Fig 1.
Pseudo code of standard HS algorithm.
Fig 2.
Flow chart of HSTLBO.
Fig 3.
Pseudo code of modified HS algorithm.
Fig 4.
Pseudo code of modified TLBO algorithm.
Table 1.
Algorithm parameter settings.
Table 2.
Sixteen complex benchmark functions (F1-F20).
Table 3.
Experimental results of HS, IHS, ITHS, NGHS, EHS and HSTLBO over 20 independent runs on 20 test functions of 1000 variables with 5E+6 FEs.
“Prec” and “Std Dev” denote the precision and standard deviation of the function error values in 20 runs, respectively. Time(s) is the mean run time over 20 independent runs on 5000000 FEs.
Fig 5.
Convergence curves of four functions.
Fig 6.
Box plots of four functions.
Table 4.
Experimental results of TLBO, ATLBO, WTLBO, TLBO_GC, ITLBO and HSTLBO over 20 independent runs on 20 test functions of 1000 variables with 5E+6 FEs.
“Prec” and “Std Dev” denote the precision and standard deviation of the function error values in 20 runs, respectively. Time(s) is the mean run time over 20 independent runs on 5000000 FEs.
Fig 7.
Convergence curves of four functions.
Fig 8.
Box plots of four functions.
Table 5.
Results of Wilcoxon’s rank sum test at 0.05 significance level between HSTLBO and other ten algorithms.
The p-value is shown (NaN denotes no difference).
Table 6.
Multi-problem based statistical pairwise comparison of HSTLBO and other ten algorithms.
(α = 0.05, D = 1000).
Fig 9.
Curves of population diversity of 11 algorithms.
Table 7.
Simulation results of five algorithms on Nikkei index 225.
Fig 10.
Optimal frontiers for unconstraint and constraint portfolio Nikkei index 225.