From: Philippe Bonnardel <100604.1637@CompuServe.COM>
Date: 29 Apr 96 19:42:04 EDT
Subject: Global optimization test result

Function:               Result:         No. function calls:     Error Tolerance:

PERM(4,50)              2.4e-07         ~75 000                 1.0e-07
PERM(4,0.5)             1.9e-07         ~350 000                1.0e-07
PERM(4,0.005)           2.2e-08         ~750 000                1.0e-07

PERMO(4,10)             4.5e-10         ~65 000                 1.0e-10
PERMO(4,1)              9.3e-12         ~200 000                1.0e-10
PERMO(4,0.1)            2.3e-11         ~200 000                1.0e-10

TRID(10)                -210.0          ~4 000                  1.0e-05
TRID(25)                -2900.0         ~50 000                 1.0e-05
TRID(50)                -22050.0        ~600 000                1.0e-05
TRID(75)                -73075.0        ~2 800 000              1.0e-05
TRID(100)               -171600.0       ~5 500 000              1.0e-05

POWERSUM(8,18,44,114)   3.2e-08         ~3 000 000              1.0e-08

The standard bounds were used.
Method : Simulated annealing (a variation of the Goffe code)


----------------

Here are the results obtained with the Amebsa algorithm.
Function:               Result:         No. function calls:     Error tolerance:

PERM(4,50)              3.2e-16         1331                    1.0e-15
PERM(4,0.5)             8.3e-17         1275                    1.0e-15
PERM(4,0.005)           2.9e-16         956                     1.0e-15

PERM(10,10^9)           1.1             51888                   1.0e-05

PERMO(4,10)             3.3e-16         480                     1.0e-15
PERMO(4,1)              1.1e-16         553                     1.0e-15
PERMO(4,0.1)            1.8e-16         581                     1.0e-15

PERMO(10,100)           1.3e-02         4300                    1.0e-05

TRID(4)                 -16.0           144                     1.0e-05
TRID(10)                -210.0          1096                    1.0e-05
TRID(20)                -1520.0         4774                    1.0e-05

POWERSUM(8,18,44,144)   5.0e-13         4716                    1.0e-15

The standard bounds were only used for the initialization.
Method    : Simplex + Simulated annealing
Algorithm : Amebsa
Authors   : W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery.
Book      : Numerical Recipes in C : The Art of Scientific Computing - 2nd ed.
ISBN      : 0-521-43108-5

But for Amebsa, the best result and/or the number of function 
calls often depend on the random numbers sequence (sometimes,  
big variations !).