Mathematical Problems in Engineering

Research Article

A Variable Neighborhood Search Algorithm for the Leather Nesting Problem

Table 9

Evaluating the performance of the VNS algorithm: car model 2.
Initial solutionVNS
Inst. After 200 s After 400 s After 600 s
PiecesUsage PiecesUsagePiecesUsagePieces Usage
1 25 54,81 21,96 26,5056,26 28,5057,56 29,75 58,17
2 31 53,18 32,05 33,0055,69 34,0057,29 35,00 58,63
3 26 55,20 22,69 27,0056,07 29,2557,86 31,50 58,94
4 29 55,72 24,84 30,2556,53 30,7557,60 33,75 59,06
5 36 55,84 34,11 35,7555,94 35,7555,94 36,50 56,50
6 34 61,82 33,11 37,0063,86 37,2564,29 37,25 64,40
7 29 60,80 23,00 29,7561,41 31,5062,64 30,25 63,61
8 51 58,22 58,78 51,0058,22 53,0060,08 54,00 60,60
9 54 57,07 65,56 54,0057,07 55,2559,51 57,25 60,84
10 33 61,56 29,51 34,7562,58 34,7563,62 34,50 64,01
. 34,80 57,42 34,56 35,9058,36 37,0059,64 37,98 60,48
11 22 54,70 24,32 24,5057,78 24,5058,36 24,50 58,53
12 39 54,99 52,38 39,0054,99 40,5055,89 40,75 57,94
13 41 54,86 52,21 41,0054,86 41,7555,37 43,75 57,58
14 39 60,98 53,89 39,0060,98 41,0062,11 41,00 62,11
15 39 52,86 58,48 39,0053,06 39,0053,67 39,50 53,91
16 33 63,44 34,33 33,0063,44 33,0063,93 33,25 63,94
17 35 62,49 33,23 35,0063,21 35,7564,29 38,00 65,83
18 52 58,93 56,82 52,0058,93 54,0060,31 54,75 60,42
19 50 55,95 76,14 50,0055,95 50,5057,28 51,25 58,41
20 29 60,30 31,73 30,5060,86 32,5061,84 36,50 63,73
. 37,90 57,95 47,35 38,3058,41 39,2559,30 40,33 60,24
21 25 57,38 33,19 25,0057,38 28,0060,96 27,75 61,42
22 39 54,99 60,14 39,0054,99 39,2555,38 41,25 56,86
23 50 59,07 69,43 50,0059,07 50,0059,07 50,00 59,17
24 31 64,53 37,23 31,0064,53 31,5064,67 31,50 64,67
25 39 52,80 70,57 39,0052,80 38,5055,24 39,50 56,01
26 30 62,50 35,50 32,0063,09 36,2564,45 37,75 64,75
27 33 64,86 39,78 33,5065,14 35,7566,41 36,00 66,54
28 50 56,69 74,65 50,0056,91 50,0057,00 51,00 57,71
29 39 61,50 63,95 39,0061,50 39,7561,79 41,50 62,84
30 32 62,11 41,71 32,2562,25 33,0062,76 39,00 65,52
. 36,80 59,64 52,61 37,0859,77 38,2060,77 39,53 61,55
31 31 61,41 43,98 31,0061,41 35,0063,42 36,75 63,84
32 39 54,35 73,25 39,0054,35 39,0054,35 39,50 55,97
33 48 59,16 77,47 48,0059,16 49,0059,68 50,00 60,21
34 31 65,21 45,09 31,0065,21 31,0065,21 31,75 65,33
35 54 60,74 91,89 54,0060,74 54,0060,74 54,00 60,74
. 40,60 60,17 66,34 40,6060,17 41,6060,68 42,40 61,22
36 31 61,99 53,78 31,0061,99 35,0064,07 38,00 64,18
37 48 59,44 91,20 48,0059,44 48,0059,44 49,50 60,03
38 47 56,75105,12 47,0056,75 48,5057,40 53,00 58,91
39 32 64,72 51,62 32,0064,72 32,0064,72 38,50 67,23
40 54 60,42106,47 54,0060,42 54,0060,42 54,00 60,42
. 42,40 60,66 81,64 42,4060,66 43,5061,21 46,60 62,15
41 34 64,87 73,84 34,0064,87 34,0064,87 39,00 66,89