Mathematical Problems in Engineering / 2018 / Article / Tab 1

Research Article

Assembly Line Balancing Based on Beam Ant Colony Optimisation

Table 1

Results of benchmark instances.

InstancesCOptimalPriority ruleACO-BSDifferenceSolutionRunning time [s]
avg.std.avg.std.

Arcus1378621222112103.4370.077
Arcus211570131413113065.41760.831
Barthol28451525115107.5750.127
Barthol285505151000.2540.022
Barthol28749504914907.8180.161
Barthol28948494814808.2770.182
Barthol29147484714708.3330.257
Barthol29346474614608.0340.201
Barthol29545464514508.1930.153
Barthol29744454414408.0130.175
Barthol29943444314309.6563.344
Barthol2101424342142011.6057.768
Barthol210441424114108.3380.182
Barthol2106404140140010.0943.506
Barthol210939403913908.6750.203
Barthol211238393813808.5830.197
Barthol211537383713708.7580.174
Barthol211836373613608.8640.127
Barthol2121353635135011.5904.274
Barthol212534353413408.8860.153
Barthol212933343313309.1450.144
Barthol213332333213209.1070.175
Barthol213731323113109.1900.115
Barthol2146293029129010.0812.874
Barthol215228292812809.3090.130
Barthol215727282712709.2330.117
Barthol216326272612609.2320.118
Barthol217025262512509.3060.109
Barthold40314151411408.0930.255
Barthold43413141311308.5970.108
Barthold47012131211208.6910.130
Barthold51311121111108.6180.131
Barthold62691091908.4230.103
Buxey418981800.8120.014
Buxey4778717016.9774.762
Gunther5491091901.0350.011
Heskiaoff2055651501.0500.031
Jackson105651500.0810.015
Kilbridge698981801.7840.065
Kilbridge797871701.7580.022
Kilbridge926761601.7360.050
Kilbridge1384541401.5670.035
Lutz21149504914908.5616.649
Lutz21244474430.52799.25384.952
Lutz21340424024007.1496.477
Lutz21437383710.48361.574105.705
Lutz21534353413407.5674.152
Lutz21631333123108.8135.541
Lutz217293029129014.6196.265
Lutz218282928128027.18511.602
Lutz21926272612608.4935.250
Lutz22025262512502.6880.081
Lutz22124252412402.7480.078
Lutz311015161510.42231.93942.531
Lutz311814151410.51682.378107.850
Mansoor623431300.1300.007
Mukherje20122232212204.6980.094
Sawyer418981800.9590.020
Sawyer4778710.316225.300145.082
Tonge25114151410.48317.31536.100
Tonge32011121111103.5750.079
Warnecke54313231131050.68547.707
Warnecke56293029129020.74014.768
Warnecke60272928107.9985.720
Warnecke62272827127021.70116.420
Warnecke6525272512504.1522.172
Warnecke68242524124013.87411.894
Warnecke71232423123014.07613.767
Warnecke8220212012003.3932.080
Warnecke9217181711704.4333.124
Warnecke10415161511502.2660.037
Warnecke11114151411403.0531.544
Wee-mag3062636216206.4442.356
Wee-mag4634353413408.8946.803
Wee-mag473233330010.0195.176
Wee-mag5231323113104.0560.040
Wee-mag5630313013004.1130.034
Scholl1394505151007.5319.124
Scholl145248494810.31624.0507.363
Scholl14834748480012.25619.041
Scholl15154647470013.60010.953
Scholl158444454410.31675.227118.097
Scholl1659424343003.5680.032
Scholl174240414010.42247.94766.518
Scholl178739403910.422174.619130.467
Scholl183438393810.422200.751111.410
Scholl188337383800149.149160.662
Scholl193536373700185.443149.573
Scholl199135363510.316200.308113.994
Scholl20493435350045.25618.299
Scholl21113334340050.16574.052
Scholl217732333210.483156.656103.493
Scholl22473132320047.58024.497
Scholl232230313010.31675.18789.942
Scholl240229302910.516141.810110.054
Scholl248828292810.48360.10169.595
Scholl258027282710.422142.472102.649
Scholl2680262726126035.80416.163
Scholl2787252625125049.83228.863

Note.indicates that an optimal solution is found; beside the average of solution indicates trickiness.

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