09 | 16.27 |
120 | 12 | 1 | 269 | 292 | 8.55 | 100.56 | 282 | 282 | 4.83 | − 3.42 | 73.66 |
120 | 12 | 2 | 329 | inf | inf | inf | 331 | 331 | 0.61 | inf | 73.93 |
120 | 12 | 3 | 277 | 309 | 11.55 | 100.06 | 291 | 291 | 5.05 | − 5.83 | 71.98 |
120 | 12 | 4 | 308 | 339 | 10.06 | 100.02 | 339 | 339 | 10.06 | 0.00 | 70.8 |
140 | 14 | 1 | 280 | 317 | 13.21 | 100.38 | 288 | 288.6 | 2.86 | − 9.15 | 84.4 |
140 | 14 | 2 | 334 | 360 | 7.78 | 100.11 | 342 | 342.8 | 2.40 | − 5.00 | 88.34 |
140 | 14 | 3 | 283 | 324 | 14.49 | 100.17 | 307 | 307.3 | 8.48 | − 5.25 | 85.73 |
140 | 14 | 4 | 326 | 346 | 6.13 | 100.31 | 346 | 346.7 | 6.13 | 0.00 | 83.88 |
160 | 16 | 1 | 309 | 354 | 14.56 | 100.23 | 347 | 348.9 | 12.30 | − 1.98 | 97.72 |
160 | 16 | 2 | (365) | inf | inf | inf | 346 | 347.6 | 5.21 | inf | 97.76 |
160 | 16 | 3 | 310 | 345 | 11.29 | 100.19 | 324 | 324.9 | 4.52 | − 6.09 | 99.32 |
180 | 18 | 2 | (392) | inf | inf | inf | 369 | 374.6 | 5.87 | inf | 110.53 |
180 | 18 | 4 | 347 | 386 | 11.24 | 100.27 | 386 | 368.6 | 11.24 | 0.00 | 110.82 |
200 | 10 | 2 | 322 | 376 | 16.77 | 101.25 | 376 | 376.8 | 16.77 | 0.00 | 121.22 |
200 | 20 | 3 | 358 | 401 | 12.01 | 100.41 | 401 | 409.8 | 12.01 | 0.00 | 116.4 |