Table 4: In this table, the performance of GAHS is compared with the other HS variants. All scores are averaged over 50 runs, and all functions except Goldstein-Price are implemented in 100 dimensions. The optimisers were allowed to run for 500,000 function evaluations except for Goldstein-Price which was allowed only 10,000 evaluations. The best results are again indicated in bold.

Ackley Griewank Rosenbrock Rastrigin Goldstein-Price%

HS
 Best 0.0142 0.0050 162.5829 0.2280 6.8464
 Standard deviation 0.0004 0.0080 49.5829 0.0130 9.3353
 Hits 50 34 0 0 42
DLHS
 Best 0.2281 0.0004 142.4515 1.3140 6.2444
 Standard deviation 0.0130 0.0070 39.5126 3.1364 8.7724
 Hits 50 50 0 32 44
EHS
 Best 0.0009 0.0001 97.2555 388.2894 4.0809
 Standard deviation 0.0006 0.0007 7.4711 20.5949 5.2910
 Hits 50 50 0 0 48
AHS
 Best 0.00030 96.4333 6.7471 3
 Standard deviation 0.00060 0.2943 2.3279 0
 Hits 5050 0 0 50
GAHS
 Best 0.0263 0.0049 96.40340.06333
 Standard deviation 0.0125 0.0021 0.78330.03370
 Hits 50 49 04450

The accuracy tolerance for awarding a successful hit on the global minimum was decreased to 0.1 for 100-dimensional Rastrigin’s function.
%Goldstein-Price was implemented in two dimensions as it is only defined in two.