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Table 6 Experimental results for ADVRP instances with \(D_{{{{{\text{max}}}}}(3)}=0.9 \times LT(2)\)

From: A hybrid metaheuristic for solving asymmetric distance-constrained vehicle routing problem

# vertices # vehicles p MS5BB (OPT) HVT
Best.Sol Aver.Sol \(\hbox {Gap}_1\) Time
40 4 1 171 171 171 0 0.55
60 3 2 (223) 225 225 0.9 1.65
60 3 3 (193) 195 195 1.04 1.54
60 6 1 (203) 206 206 1.48 1.54
60 6 2 254 244 244 0 1.58
60 6 4 (239) 229 229 0 1.43
80 8 1 231 236 236 2.16 4.78
80 8 2 (282) 271 271 0 4.98
80 8 3 (243) 243 243 0 4.88
80 8 4 238 261 261 9.66 4.77
100 5 1 inf 270 270 inf 17.41
100 5 2 256 Inf inf inf 17.98
100 10 1 232 253 253 9.05 17.12
100 10 2 309 299 299 0 17.23
100 10 3 (271) 276 276 1.85 17.54
100 10 4 (inf) 280 280 inf 17.12
120 12 1 269 303 303 12.64 74.32
120 12 2 (330) 333 333 0.91 73.93
120 12 4 308 346 346 12.34 71.32
140 14 1 280 310 312 10.71 84.65
140 14 2 334 347 348 3.89 89.65
140 14 4 326 354 356 8.59 84.65
160 16 1 309 346 348 11.97 95.65
160 16 2 365 377 379 3.29 94.68
160 16 4 (328) 365 367 11.28 105.65
180 18 2 392 408 408 4.08 98.65
180 18 3 (inf) 395 398 inf 114.65
180 18 4 347 394 395 13.54 99.65
200 20 2 394 424 427 7.61 114.65
200 20 4 364 414 418 13.74 165.23