Mathematical Problems in Engineering

Research Article

A Variable Neighborhood Search Algorithm for the Leather Nesting Problem

Table 8

Evaluating the performance of the VNS algorithm: car model 1 (part II).
Initial solutionVNS
Inst. After 200 s After 400 s After 600 s
PiecesUsage PiecesUsagePiecesUsagePieces Usage
11; 1 20 58,51 19,50 20,0059,99 23,0061,06 29,00 61,27
11; 2 24 60,48 23,76 24,0060,48 24,0060,48 24,00 60,48
11; 3 22 59,45 28,67 22,0059,45 25,0061,03 27,50 62,62
12; 1 19 60,18 21,63 20,2561,61 22,0061,79 28,50 62,54
12; 2 22 60,52 24,69 22,0060,94 24,0062,24 25,75 62,53
12; 3 25 61,38 31,02 25,0061,38 25,0061,38 30,75 64,33
13; 1 19 58,19 18,28 20,5060,28 21,2561,98 26,00 64,42
13; 2 21 58,27 21,64 21,0058,27 23,7559,61 26,75 61,56
13; 3 23 59,53 25,86 23,0059,53 25,0062,75 28,25 63,73
14; 1 20 60,19 20,74 20,0060,19 25,2563,77 25,25 63,77
14; 2 23 59,94 25,22 23,0059,94 24,7560,53 26,50 61,11
14; 3 23 59,62 29,89 23,0059,62 25,5061,53 27,75 63,07
15; 1 19 58,12 17,75 20,0059,17 24,7562,73 25,50 63,78
15; 2 24 61,55 22,05 24,0061,55 26,0062,41 26,00 62,41
15; 3 23 59,81 25,21 23,0059,81 26,2563,99 29,25 64,42
. 21,80 59,72 23,73 22,0560,15 24,3761,82 27,12 62,80
16; 1 19 58,19 24,57 19,7559,44 20,5060,71 22,25 62,76
16; 2 21 58,27 29,69 21,0058,27 24,0059,82 26,00 60,67
16; 3 23 59,53 37,42 23,0059,53 24,5059,75 27,25 63,65
17; 1 19 59,15 23,91 19,2559,60 23,0061,81 25,00 61,94
17; 2 21 59,09 28,67 21,0059,09 23,5061,76 24,75 62,55
17; 3 23 59,96 35,12 23,0059,96 25,0064,19 26,75 64,21
18; 1 19 58,12 22,15 20,0059,65 21,0060,40 24,50 62,63
18; 2 24 61,55 27,99 24,0061,55 25,7563,23 26,00 63,24
18; 3 23 60,33 33,58 23,0060,33 24,5062,97 26,25 62,17
. 21,33 59,35 29,23 21,5659,71 23,5361,63 25,42 62,65
19; 1 49 69,68 38,48 49,0069,68 49,2569,94 50,00 71,44
19; 2 45 67,27 41,82 45,0067,27 46,5067,48 46,25 67,54
19; 3 47 66,57 51,30 47,0066,57 47,0066,57 45,25 68,71
20; 1 76 73,17 51,42 76,0073,17 78,0073,55 80,50 74,21
20; 2 69 72,29 52,96 69,0072,29 69,0072,29 66,75 72,34
20; 3 81 72,42 64,93 81,0072,42 81,0072,42 95,75 72,66
21; 1 48 69,05 38,04 48,0069,05 46,2569,56 44,00 70,84
21; 2 43 67,57 40,68 43,0067,57 43,0067,57 43,00 67,57
21; 3 46 66,78 48,15 46,0066,78 45,7566,95 50,50 68,05
. 56,00 69,42 47,53 56,0069,42 56,1969,59 58,00 70,37
22; 1 84 73,88 99,30 84,0073,88 84,0073,88 84,67 74,08
22; 2 81 74,51100,37 81,0074,51 81,0074,51 81,00 74,52
22; 3 90 73,78116,76 90,0073,78 90,0073,78 90,00 73,86
. 85,00 74,06105,48 85,0074,06 85,0074,06 85,22 74,15