Research Article

Modified Backtracking Search Optimization Algorithm Inspired by Simulated Annealing for Constrained Engineering Optimization Problems

Table 7

Comparison of the best values and FEs obtained by BSAISA and other algorithms.

Alg.BSAISASRFSACDEAMAMABCRPGABSA-SA
Fun.Best (FEs)Best (FEs)Best (FEs)Best (FEs)Best (FEs)Best (FEs)Best (FEs)Best (FEs)

G01−15−15.000−14.993316−15.000000−15.000−15.000−15.000−15.000000
(84,630)(148,200)(205,748)(100,100)(350,000)(350,000)(350,000)(350,000)
G02−0.8036−0.8035−0.7549−0.8036−0.8035−0.8036−0.8036−0.8036
(349,500)(217,200)(227,832)(100,100)(350,000)(350,000)(350,000)(350,000)
G03−1.000498−1.000−1.0000015−0.995413−1.000−1.000−1.000−1.000498
(58,560)(229,200)(314,938)(100,100)(350,000)(350,000)(350,000)(350,000)
G04−30665.539−30665.539−30665.538−30665.539−30665.538−30665.539−30665.539−30665.539
(121,650)(88,200)(86,154)(100,100)(350,000)(350,000)(350,000)(350,000)
G055126.4975126.4975126.49815126.5715126.5125126.4875126.5445126.497
(238,410)(51,600)(47,661)(100,100)(350,000)(350,000)(350,000)(350,000)
G06−6961.814−6961.814−6961.814−6961.814−6961.807−6961.814−6961.814−6961.814
(89,550)(118,000)(44,538)(100,100)(350,000)(350,000)(350,000)(350,000)
G0724.30724.30724.31124.30624.31524.32424.33324.306
(15,060)(143,000)(404,501)(100,100)(350,000)(350,000)(350,000)(350,000)
G08−0.095825−0.095825−0.095825−0.095825−0.095825−0.095825−0.095825−0.095825
(30,930)(76,200)(56,476)(100,100)(350,000)(350,000)(350,000)(350,000)
G09680.630057680.630680.63008680.630057680.645680.631680.631680.6301
(347,760)(111,400)(324,569)(100,100)(350,000)(350,000)(350,000)(350,000)
G107049.2497054.3167059.8647049.2487281.9577058.8237049.8617049.278
(346,980)(128,400)(243,520)(100,100)(350,000)(350,000)(350,000)(350,000)
G110.7499000.7500.7499990.7499000.7500.7500.7490.749900
(87,870)(11,400)(23,722)(100,100)(350,000)(350,000)(350,000)(350,000)
G12−1−1.000000−1.000000−1.000000−1.000−1.000NA−1.000000
(5430)(16,400)(59,355)(100,100)(350,000)(350,000)(350,000)
G130.05394150.0539570.05394980.0561800.0539470.757NA0.0539415
(349,800)(69,800)(120,268)(100,100)(350,000)(350,000)(350,000)
Nu.
RK15728463

Note. “NA” means not available. The same as Tables 8, 10, 11, 12, 13, 14, 15, and 17. “RK” represents the comprehensive ranking of each algorithm on the set of benchmarks. “Nu.” represents the sum of the number of winners and the number of the optimal function values for each algorithm on the set of benchmarks.