Mathematical Problems in Engineering

Research Article

A Variable Neighborhood Search Algorithm for the Leather Nesting Problem

Table 7

Evaluating the performance of the VNS algorithm: car model 1 (part I).
Initial solutionVNS
Inst.After 200 sAfter 400 sAfter 600 s
PiecesUsage PiecesUsagePiecesUsagePieces Usage
1; 1 2259,5312,86 22,5059,61 25,0060,01 27,50 61,09
1; 2 2357,9315,04 27,5059,31 29,7559,93 31,00 60,14
1; 3 2561,5719,12 25,0062,34 25,7562,95 26,75 63,12
2; 1 1656,1113,01 16,5057,63 18,0057,90 20,75 58,97
2; 2 1754,4314,43 19,0055,67 24,2558,27 25,25 58,95
2; 3 2055,7718,25 20,5057,18 23,0059,04 25,00 60,24
3; 1 946,02 9,00 14,7554,60 15,5055,26 17,25 55,19
3; 2 1451,9211,98 15,7552,84 18,0054,78 18,00 54,91
3; 3 1854,7714,89 18,5056,04 22,0057,41 23,50 59,76
4; 1 1251,6811,01 15,7555,31 16,0056,10 16,00 56,10
4; 2 1350,1312,45 16,0052,58 18,2554,68 19,00 55,51
4; 3 1551,8716,31 15,7552,82 18,7556,96 21,00 58,81
5; 1 1351,51 9,06 21,0060,67 25,2560,81 24,50 61,77
5; 2 1855,3811,87 21,2558,00 24,2559,24 27,25 60,30
5; 3 2660,9916,86 26,0060,99 34,5061,53 34,75 61,56
. 17,4054,6413,74 19,7257,04 22,5558,32 23,83 59,10
6; 1 2059,1216,49 20,5059,67 23,5061,28 25,75 62,27
6; 2 2461,5618,72 24,7561,82 25,0062,26 25,00 62,26
6; 3 2360,3622,39 24,5060,99 25,5061,75 25,75 62,53
7; 1 1757,5018,43 18,2559,07 19,2561,77 19,75 62,22
7; 2 1957,5820,85 20,0059,10 22,7559,34 24,75 60,77
7; 3 2258,6126,46 24,0061,27 24,2561,55 24,25 61,55
8; 1 2058,9215,53 21,0059,90 22,7561,66 24,25 62,46
8; 2 2260,0619,53 22,7560,32 23,0061,03 25,50 61,57
8; 3 2460,5123,06 24,0060,51 25,2560,93 27,75 63,10
9; 1 1250,7816,58 13,7554,04 14,7554,47 15,25 54,90
9; 2 1350,1319,33 13,0050,13 17,2557,01 18,50 58,05
9; 3 1450,4023,81 14,5051,13 18,0054,88 21,00 58,78
10; 1 2058,9215,26 21,0060,55 22,5061,90 27,75 62,52
10; 2 2360,6519,40 24,5063,06 25,2564,01 25,25 64,01
10; 3 2561,3723,48 27,2562,41 28,7563,47 29,00 63,69
. 19,8757,7619,95 20,9258,93 22,5260,49 23,97 61,38