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Table 5:
Differences between Algorithms 3 and 4. Only those functions are listed for which both algorithms found different minimum cost function values. In half of the listed cases (marked with an asterisk (*)), both algorithms are mathematically identical, since the removed branches from Algorithm 3 were actually never executed. In the remaining half of the cases, the number of executions of the removed branches equals a half percent or less of all iterations. All the exactly computed minima (up to at least double precision) are written in bold.
Algorithm 3Algorithm 4
Test Function (n)NCFMinimumNCFMinimum
Rosenbrock (2) 867 4.4373 692 1.2325 
Gulf research (3) 16324 4.3122 15119 1.3240 
Brown almost linear (5) 2788 0.0 2129 8.0118 
Brown almost linear (7) 4104 7.8886 3249 1.9721 
Variably dimensioned (8) 7160 1.0292 5816 9.3184 
Penalty II (10) 1543 3.0000 30721 2.9366 
Quadratic (16) 112564 0.0 48917 1.6304 
Quadratic (24) 158849 8.0493 48918 1.5467 
Algorithm 3Algorithm 4
Test Function (n)NCFMinimumNCFMinimum
Rosenbrock (2) 867 4.4373 692 1.2325 
Gulf research (3) 16324 4.3122 15119 1.3240 
Brown almost linear (5) 2788 0.0 2129 8.0118 
Brown almost linear (7) 4104 7.8886 3249 1.9721 
Variably dimensioned (8) 7160 1.0292 5816 9.3184 
Penalty II (10) 1543 3.0000 30721 2.9366 
Quadratic (16) 112564 0.0 48917 1.6304 
Quadratic (24) 158849 8.0493 48918 1.5467 
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