Research Article

Annealing Ant Colony Optimization with Mutation Operator for Solving TSP

Table 3

A comparison of the proposed algorithm with Chen and Chien [27] and Wang et al. [41] according to the best solution, average solution, standard deviation, the percentage deviation of the average solution (), and the percentage deviation of the best solution () found by the algorithms.

InstanceOpt.MethodBestAverageStd. dev.

eil51426Proposed algorithm4264260.0000.0000.000
Chen and Chien [27]427427.270.4500.2350.298
Wang et al. [41]426426N/A0.0000.000
eil76538Proposed algorithm5385380.0000.0000.000
Chen and Chien [27]538540.22.9400.0000.409
Wang et al. [41]538538N/A0.0000.000
eil101629Proposed algorithm6296290.0000.0000.000
Chen and Chien [27]630635.233.5900.1590.990
Wang et al. [41]629629N/A0.0000.000
berlin527542Proposed algorithm754275420.0000.0000.000
Chen and Chien [27]754275420.0000.0000.000
Wang et al. [41]75427542N/A0.0000.000
bier127118282Proposed algorithm1182821182820.0000.0000.000
Chen and Chien [27]118282119421.8580.8300.0000.964
Wang et al. [41]118282118282ā€‰0.0000.000
ch1306110Proposed algorithm611061100.0000.0000.000
Chen and Chien [27]61416205.6343.7000.5071.565
Wang et al. [41]61106112.4ā€‰0.0000.039
ch1506528Proposed algorithm652865280.0000.0000.000
Chen and Chien [27]65286563.722.4500.0000.547
Wang et al. [41]65286531.84N/A0.0000.059
rd1007910Proposed algorithm791079100.0000.0000.000
Chen and Chien [27]79107987.5762.0600.0000.981
Wang et al. [41]79107910N/A0.0000.000
lin10514379Proposed algorithm14379143790.0000.0000.000
Chen and Chien [27]1437914406.3737.2800.0000.190
Wang et al. [41]1437914379N/A0.0000.000
lin31842029Proposed algorithm4202942042.442.3750.0000.032
Chen and Chien [27]4248743002.9307.5101.0902.317
Wang et al. [41]4208142204.16N/A0.1240.417
kroA10021282Proposed algorithm21282212820.0000.0000.000
Chen and Chien [27]2128221370.47123.3600.0000.416
Wang et al. [41]2128221284.24N/A0.0000.011
kroA15026524Proposed algorithm26524265240.0000.0000.000
Chen and Chien [27]2652426899.2133.0200.0001.415
Wang et al. [41]2652426528.12N/A0.0000.016
kroA20029368Proposed algorithm29368293680.0000.0000.000
Chen and Chien [27]2938329738.73356.0700.0511.262
Wang et al. [41]2936829374.84N/A0.0000.023
kroB10022141Proposed algorithm22141221410.0000.0000.000
Chen and Chien [27]2214122282.87183.9900.0000.641
Wang et al. [41]2214122186.28N/A0.0000.205
kroB15026130Proposed algorithm26130261300.0000.0000.000
Chen and Chien [27]2613026448.33266.7600.0001.218
Wang et al. [41]2613026133.2N/A0.0000.012
kroB20029437Proposed algorithm29437294370.0000.0000.000
Chen and Chien [27]2954130035.23357.4800.3532.032
Wang et al. [41]2943729439.64N/A0.0000.009
kroC10020749Proposed algorithm20749207490.0000.0000.000
Chen and Chien [27]2074920878.97158.6400.0000.626
Wang et al. [41]2074920749N/A0.0000.000
kroD10021294Proposed algorithm21294212940.0000.0000.000
Chen and Chien [27]2130921620.47226.6000.0701.533
Wang et al. [41]2129421297.2N/A0.0000.015
kroE10022068Proposed algorithm22068220680.0000.0000.000
Chen and Chien [27]2206822183.47103.3200.0000.523
Wang et al. [41]2206822075.52N/A0.0000.034
rat5756773Proposed algorithm67776787.110.1260.0590.208
Chen and Chien [27]68916933.8727.6201.7422.375
Wang et al. [41]68076830.88N/A0.5020.855
rat7838806Proposed algorithm88118829.715.0190.0570.269
Chen and Chien [27]89889079.2352.6902.0673.103
Wang et al. [41]88598877.92N/A0.6020.817
rl1323270199Proposed algorithm270309270841.7403.4340.0410.238
Chen and Chien [27]277642280181.51761.6602.7553.694
Wang et al. [41]270919271481.6N/A0.2660.475
fl140020127Proposed algorithm2019420233.426.0140.3330.529
Chen and Chien [27]2059321349.63527.8802.3156.075
Wang et al. [41]2031420428.48N/A0.9291.498
d165562128Proposed algorithm6229162457.590.3880.2620.530
Chen and Chien [27]6415165621.131031.9403.2565.622
Wang et al. [41]6246362670.52N/A0.5390.873